Commit 8028ebc268ea830f59c6112a36f24f5e009d6f35
2018-04-11T23:12:13
remove pre_gen/mpi.c from repo
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diff --git a/.gitignore b/.gitignore
index 38b3426..ccae001 100644
--- a/.gitignore
+++ b/.gitignore
@@ -12,6 +12,7 @@ Release/
.coveralls.yml
coverage*/
coverage.info
+pre_gen/*
# suppress output of build process and *nix/windows test executables
timing
diff --git a/pre_gen/mpi.c b/pre_gen/mpi.c
deleted file mode 100644
index 57a165b..0000000
--- a/pre_gen/mpi.c
+++ /dev/null
@@ -1,10108 +0,0 @@
-/* Start: bn_error.c */
-#include <tommath_private.h>
-#ifdef BN_ERROR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-static const struct {
- int code;
- const char *msg;
-} msgs[] = {
- { MP_OKAY, "Successful" },
- { MP_MEM, "Out of heap" },
- { MP_VAL, "Value out of range" }
-};
-
-/* return a char * string for a given code */
-const char *mp_error_to_string(int code)
-{
- int x;
-
- /* scan the lookup table for the given message */
- for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
- if (msgs[x].code == code) {
- return msgs[x].msg;
- }
- }
-
- /* generic reply for invalid code */
- return "Invalid error code";
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_error.c */
-
-/* Start: bn_fast_mp_invmod.c */
-#include <tommath_private.h>
-#ifdef BN_FAST_MP_INVMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* computes the modular inverse via binary extended euclidean algorithm,
- * that is c = 1/a mod b
- *
- * Based on slow invmod except this is optimized for the case where b is
- * odd as per HAC Note 14.64 on pp. 610
- */
-int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
-{
- mp_int x, y, u, v, B, D;
- int res, neg;
-
- /* 2. [modified] b must be odd */
- if (mp_iseven (b) == MP_YES) {
- return MP_VAL;
- }
-
- /* init all our temps */
- if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
- return res;
- }
-
- /* x == modulus, y == value to invert */
- if ((res = mp_copy (b, &x)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* we need y = |a| */
- if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
- if ((res = mp_copy (&x, &u)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_copy (&y, &v)) != MP_OKAY) {
- goto LBL_ERR;
- }
- mp_set (&D, 1);
-
-top:
- /* 4. while u is even do */
- while (mp_iseven (&u) == MP_YES) {
- /* 4.1 u = u/2 */
- if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* 4.2 if B is odd then */
- if (mp_isodd (&B) == MP_YES) {
- if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
- /* B = B/2 */
- if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
-
- /* 5. while v is even do */
- while (mp_iseven (&v) == MP_YES) {
- /* 5.1 v = v/2 */
- if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* 5.2 if D is odd then */
- if (mp_isodd (&D) == MP_YES) {
- /* D = (D-x)/2 */
- if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
- /* D = D/2 */
- if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
-
- /* 6. if u >= v then */
- if (mp_cmp (&u, &v) != MP_LT) {
- /* u = u - v, B = B - D */
- if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
- goto LBL_ERR;
- }
- } else {
- /* v - v - u, D = D - B */
- if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
-
- /* if not zero goto step 4 */
- if (mp_iszero (&u) == MP_NO) {
- goto top;
- }
-
- /* now a = C, b = D, gcd == g*v */
-
- /* if v != 1 then there is no inverse */
- if (mp_cmp_d (&v, 1) != MP_EQ) {
- res = MP_VAL;
- goto LBL_ERR;
- }
-
- /* b is now the inverse */
- neg = a->sign;
- while (D.sign == MP_NEG) {
- if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
- mp_exch (&D, c);
- c->sign = neg;
- res = MP_OKAY;
-
-LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_fast_mp_invmod.c */
-
-/* Start: bn_fast_mp_montgomery_reduce.c */
-#include <tommath_private.h>
-#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* computes xR**-1 == x (mod N) via Montgomery Reduction
- *
- * This is an optimized implementation of montgomery_reduce
- * which uses the comba method to quickly calculate the columns of the
- * reduction.
- *
- * Based on Algorithm 14.32 on pp.601 of HAC.
-*/
-int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
-{
- int ix, res, olduse;
- mp_word W[MP_WARRAY];
-
- /* get old used count */
- olduse = x->used;
-
- /* grow a as required */
- if (x->alloc < (n->used + 1)) {
- if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
- return res;
- }
- }
-
- /* first we have to get the digits of the input into
- * an array of double precision words W[...]
- */
- {
- mp_word *_W;
- mp_digit *tmpx;
-
- /* alias for the W[] array */
- _W = W;
-
- /* alias for the digits of x*/
- tmpx = x->dp;
-
- /* copy the digits of a into W[0..a->used-1] */
- for (ix = 0; ix < x->used; ix++) {
- *_W++ = *tmpx++;
- }
-
- /* zero the high words of W[a->used..m->used*2] */
- for (; ix < ((n->used * 2) + 1); ix++) {
- *_W++ = 0;
- }
- }
-
- /* now we proceed to zero successive digits
- * from the least significant upwards
- */
- for (ix = 0; ix < n->used; ix++) {
- /* mu = ai * m' mod b
- *
- * We avoid a double precision multiplication (which isn't required)
- * by casting the value down to a mp_digit. Note this requires
- * that W[ix-1] have the carry cleared (see after the inner loop)
- */
- mp_digit mu;
- mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
-
- /* a = a + mu * m * b**i
- *
- * This is computed in place and on the fly. The multiplication
- * by b**i is handled by offseting which columns the results
- * are added to.
- *
- * Note the comba method normally doesn't handle carries in the
- * inner loop In this case we fix the carry from the previous
- * column since the Montgomery reduction requires digits of the
- * result (so far) [see above] to work. This is
- * handled by fixing up one carry after the inner loop. The
- * carry fixups are done in order so after these loops the
- * first m->used words of W[] have the carries fixed
- */
- {
- int iy;
- mp_digit *tmpn;
- mp_word *_W;
-
- /* alias for the digits of the modulus */
- tmpn = n->dp;
-
- /* Alias for the columns set by an offset of ix */
- _W = W + ix;
-
- /* inner loop */
- for (iy = 0; iy < n->used; iy++) {
- *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
- }
- }
-
- /* now fix carry for next digit, W[ix+1] */
- W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
- }
-
- /* now we have to propagate the carries and
- * shift the words downward [all those least
- * significant digits we zeroed].
- */
- {
- mp_digit *tmpx;
- mp_word *_W, *_W1;
-
- /* nox fix rest of carries */
-
- /* alias for current word */
- _W1 = W + ix;
-
- /* alias for next word, where the carry goes */
- _W = W + ++ix;
-
- for (; ix <= ((n->used * 2) + 1); ix++) {
- *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
- }
-
- /* copy out, A = A/b**n
- *
- * The result is A/b**n but instead of converting from an
- * array of mp_word to mp_digit than calling mp_rshd
- * we just copy them in the right order
- */
-
- /* alias for destination word */
- tmpx = x->dp;
-
- /* alias for shifted double precision result */
- _W = W + n->used;
-
- for (ix = 0; ix < (n->used + 1); ix++) {
- *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
- }
-
- /* zero oldused digits, if the input a was larger than
- * m->used+1 we'll have to clear the digits
- */
- for (; ix < olduse; ix++) {
- *tmpx++ = 0;
- }
- }
-
- /* set the max used and clamp */
- x->used = n->used + 1;
- mp_clamp (x);
-
- /* if A >= m then A = A - m */
- if (mp_cmp_mag (x, n) != MP_LT) {
- return s_mp_sub (x, n, x);
- }
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_fast_mp_montgomery_reduce.c */
-
-/* Start: bn_fast_s_mp_mul_digs.c */
-#include <tommath_private.h>
-#ifdef BN_FAST_S_MP_MUL_DIGS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* Fast (comba) multiplier
- *
- * This is the fast column-array [comba] multiplier. It is
- * designed to compute the columns of the product first
- * then handle the carries afterwards. This has the effect
- * of making the nested loops that compute the columns very
- * simple and schedulable on super-scalar processors.
- *
- * This has been modified to produce a variable number of
- * digits of output so if say only a half-product is required
- * you don't have to compute the upper half (a feature
- * required for fast Barrett reduction).
- *
- * Based on Algorithm 14.12 on pp.595 of HAC.
- *
- */
-int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
- int olduse, res, pa, ix, iz;
- mp_digit W[MP_WARRAY];
- mp_word _W;
-
- /* grow the destination as required */
- if (c->alloc < digs) {
- if ((res = mp_grow (c, digs)) != MP_OKAY) {
- return res;
- }
- }
-
- /* number of output digits to produce */
- pa = MIN(digs, a->used + b->used);
-
- /* clear the carry */
- _W = 0;
- for (ix = 0; ix < pa; ix++) {
- int tx, ty;
- int iy;
- mp_digit *tmpx, *tmpy;
-
- /* get offsets into the two bignums */
- ty = MIN(b->used-1, ix);
- tx = ix - ty;
-
- /* setup temp aliases */
- tmpx = a->dp + tx;
- tmpy = b->dp + ty;
-
- /* this is the number of times the loop will iterrate, essentially
- while (tx++ < a->used && ty-- >= 0) { ... }
- */
- iy = MIN(a->used-tx, ty+1);
-
- /* execute loop */
- for (iz = 0; iz < iy; ++iz) {
- _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
-
- }
-
- /* store term */
- W[ix] = ((mp_digit)_W) & MP_MASK;
-
- /* make next carry */
- _W = _W >> ((mp_word)DIGIT_BIT);
- }
-
- /* setup dest */
- olduse = c->used;
- c->used = pa;
-
- {
- mp_digit *tmpc;
- tmpc = c->dp;
- for (ix = 0; ix < (pa + 1); ix++) {
- /* now extract the previous digit [below the carry] */
- *tmpc++ = W[ix];
- }
-
- /* clear unused digits [that existed in the old copy of c] */
- for (; ix < olduse; ix++) {
- *tmpc++ = 0;
- }
- }
- mp_clamp (c);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_fast_s_mp_mul_digs.c */
-
-/* Start: bn_fast_s_mp_mul_high_digs.c */
-#include <tommath_private.h>
-#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* this is a modified version of fast_s_mul_digs that only produces
- * output digits *above* digs. See the comments for fast_s_mul_digs
- * to see how it works.
- *
- * This is used in the Barrett reduction since for one of the multiplications
- * only the higher digits were needed. This essentially halves the work.
- *
- * Based on Algorithm 14.12 on pp.595 of HAC.
- */
-int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
- int olduse, res, pa, ix, iz;
- mp_digit W[MP_WARRAY];
- mp_word _W;
-
- /* grow the destination as required */
- pa = a->used + b->used;
- if (c->alloc < pa) {
- if ((res = mp_grow (c, pa)) != MP_OKAY) {
- return res;
- }
- }
-
- /* number of output digits to produce */
- pa = a->used + b->used;
- _W = 0;
- for (ix = digs; ix < pa; ix++) {
- int tx, ty, iy;
- mp_digit *tmpx, *tmpy;
-
- /* get offsets into the two bignums */
- ty = MIN(b->used-1, ix);
- tx = ix - ty;
-
- /* setup temp aliases */
- tmpx = a->dp + tx;
- tmpy = b->dp + ty;
-
- /* this is the number of times the loop will iterrate, essentially its
- while (tx++ < a->used && ty-- >= 0) { ... }
- */
- iy = MIN(a->used-tx, ty+1);
-
- /* execute loop */
- for (iz = 0; iz < iy; iz++) {
- _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
- }
-
- /* store term */
- W[ix] = ((mp_digit)_W) & MP_MASK;
-
- /* make next carry */
- _W = _W >> ((mp_word)DIGIT_BIT);
- }
-
- /* setup dest */
- olduse = c->used;
- c->used = pa;
-
- {
- mp_digit *tmpc;
-
- tmpc = c->dp + digs;
- for (ix = digs; ix < pa; ix++) {
- /* now extract the previous digit [below the carry] */
- *tmpc++ = W[ix];
- }
-
- /* clear unused digits [that existed in the old copy of c] */
- for (; ix < olduse; ix++) {
- *tmpc++ = 0;
- }
- }
- mp_clamp (c);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_fast_s_mp_mul_high_digs.c */
-
-/* Start: bn_fast_s_mp_sqr.c */
-#include <tommath_private.h>
-#ifdef BN_FAST_S_MP_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* the jist of squaring...
- * you do like mult except the offset of the tmpx [one that
- * starts closer to zero] can't equal the offset of tmpy.
- * So basically you set up iy like before then you min it with
- * (ty-tx) so that it never happens. You double all those
- * you add in the inner loop
-
-After that loop you do the squares and add them in.
-*/
-
-int fast_s_mp_sqr (mp_int * a, mp_int * b)
-{
- int olduse, res, pa, ix, iz;
- mp_digit W[MP_WARRAY], *tmpx;
- mp_word W1;
-
- /* grow the destination as required */
- pa = a->used + a->used;
- if (b->alloc < pa) {
- if ((res = mp_grow (b, pa)) != MP_OKAY) {
- return res;
- }
- }
-
- /* number of output digits to produce */
- W1 = 0;
- for (ix = 0; ix < pa; ix++) {
- int tx, ty, iy;
- mp_word _W;
- mp_digit *tmpy;
-
- /* clear counter */
- _W = 0;
-
- /* get offsets into the two bignums */
- ty = MIN(a->used-1, ix);
- tx = ix - ty;
-
- /* setup temp aliases */
- tmpx = a->dp + tx;
- tmpy = a->dp + ty;
-
- /* this is the number of times the loop will iterrate, essentially
- while (tx++ < a->used && ty-- >= 0) { ... }
- */
- iy = MIN(a->used-tx, ty+1);
-
- /* now for squaring tx can never equal ty
- * we halve the distance since they approach at a rate of 2x
- * and we have to round because odd cases need to be executed
- */
- iy = MIN(iy, ((ty-tx)+1)>>1);
-
- /* execute loop */
- for (iz = 0; iz < iy; iz++) {
- _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
- }
-
- /* double the inner product and add carry */
- _W = _W + _W + W1;
-
- /* even columns have the square term in them */
- if ((ix&1) == 0) {
- _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
- }
-
- /* store it */
- W[ix] = (mp_digit)(_W & MP_MASK);
-
- /* make next carry */
- W1 = _W >> ((mp_word)DIGIT_BIT);
- }
-
- /* setup dest */
- olduse = b->used;
- b->used = a->used+a->used;
-
- {
- mp_digit *tmpb;
- tmpb = b->dp;
- for (ix = 0; ix < pa; ix++) {
- *tmpb++ = W[ix] & MP_MASK;
- }
-
- /* clear unused digits [that existed in the old copy of c] */
- for (; ix < olduse; ix++) {
- *tmpb++ = 0;
- }
- }
- mp_clamp (b);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_fast_s_mp_sqr.c */
-
-/* Start: bn_mp_2expt.c */
-#include <tommath_private.h>
-#ifdef BN_MP_2EXPT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* computes a = 2**b
- *
- * Simple algorithm which zeroes the int, grows it then just sets one bit
- * as required.
- */
-int
-mp_2expt (mp_int * a, int b)
-{
- int res;
-
- /* zero a as per default */
- mp_zero (a);
-
- /* grow a to accomodate the single bit */
- if ((res = mp_grow (a, (b / DIGIT_BIT) + 1)) != MP_OKAY) {
- return res;
- }
-
- /* set the used count of where the bit will go */
- a->used = (b / DIGIT_BIT) + 1;
-
- /* put the single bit in its place */
- a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
-
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_2expt.c */
-
-/* Start: bn_mp_abs.c */
-#include <tommath_private.h>
-#ifdef BN_MP_ABS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* b = |a|
- *
- * Simple function copies the input and fixes the sign to positive
- */
-int
-mp_abs (mp_int * a, mp_int * b)
-{
- int res;
-
- /* copy a to b */
- if (a != b) {
- if ((res = mp_copy (a, b)) != MP_OKAY) {
- return res;
- }
- }
-
- /* force the sign of b to positive */
- b->sign = MP_ZPOS;
-
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_abs.c */
-
-/* Start: bn_mp_add.c */
-#include <tommath_private.h>
-#ifdef BN_MP_ADD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* high level addition (handles signs) */
-int mp_add (mp_int * a, mp_int * b, mp_int * c)
-{
- int sa, sb, res;
-
- /* get sign of both inputs */
- sa = a->sign;
- sb = b->sign;
-
- /* handle two cases, not four */
- if (sa == sb) {
- /* both positive or both negative */
- /* add their magnitudes, copy the sign */
- c->sign = sa;
- res = s_mp_add (a, b, c);
- } else {
- /* one positive, the other negative */
- /* subtract the one with the greater magnitude from */
- /* the one of the lesser magnitude. The result gets */
- /* the sign of the one with the greater magnitude. */
- if (mp_cmp_mag (a, b) == MP_LT) {
- c->sign = sb;
- res = s_mp_sub (b, a, c);
- } else {
- c->sign = sa;
- res = s_mp_sub (a, b, c);
- }
- }
- return res;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_add.c */
-
-/* Start: bn_mp_add_d.c */
-#include <tommath_private.h>
-#ifdef BN_MP_ADD_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* single digit addition */
-int
-mp_add_d (mp_int * a, mp_digit b, mp_int * c)
-{
- int res, ix, oldused;
- mp_digit *tmpa, *tmpc, mu;
-
- /* grow c as required */
- if (c->alloc < (a->used + 1)) {
- if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
- return res;
- }
- }
-
- /* if a is negative and |a| >= b, call c = |a| - b */
- if ((a->sign == MP_NEG) && ((a->used > 1) || (a->dp[0] >= b))) {
- /* temporarily fix sign of a */
- a->sign = MP_ZPOS;
-
- /* c = |a| - b */
- res = mp_sub_d(a, b, c);
-
- /* fix sign */
- a->sign = c->sign = MP_NEG;
-
- /* clamp */
- mp_clamp(c);
-
- return res;
- }
-
- /* old number of used digits in c */
- oldused = c->used;
-
- /* source alias */
- tmpa = a->dp;
-
- /* destination alias */
- tmpc = c->dp;
-
- /* if a is positive */
- if (a->sign == MP_ZPOS) {
- /* add digit, after this we're propagating
- * the carry.
- */
- *tmpc = *tmpa++ + b;
- mu = *tmpc >> DIGIT_BIT;
- *tmpc++ &= MP_MASK;
-
- /* now handle rest of the digits */
- for (ix = 1; ix < a->used; ix++) {
- *tmpc = *tmpa++ + mu;
- mu = *tmpc >> DIGIT_BIT;
- *tmpc++ &= MP_MASK;
- }
- /* set final carry */
- ix++;
- *tmpc++ = mu;
-
- /* setup size */
- c->used = a->used + 1;
- } else {
- /* a was negative and |a| < b */
- c->used = 1;
-
- /* the result is a single digit */
- if (a->used == 1) {
- *tmpc++ = b - a->dp[0];
- } else {
- *tmpc++ = b;
- }
-
- /* setup count so the clearing of oldused
- * can fall through correctly
- */
- ix = 1;
- }
-
- /* sign always positive */
- c->sign = MP_ZPOS;
-
- /* now zero to oldused */
- while (ix++ < oldused) {
- *tmpc++ = 0;
- }
- mp_clamp(c);
-
- return MP_OKAY;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_add_d.c */
-
-/* Start: bn_mp_addmod.c */
-#include <tommath_private.h>
-#ifdef BN_MP_ADDMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* d = a + b (mod c) */
-int
-mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
- int res;
- mp_int t;
-
- if ((res = mp_init (&t)) != MP_OKAY) {
- return res;
- }
-
- if ((res = mp_add (a, b, &t)) != MP_OKAY) {
- mp_clear (&t);
- return res;
- }
- res = mp_mod (&t, c, d);
- mp_clear (&t);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_addmod.c */
-
-/* Start: bn_mp_and.c */
-#include <tommath_private.h>
-#ifdef BN_MP_AND_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* AND two ints together */
-int
-mp_and (mp_int * a, mp_int * b, mp_int * c)
-{
- int res, ix, px;
- mp_int t, *x;
-
- if (a->used > b->used) {
- if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
- return res;
- }
- px = b->used;
- x = b;
- } else {
- if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
- return res;
- }
- px = a->used;
- x = a;
- }
-
- for (ix = 0; ix < px; ix++) {
- t.dp[ix] &= x->dp[ix];
- }
-
- /* zero digits above the last from the smallest mp_int */
- for (; ix < t.used; ix++) {
- t.dp[ix] = 0;
- }
-
- mp_clamp (&t);
- mp_exch (c, &t);
- mp_clear (&t);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_and.c */
-
-/* Start: bn_mp_clamp.c */
-#include <tommath_private.h>
-#ifdef BN_MP_CLAMP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* trim unused digits
- *
- * This is used to ensure that leading zero digits are
- * trimed and the leading "used" digit will be non-zero
- * Typically very fast. Also fixes the sign if there
- * are no more leading digits
- */
-void
-mp_clamp (mp_int * a)
-{
- /* decrease used while the most significant digit is
- * zero.
- */
- while ((a->used > 0) && (a->dp[a->used - 1] == 0)) {
- --(a->used);
- }
-
- /* reset the sign flag if used == 0 */
- if (a->used == 0) {
- a->sign = MP_ZPOS;
- }
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_clamp.c */
-
-/* Start: bn_mp_clear.c */
-#include <tommath_private.h>
-#ifdef BN_MP_CLEAR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* clear one (frees) */
-void
-mp_clear (mp_int * a)
-{
- int i;
-
- /* only do anything if a hasn't been freed previously */
- if (a->dp != NULL) {
- /* first zero the digits */
- for (i = 0; i < a->used; i++) {
- a->dp[i] = 0;
- }
-
- /* free ram */
- XFREE(a->dp);
-
- /* reset members to make debugging easier */
- a->dp = NULL;
- a->alloc = a->used = 0;
- a->sign = MP_ZPOS;
- }
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_clear.c */
-
-/* Start: bn_mp_clear_multi.c */
-#include <tommath_private.h>
-#ifdef BN_MP_CLEAR_MULTI_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-#include <stdarg.h>
-
-void mp_clear_multi(mp_int *mp, ...)
-{
- mp_int* next_mp = mp;
- va_list args;
- va_start(args, mp);
- while (next_mp != NULL) {
- mp_clear(next_mp);
- next_mp = va_arg(args, mp_int*);
- }
- va_end(args);
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_clear_multi.c */
-
-/* Start: bn_mp_cmp.c */
-#include <tommath_private.h>
-#ifdef BN_MP_CMP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* compare two ints (signed)*/
-int
-mp_cmp (mp_int * a, mp_int * b)
-{
- /* compare based on sign */
- if (a->sign != b->sign) {
- if (a->sign == MP_NEG) {
- return MP_LT;
- } else {
- return MP_GT;
- }
- }
-
- /* compare digits */
- if (a->sign == MP_NEG) {
- /* if negative compare opposite direction */
- return mp_cmp_mag(b, a);
- } else {
- return mp_cmp_mag(a, b);
- }
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_cmp.c */
-
-/* Start: bn_mp_cmp_d.c */
-#include <tommath_private.h>
-#ifdef BN_MP_CMP_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* compare a digit */
-int mp_cmp_d(mp_int * a, mp_digit b)
-{
- /* compare based on sign */
- if (a->sign == MP_NEG) {
- return MP_LT;
- }
-
- /* compare based on magnitude */
- if (a->used > 1) {
- return MP_GT;
- }
-
- /* compare the only digit of a to b */
- if (a->dp[0] > b) {
- return MP_GT;
- } else if (a->dp[0] < b) {
- return MP_LT;
- } else {
- return MP_EQ;
- }
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_cmp_d.c */
-
-/* Start: bn_mp_cmp_mag.c */
-#include <tommath_private.h>
-#ifdef BN_MP_CMP_MAG_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* compare maginitude of two ints (unsigned) */
-int mp_cmp_mag (mp_int * a, mp_int * b)
-{
- int n;
- mp_digit *tmpa, *tmpb;
-
- /* compare based on # of non-zero digits */
- if (a->used > b->used) {
- return MP_GT;
- }
-
- if (a->used < b->used) {
- return MP_LT;
- }
-
- /* alias for a */
- tmpa = a->dp + (a->used - 1);
-
- /* alias for b */
- tmpb = b->dp + (a->used - 1);
-
- /* compare based on digits */
- for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
- if (*tmpa > *tmpb) {
- return MP_GT;
- }
-
- if (*tmpa < *tmpb) {
- return MP_LT;
- }
- }
- return MP_EQ;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_cmp_mag.c */
-
-/* Start: bn_mp_cnt_lsb.c */
-#include <tommath_private.h>
-#ifdef BN_MP_CNT_LSB_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-static const int lnz[16] = {
- 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
-};
-
-/* Counts the number of lsbs which are zero before the first zero bit */
-int mp_cnt_lsb(mp_int *a)
-{
- int x;
- mp_digit q, qq;
-
- /* easy out */
- if (mp_iszero(a) == MP_YES) {
- return 0;
- }
-
- /* scan lower digits until non-zero */
- for (x = 0; (x < a->used) && (a->dp[x] == 0); x++) {}
- q = a->dp[x];
- x *= DIGIT_BIT;
-
- /* now scan this digit until a 1 is found */
- if ((q & 1) == 0) {
- do {
- qq = q & 15;
- x += lnz[qq];
- q >>= 4;
- } while (qq == 0);
- }
- return x;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_cnt_lsb.c */
-
-/* Start: bn_mp_copy.c */
-#include <tommath_private.h>
-#ifdef BN_MP_COPY_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* copy, b = a */
-int
-mp_copy (mp_int * a, mp_int * b)
-{
- int res, n;
-
- /* if dst == src do nothing */
- if (a == b) {
- return MP_OKAY;
- }
-
- /* grow dest */
- if (b->alloc < a->used) {
- if ((res = mp_grow (b, a->used)) != MP_OKAY) {
- return res;
- }
- }
-
- /* zero b and copy the parameters over */
- {
- mp_digit *tmpa, *tmpb;
-
- /* pointer aliases */
-
- /* source */
- tmpa = a->dp;
-
- /* destination */
- tmpb = b->dp;
-
- /* copy all the digits */
- for (n = 0; n < a->used; n++) {
- *tmpb++ = *tmpa++;
- }
-
- /* clear high digits */
- for (; n < b->used; n++) {
- *tmpb++ = 0;
- }
- }
-
- /* copy used count and sign */
- b->used = a->used;
- b->sign = a->sign;
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_copy.c */
-
-/* Start: bn_mp_count_bits.c */
-#include <tommath_private.h>
-#ifdef BN_MP_COUNT_BITS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* returns the number of bits in an int */
-int
-mp_count_bits (mp_int * a)
-{
- int r;
- mp_digit q;
-
- /* shortcut */
- if (a->used == 0) {
- return 0;
- }
-
- /* get number of digits and add that */
- r = (a->used - 1) * DIGIT_BIT;
-
- /* take the last digit and count the bits in it */
- q = a->dp[a->used - 1];
- while (q > ((mp_digit) 0)) {
- ++r;
- q >>= ((mp_digit) 1);
- }
- return r;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_count_bits.c */
-
-/* Start: bn_mp_div.c */
-#include <tommath_private.h>
-#ifdef BN_MP_DIV_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-#ifdef BN_MP_DIV_SMALL
-
-/* slower bit-bang division... also smaller */
-int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
- mp_int ta, tb, tq, q;
- int res, n, n2;
-
- /* is divisor zero ? */
- if (mp_iszero (b) == MP_YES) {
- return MP_VAL;
- }
-
- /* if a < b then q=0, r = a */
- if (mp_cmp_mag (a, b) == MP_LT) {
- if (d != NULL) {
- res = mp_copy (a, d);
- } else {
- res = MP_OKAY;
- }
- if (c != NULL) {
- mp_zero (c);
- }
- return res;
- }
-
- /* init our temps */
- if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) {
- return res;
- }
-
-
- mp_set(&tq, 1);
- n = mp_count_bits(a) - mp_count_bits(b);
- if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
- ((res = mp_abs(b, &tb)) != MP_OKAY) ||
- ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
- ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
- goto LBL_ERR;
- }
-
- while (n-- >= 0) {
- if (mp_cmp(&tb, &ta) != MP_GT) {
- if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
- ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
- goto LBL_ERR;
- }
- }
- if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
- ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
- goto LBL_ERR;
- }
- }
-
- /* now q == quotient and ta == remainder */
- n = a->sign;
- n2 = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
- if (c != NULL) {
- mp_exch(c, &q);
- c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
- }
- if (d != NULL) {
- mp_exch(d, &ta);
- d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
- }
-LBL_ERR:
- mp_clear_multi(&ta, &tb, &tq, &q, NULL);
- return res;
-}
-
-#else
-
-/* integer signed division.
- * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
- * HAC pp.598 Algorithm 14.20
- *
- * Note that the description in HAC is horribly
- * incomplete. For example, it doesn't consider
- * the case where digits are removed from 'x' in
- * the inner loop. It also doesn't consider the
- * case that y has fewer than three digits, etc..
- *
- * The overall algorithm is as described as
- * 14.20 from HAC but fixed to treat these cases.
-*/
-int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
- mp_int q, x, y, t1, t2;
- int res, n, t, i, norm, neg;
-
- /* is divisor zero ? */
- if (mp_iszero (b) == MP_YES) {
- return MP_VAL;
- }
-
- /* if a < b then q=0, r = a */
- if (mp_cmp_mag (a, b) == MP_LT) {
- if (d != NULL) {
- res = mp_copy (a, d);
- } else {
- res = MP_OKAY;
- }
- if (c != NULL) {
- mp_zero (c);
- }
- return res;
- }
-
- if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
- return res;
- }
- q.used = a->used + 2;
-
- if ((res = mp_init (&t1)) != MP_OKAY) {
- goto LBL_Q;
- }
-
- if ((res = mp_init (&t2)) != MP_OKAY) {
- goto LBL_T1;
- }
-
- if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
- goto LBL_T2;
- }
-
- if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
- goto LBL_X;
- }
-
- /* fix the sign */
- neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
- x.sign = y.sign = MP_ZPOS;
-
- /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
- norm = mp_count_bits(&y) % DIGIT_BIT;
- if (norm < (int)(DIGIT_BIT-1)) {
- norm = (DIGIT_BIT-1) - norm;
- if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
- goto LBL_Y;
- }
- if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
- goto LBL_Y;
- }
- } else {
- norm = 0;
- }
-
- /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
- n = x.used - 1;
- t = y.used - 1;
-
- /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
- if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
- goto LBL_Y;
- }
-
- while (mp_cmp (&x, &y) != MP_LT) {
- ++(q.dp[n - t]);
- if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
- goto LBL_Y;
- }
- }
-
- /* reset y by shifting it back down */
- mp_rshd (&y, n - t);
-
- /* step 3. for i from n down to (t + 1) */
- for (i = n; i >= (t + 1); i--) {
- if (i > x.used) {
- continue;
- }
-
- /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
- * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
- if (x.dp[i] == y.dp[t]) {
- q.dp[(i - t) - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
- } else {
- mp_word tmp;
- tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
- tmp |= ((mp_word) x.dp[i - 1]);
- tmp /= ((mp_word) y.dp[t]);
- if (tmp > (mp_word) MP_MASK) {
- tmp = MP_MASK;
- }
- q.dp[(i - t) - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
- }
-
- /* while (q{i-t-1} * (yt * b + y{t-1})) >
- xi * b**2 + xi-1 * b + xi-2
-
- do q{i-t-1} -= 1;
- */
- q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] + 1) & MP_MASK;
- do {
- q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1) & MP_MASK;
-
- /* find left hand */
- mp_zero (&t1);
- t1.dp[0] = ((t - 1) < 0) ? 0 : y.dp[t - 1];
- t1.dp[1] = y.dp[t];
- t1.used = 2;
- if ((res = mp_mul_d (&t1, q.dp[(i - t) - 1], &t1)) != MP_OKAY) {
- goto LBL_Y;
- }
-
- /* find right hand */
- t2.dp[0] = ((i - 2) < 0) ? 0 : x.dp[i - 2];
- t2.dp[1] = ((i - 1) < 0) ? 0 : x.dp[i - 1];
- t2.dp[2] = x.dp[i];
- t2.used = 3;
- } while (mp_cmp_mag(&t1, &t2) == MP_GT);
-
- /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
- if ((res = mp_mul_d (&y, q.dp[(i - t) - 1], &t1)) != MP_OKAY) {
- goto LBL_Y;
- }
-
- if ((res = mp_lshd (&t1, (i - t) - 1)) != MP_OKAY) {
- goto LBL_Y;
- }
-
- if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
- goto LBL_Y;
- }
-
- /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
- if (x.sign == MP_NEG) {
- if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
- goto LBL_Y;
- }
- if ((res = mp_lshd (&t1, (i - t) - 1)) != MP_OKAY) {
- goto LBL_Y;
- }
- if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
- goto LBL_Y;
- }
-
- q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1UL) & MP_MASK;
- }
- }
-
- /* now q is the quotient and x is the remainder
- * [which we have to normalize]
- */
-
- /* get sign before writing to c */
- x.sign = (x.used == 0) ? MP_ZPOS : a->sign;
-
- if (c != NULL) {
- mp_clamp (&q);
- mp_exch (&q, c);
- c->sign = neg;
- }
-
- if (d != NULL) {
- if ((res = mp_div_2d (&x, norm, &x, NULL)) != MP_OKAY) {
- goto LBL_Y;
- }
- mp_exch (&x, d);
- }
-
- res = MP_OKAY;
-
-LBL_Y:mp_clear (&y);
-LBL_X:mp_clear (&x);
-LBL_T2:mp_clear (&t2);
-LBL_T1:mp_clear (&t1);
-LBL_Q:mp_clear (&q);
- return res;
-}
-
-#endif
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_div.c */
-
-/* Start: bn_mp_div_2.c */
-#include <tommath_private.h>
-#ifdef BN_MP_DIV_2_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* b = a/2 */
-int mp_div_2(mp_int * a, mp_int * b)
-{
- int x, res, oldused;
-
- /* copy */
- if (b->alloc < a->used) {
- if ((res = mp_grow (b, a->used)) != MP_OKAY) {
- return res;
- }
- }
-
- oldused = b->used;
- b->used = a->used;
- {
- mp_digit r, rr, *tmpa, *tmpb;
-
- /* source alias */
- tmpa = a->dp + b->used - 1;
-
- /* dest alias */
- tmpb = b->dp + b->used - 1;
-
- /* carry */
- r = 0;
- for (x = b->used - 1; x >= 0; x--) {
- /* get the carry for the next iteration */
- rr = *tmpa & 1;
-
- /* shift the current digit, add in carry and store */
- *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
-
- /* forward carry to next iteration */
- r = rr;
- }
-
- /* zero excess digits */
- tmpb = b->dp + b->used;
- for (x = b->used; x < oldused; x++) {
- *tmpb++ = 0;
- }
- }
- b->sign = a->sign;
- mp_clamp (b);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_div_2.c */
-
-/* Start: bn_mp_div_2d.c */
-#include <tommath_private.h>
-#ifdef BN_MP_DIV_2D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
-int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
-{
- mp_digit D, r, rr;
- int x, res;
-
- /* if the shift count is <= 0 then we do no work */
- if (b <= 0) {
- res = mp_copy (a, c);
- if (d != NULL) {
- mp_zero (d);
- }
- return res;
- }
-
- /* copy */
- if ((res = mp_copy (a, c)) != MP_OKAY) {
- return res;
- }
- /* 'a' should not be used after here - it might be the same as d */
-
- /* get the remainder */
- if (d != NULL) {
- if ((res = mp_mod_2d (a, b, d)) != MP_OKAY) {
- return res;
- }
- }
-
- /* shift by as many digits in the bit count */
- if (b >= (int)DIGIT_BIT) {
- mp_rshd (c, b / DIGIT_BIT);
- }
-
- /* shift any bit count < DIGIT_BIT */
- D = (mp_digit) (b % DIGIT_BIT);
- if (D != 0) {
- mp_digit *tmpc, mask, shift;
-
- /* mask */
- mask = (((mp_digit)1) << D) - 1;
-
- /* shift for lsb */
- shift = DIGIT_BIT - D;
-
- /* alias */
- tmpc = c->dp + (c->used - 1);
-
- /* carry */
- r = 0;
- for (x = c->used - 1; x >= 0; x--) {
- /* get the lower bits of this word in a temp */
- rr = *tmpc & mask;
-
- /* shift the current word and mix in the carry bits from the previous word */
- *tmpc = (*tmpc >> D) | (r << shift);
- --tmpc;
-
- /* set the carry to the carry bits of the current word found above */
- r = rr;
- }
- }
- mp_clamp (c);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_div_2d.c */
-
-/* Start: bn_mp_div_3.c */
-#include <tommath_private.h>
-#ifdef BN_MP_DIV_3_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* divide by three (based on routine from MPI and the GMP manual) */
-int
-mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
-{
- mp_int q;
- mp_word w, t;
- mp_digit b;
- int res, ix;
-
- /* b = 2**DIGIT_BIT / 3 */
- b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3);
-
- if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
- return res;
- }
-
- q.used = a->used;
- q.sign = a->sign;
- w = 0;
- for (ix = a->used - 1; ix >= 0; ix--) {
- w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
-
- if (w >= 3) {
- /* multiply w by [1/3] */
- t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
-
- /* now subtract 3 * [w/3] from w, to get the remainder */
- w -= t+t+t;
-
- /* fixup the remainder as required since
- * the optimization is not exact.
- */
- while (w >= 3) {
- t += 1;
- w -= 3;
- }
- } else {
- t = 0;
- }
- q.dp[ix] = (mp_digit)t;
- }
-
- /* [optional] store the remainder */
- if (d != NULL) {
- *d = (mp_digit)w;
- }
-
- /* [optional] store the quotient */
- if (c != NULL) {
- mp_clamp(&q);
- mp_exch(&q, c);
- }
- mp_clear(&q);
-
- return res;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_div_3.c */
-
-/* Start: bn_mp_div_d.c */
-#include <tommath_private.h>
-#ifdef BN_MP_DIV_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-static int s_is_power_of_two(mp_digit b, int *p)
-{
- int x;
-
- /* fast return if no power of two */
- if ((b == 0) || ((b & (b-1)) != 0)) {
- return 0;
- }
-
- for (x = 0; x < DIGIT_BIT; x++) {
- if (b == (((mp_digit)1)<<x)) {
- *p = x;
- return 1;
- }
- }
- return 0;
-}
-
-/* single digit division (based on routine from MPI) */
-int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
-{
- mp_int q;
- mp_word w;
- mp_digit t;
- int res, ix;
-
- /* cannot divide by zero */
- if (b == 0) {
- return MP_VAL;
- }
-
- /* quick outs */
- if ((b == 1) || (mp_iszero(a) == MP_YES)) {
- if (d != NULL) {
- *d = 0;
- }
- if (c != NULL) {
- return mp_copy(a, c);
- }
- return MP_OKAY;
- }
-
- /* power of two ? */
- if (s_is_power_of_two(b, &ix) == 1) {
- if (d != NULL) {
- *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
- }
- if (c != NULL) {
- return mp_div_2d(a, ix, c, NULL);
- }
- return MP_OKAY;
- }
-
-#ifdef BN_MP_DIV_3_C
- /* three? */
- if (b == 3) {
- return mp_div_3(a, c, d);
- }
-#endif
-
- /* no easy answer [c'est la vie]. Just division */
- if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
- return res;
- }
-
- q.used = a->used;
- q.sign = a->sign;
- w = 0;
- for (ix = a->used - 1; ix >= 0; ix--) {
- w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
-
- if (w >= b) {
- t = (mp_digit)(w / b);
- w -= ((mp_word)t) * ((mp_word)b);
- } else {
- t = 0;
- }
- q.dp[ix] = (mp_digit)t;
- }
-
- if (d != NULL) {
- *d = (mp_digit)w;
- }
-
- if (c != NULL) {
- mp_clamp(&q);
- mp_exch(&q, c);
- }
- mp_clear(&q);
-
- return res;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_div_d.c */
-
-/* Start: bn_mp_dr_is_modulus.c */
-#include <tommath_private.h>
-#ifdef BN_MP_DR_IS_MODULUS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* determines if a number is a valid DR modulus */
-int mp_dr_is_modulus(mp_int *a)
-{
- int ix;
-
- /* must be at least two digits */
- if (a->used < 2) {
- return 0;
- }
-
- /* must be of the form b**k - a [a <= b] so all
- * but the first digit must be equal to -1 (mod b).
- */
- for (ix = 1; ix < a->used; ix++) {
- if (a->dp[ix] != MP_MASK) {
- return 0;
- }
- }
- return 1;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_dr_is_modulus.c */
-
-/* Start: bn_mp_dr_reduce.c */
-#include <tommath_private.h>
-#ifdef BN_MP_DR_REDUCE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
- *
- * Based on algorithm from the paper
- *
- * "Generating Efficient Primes for Discrete Log Cryptosystems"
- * Chae Hoon Lim, Pil Joong Lee,
- * POSTECH Information Research Laboratories
- *
- * The modulus must be of a special format [see manual]
- *
- * Has been modified to use algorithm 7.10 from the LTM book instead
- *
- * Input x must be in the range 0 <= x <= (n-1)**2
- */
-int
-mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
-{
- int err, i, m;
- mp_word r;
- mp_digit mu, *tmpx1, *tmpx2;
-
- /* m = digits in modulus */
- m = n->used;
-
- /* ensure that "x" has at least 2m digits */
- if (x->alloc < (m + m)) {
- if ((err = mp_grow (x, m + m)) != MP_OKAY) {
- return err;
- }
- }
-
-/* top of loop, this is where the code resumes if
- * another reduction pass is required.
- */
-top:
- /* aliases for digits */
- /* alias for lower half of x */
- tmpx1 = x->dp;
-
- /* alias for upper half of x, or x/B**m */
- tmpx2 = x->dp + m;
-
- /* set carry to zero */
- mu = 0;
-
- /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
- for (i = 0; i < m; i++) {
- r = (((mp_word)*tmpx2++) * (mp_word)k) + *tmpx1 + mu;
- *tmpx1++ = (mp_digit)(r & MP_MASK);
- mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
- }
-
- /* set final carry */
- *tmpx1++ = mu;
-
- /* zero words above m */
- for (i = m + 1; i < x->used; i++) {
- *tmpx1++ = 0;
- }
-
- /* clamp, sub and return */
- mp_clamp (x);
-
- /* if x >= n then subtract and reduce again
- * Each successive "recursion" makes the input smaller and smaller.
- */
- if (mp_cmp_mag (x, n) != MP_LT) {
- if ((err = s_mp_sub(x, n, x)) != MP_OKAY) {
- return err;
- }
- goto top;
- }
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_dr_reduce.c */
-
-/* Start: bn_mp_dr_setup.c */
-#include <tommath_private.h>
-#ifdef BN_MP_DR_SETUP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* determines the setup value */
-void mp_dr_setup(mp_int *a, mp_digit *d)
-{
- /* the casts are required if DIGIT_BIT is one less than
- * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
- */
- *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
- ((mp_word)a->dp[0]));
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_dr_setup.c */
-
-/* Start: bn_mp_exch.c */
-#include <tommath_private.h>
-#ifdef BN_MP_EXCH_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* swap the elements of two integers, for cases where you can't simply swap the
- * mp_int pointers around
- */
-void
-mp_exch (mp_int * a, mp_int * b)
-{
- mp_int t;
-
- t = *a;
- *a = *b;
- *b = t;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_exch.c */
-
-/* Start: bn_mp_export.c */
-#include <tommath_private.h>
-#ifdef BN_MP_EXPORT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* based on gmp's mpz_export.
- * see http://gmplib.org/manual/Integer-Import-and-Export.html
- */
-int mp_export(void* rop, size_t* countp, int order, size_t size,
- int endian, size_t nails, mp_int* op) {
- int result;
- size_t odd_nails, nail_bytes, i, j, bits, count;
- unsigned char odd_nail_mask;
-
- mp_int t;
-
- if ((result = mp_init_copy(&t, op)) != MP_OKAY) {
- return result;
- }
-
- if (endian == 0) {
- union {
- unsigned int i;
- char c[4];
- } lint;
- lint.i = 0x01020304;
-
- endian = (lint.c[0] == 4) ? -1 : 1;
- }
-
- odd_nails = (nails % 8);
- odd_nail_mask = 0xff;
- for (i = 0; i < odd_nails; ++i) {
- odd_nail_mask ^= (1 << (7 - i));
- }
- nail_bytes = nails / 8;
-
- bits = mp_count_bits(&t);
- count = (bits / ((size * 8) - nails)) + (((bits % ((size * 8) - nails)) != 0) ? 1 : 0);
-
- for (i = 0; i < count; ++i) {
- for (j = 0; j < size; ++j) {
- unsigned char* byte = (
- (unsigned char*)rop +
- (((order == -1) ? i : ((count - 1) - i)) * size) +
- ((endian == -1) ? j : ((size - 1) - j))
- );
-
- if (j >= (size - nail_bytes)) {
- *byte = 0;
- continue;
- }
-
- *byte = (unsigned char)((j == ((size - nail_bytes) - 1)) ? (t.dp[0] & odd_nail_mask) : (t.dp[0] & 0xFF));
-
- if ((result = mp_div_2d(&t, ((j == ((size - nail_bytes) - 1)) ? (8 - odd_nails) : 8), &t, NULL)) != MP_OKAY) {
- mp_clear(&t);
- return result;
- }
- }
- }
-
- mp_clear(&t);
-
- if (countp != NULL) {
- *countp = count;
- }
-
- return MP_OKAY;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_export.c */
-
-/* Start: bn_mp_expt_d.c */
-#include <tommath_private.h>
-#ifdef BN_MP_EXPT_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* wrapper function for mp_expt_d_ex() */
-int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
-{
- return mp_expt_d_ex(a, b, c, 0);
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_expt_d.c */
-
-/* Start: bn_mp_expt_d_ex.c */
-#include <tommath_private.h>
-#ifdef BN_MP_EXPT_D_EX_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* calculate c = a**b using a square-multiply algorithm */
-int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
-{
- int res;
- unsigned int x;
-
- mp_int g;
-
- if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
- return res;
- }
-
- /* set initial result */
- mp_set (c, 1);
-
- if (fast != 0) {
- while (b > 0) {
- /* if the bit is set multiply */
- if ((b & 1) != 0) {
- if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
- mp_clear (&g);
- return res;
- }
- }
-
- /* square */
- if (b > 1) {
- if ((res = mp_sqr (&g, &g)) != MP_OKAY) {
- mp_clear (&g);
- return res;
- }
- }
-
- /* shift to next bit */
- b >>= 1;
- }
- }
- else {
- for (x = 0; x < DIGIT_BIT; x++) {
- /* square */
- if ((res = mp_sqr (c, c)) != MP_OKAY) {
- mp_clear (&g);
- return res;
- }
-
- /* if the bit is set multiply */
- if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) {
- if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
- mp_clear (&g);
- return res;
- }
- }
-
- /* shift to next bit */
- b <<= 1;
- }
- } /* if ... else */
-
- mp_clear (&g);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_expt_d_ex.c */
-
-/* Start: bn_mp_exptmod.c */
-#include <tommath_private.h>
-#ifdef BN_MP_EXPTMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-
-/* this is a shell function that calls either the normal or Montgomery
- * exptmod functions. Originally the call to the montgomery code was
- * embedded in the normal function but that wasted alot of stack space
- * for nothing (since 99% of the time the Montgomery code would be called)
- */
-int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
-{
- int dr;
-
- /* modulus P must be positive */
- if (P->sign == MP_NEG) {
- return MP_VAL;
- }
-
- /* if exponent X is negative we have to recurse */
- if (X->sign == MP_NEG) {
-#ifdef BN_MP_INVMOD_C
- mp_int tmpG, tmpX;
- int err;
-
- /* first compute 1/G mod P */
- if ((err = mp_init(&tmpG)) != MP_OKAY) {
- return err;
- }
- if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
- mp_clear(&tmpG);
- return err;
- }
-
- /* now get |X| */
- if ((err = mp_init(&tmpX)) != MP_OKAY) {
- mp_clear(&tmpG);
- return err;
- }
- if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
- mp_clear_multi(&tmpG, &tmpX, NULL);
- return err;
- }
-
- /* and now compute (1/G)**|X| instead of G**X [X < 0] */
- err = mp_exptmod(&tmpG, &tmpX, P, Y);
- mp_clear_multi(&tmpG, &tmpX, NULL);
- return err;
-#else
- /* no invmod */
- return MP_VAL;
-#endif
- }
-
-/* modified diminished radix reduction */
-#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C)
- if (mp_reduce_is_2k_l(P) == MP_YES) {
- return s_mp_exptmod(G, X, P, Y, 1);
- }
-#endif
-
-#ifdef BN_MP_DR_IS_MODULUS_C
- /* is it a DR modulus? */
- dr = mp_dr_is_modulus(P);
-#else
- /* default to no */
- dr = 0;
-#endif
-
-#ifdef BN_MP_REDUCE_IS_2K_C
- /* if not, is it a unrestricted DR modulus? */
- if (dr == 0) {
- dr = mp_reduce_is_2k(P) << 1;
- }
-#endif
-
- /* if the modulus is odd or dr != 0 use the montgomery method */
-#ifdef BN_MP_EXPTMOD_FAST_C
- if ((mp_isodd (P) == MP_YES) || (dr != 0)) {
- return mp_exptmod_fast (G, X, P, Y, dr);
- } else {
-#endif
-#ifdef BN_S_MP_EXPTMOD_C
- /* otherwise use the generic Barrett reduction technique */
- return s_mp_exptmod (G, X, P, Y, 0);
-#else
- /* no exptmod for evens */
- return MP_VAL;
-#endif
-#ifdef BN_MP_EXPTMOD_FAST_C
- }
-#endif
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_exptmod.c */
-
-/* Start: bn_mp_exptmod_fast.c */
-#include <tommath_private.h>
-#ifdef BN_MP_EXPTMOD_FAST_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
- *
- * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
- * The value of k changes based on the size of the exponent.
- *
- * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
- */
-
-#ifdef MP_LOW_MEM
- #define TAB_SIZE 32
-#else
- #define TAB_SIZE 256
-#endif
-
-int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
-{
- mp_int M[TAB_SIZE], res;
- mp_digit buf, mp;
- int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
-
- /* use a pointer to the reduction algorithm. This allows us to use
- * one of many reduction algorithms without modding the guts of
- * the code with if statements everywhere.
- */
- int (*redux)(mp_int*,mp_int*,mp_digit);
-
- /* find window size */
- x = mp_count_bits (X);
- if (x <= 7) {
- winsize = 2;
- } else if (x <= 36) {
- winsize = 3;
- } else if (x <= 140) {
- winsize = 4;
- } else if (x <= 450) {
- winsize = 5;
- } else if (x <= 1303) {
- winsize = 6;
- } else if (x <= 3529) {
- winsize = 7;
- } else {
- winsize = 8;
- }
-
-#ifdef MP_LOW_MEM
- if (winsize > 5) {
- winsize = 5;
- }
-#endif
-
- /* init M array */
- /* init first cell */
- if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) {
- return err;
- }
-
- /* now init the second half of the array */
- for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
- if ((err = mp_init_size(&M[x], P->alloc)) != MP_OKAY) {
- for (y = 1<<(winsize-1); y < x; y++) {
- mp_clear (&M[y]);
- }
- mp_clear(&M[1]);
- return err;
- }
- }
-
- /* determine and setup reduction code */
- if (redmode == 0) {
-#ifdef BN_MP_MONTGOMERY_SETUP_C
- /* now setup montgomery */
- if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
- goto LBL_M;
- }
-#else
- err = MP_VAL;
- goto LBL_M;
-#endif
-
- /* automatically pick the comba one if available (saves quite a few calls/ifs) */
-#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
- if ((((P->used * 2) + 1) < MP_WARRAY) &&
- (P->used < (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
- redux = fast_mp_montgomery_reduce;
- } else
-#endif
- {
-#ifdef BN_MP_MONTGOMERY_REDUCE_C
- /* use slower baseline Montgomery method */
- redux = mp_montgomery_reduce;
-#else
- err = MP_VAL;
- goto LBL_M;
-#endif
- }
- } else if (redmode == 1) {
-#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
- /* setup DR reduction for moduli of the form B**k - b */
- mp_dr_setup(P, &mp);
- redux = mp_dr_reduce;
-#else
- err = MP_VAL;
- goto LBL_M;
-#endif
- } else {
-#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
- /* setup DR reduction for moduli of the form 2**k - b */
- if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
- goto LBL_M;
- }
- redux = mp_reduce_2k;
-#else
- err = MP_VAL;
- goto LBL_M;
-#endif
- }
-
- /* setup result */
- if ((err = mp_init_size (&res, P->alloc)) != MP_OKAY) {
- goto LBL_M;
- }
-
- /* create M table
- *
-
- *
- * The first half of the table is not computed though accept for M[0] and M[1]
- */
-
- if (redmode == 0) {
-#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
- /* now we need R mod m */
- if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
- goto LBL_RES;
- }
-
- /* now set M[1] to G * R mod m */
- if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
- goto LBL_RES;
- }
-#else
- err = MP_VAL;
- goto LBL_RES;
-#endif
- } else {
- mp_set(&res, 1);
- if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
- goto LBL_RES;
- }
- }
-
- /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
- if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
- goto LBL_RES;
- }
-
- for (x = 0; x < (winsize - 1); x++) {
- if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
- goto LBL_RES;
- }
- if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
- goto LBL_RES;
- }
- }
-
- /* create upper table */
- for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
- if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
- goto LBL_RES;
- }
- if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
- goto LBL_RES;
- }
- }
-
- /* set initial mode and bit cnt */
- mode = 0;
- bitcnt = 1;
- buf = 0;
- digidx = X->used - 1;
- bitcpy = 0;
- bitbuf = 0;
-
- for (;;) {
- /* grab next digit as required */
- if (--bitcnt == 0) {
- /* if digidx == -1 we are out of digits so break */
- if (digidx == -1) {
- break;
- }
- /* read next digit and reset bitcnt */
- buf = X->dp[digidx--];
- bitcnt = (int)DIGIT_BIT;
- }
-
- /* grab the next msb from the exponent */
- y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
- buf <<= (mp_digit)1;
-
- /* if the bit is zero and mode == 0 then we ignore it
- * These represent the leading zero bits before the first 1 bit
- * in the exponent. Technically this opt is not required but it
- * does lower the # of trivial squaring/reductions used
- */
- if ((mode == 0) && (y == 0)) {
- continue;
- }
-
- /* if the bit is zero and mode == 1 then we square */
- if ((mode == 1) && (y == 0)) {
- if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
- goto LBL_RES;
- }
- if ((err = redux (&res, P, mp)) != MP_OKAY) {
- goto LBL_RES;
- }
- continue;
- }
-
- /* else we add it to the window */
- bitbuf |= (y << (winsize - ++bitcpy));
- mode = 2;
-
- if (bitcpy == winsize) {
- /* ok window is filled so square as required and multiply */
- /* square first */
- for (x = 0; x < winsize; x++) {
- if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
- goto LBL_RES;
- }
- if ((err = redux (&res, P, mp)) != MP_OKAY) {
- goto LBL_RES;
- }
- }
-
- /* then multiply */
- if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
- goto LBL_RES;
- }
- if ((err = redux (&res, P, mp)) != MP_OKAY) {
- goto LBL_RES;
- }
-
- /* empty window and reset */
- bitcpy = 0;
- bitbuf = 0;
- mode = 1;
- }
- }
-
- /* if bits remain then square/multiply */
- if ((mode == 2) && (bitcpy > 0)) {
- /* square then multiply if the bit is set */
- for (x = 0; x < bitcpy; x++) {
- if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
- goto LBL_RES;
- }
- if ((err = redux (&res, P, mp)) != MP_OKAY) {
- goto LBL_RES;
- }
-
- /* get next bit of the window */
- bitbuf <<= 1;
- if ((bitbuf & (1 << winsize)) != 0) {
- /* then multiply */
- if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
- goto LBL_RES;
- }
- if ((err = redux (&res, P, mp)) != MP_OKAY) {
- goto LBL_RES;
- }
- }
- }
- }
-
- if (redmode == 0) {
- /* fixup result if Montgomery reduction is used
- * recall that any value in a Montgomery system is
- * actually multiplied by R mod n. So we have
- * to reduce one more time to cancel out the factor
- * of R.
- */
- if ((err = redux(&res, P, mp)) != MP_OKAY) {
- goto LBL_RES;
- }
- }
-
- /* swap res with Y */
- mp_exch (&res, Y);
- err = MP_OKAY;
-LBL_RES:mp_clear (&res);
-LBL_M:
- mp_clear(&M[1]);
- for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
- mp_clear (&M[x]);
- }
- return err;
-}
-#endif
-
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_exptmod_fast.c */
-
-/* Start: bn_mp_exteuclid.c */
-#include <tommath_private.h>
-#ifdef BN_MP_EXTEUCLID_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* Extended euclidean algorithm of (a, b) produces
- a*u1 + b*u2 = u3
- */
-int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
-{
- mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
- int err;
-
- if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
- return err;
- }
-
- /* initialize, (u1,u2,u3) = (1,0,a) */
- mp_set(&u1, 1);
- if ((err = mp_copy(a, &u3)) != MP_OKAY) { goto LBL_ERR; }
-
- /* initialize, (v1,v2,v3) = (0,1,b) */
- mp_set(&v2, 1);
- if ((err = mp_copy(b, &v3)) != MP_OKAY) { goto LBL_ERR; }
-
- /* loop while v3 != 0 */
- while (mp_iszero(&v3) == MP_NO) {
- /* q = u3/v3 */
- if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) { goto LBL_ERR; }
-
- /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
- if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) { goto LBL_ERR; }
- if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) { goto LBL_ERR; }
- if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) { goto LBL_ERR; }
- if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) { goto LBL_ERR; }
- if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) { goto LBL_ERR; }
- if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) { goto LBL_ERR; }
-
- /* (u1,u2,u3) = (v1,v2,v3) */
- if ((err = mp_copy(&v1, &u1)) != MP_OKAY) { goto LBL_ERR; }
- if ((err = mp_copy(&v2, &u2)) != MP_OKAY) { goto LBL_ERR; }
- if ((err = mp_copy(&v3, &u3)) != MP_OKAY) { goto LBL_ERR; }
-
- /* (v1,v2,v3) = (t1,t2,t3) */
- if ((err = mp_copy(&t1, &v1)) != MP_OKAY) { goto LBL_ERR; }
- if ((err = mp_copy(&t2, &v2)) != MP_OKAY) { goto LBL_ERR; }
- if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto LBL_ERR; }
- }
-
- /* make sure U3 >= 0 */
- if (u3.sign == MP_NEG) {
- if ((err = mp_neg(&u1, &u1)) != MP_OKAY) { goto LBL_ERR; }
- if ((err = mp_neg(&u2, &u2)) != MP_OKAY) { goto LBL_ERR; }
- if ((err = mp_neg(&u3, &u3)) != MP_OKAY) { goto LBL_ERR; }
- }
-
- /* copy result out */
- if (U1 != NULL) { mp_exch(U1, &u1); }
- if (U2 != NULL) { mp_exch(U2, &u2); }
- if (U3 != NULL) { mp_exch(U3, &u3); }
-
- err = MP_OKAY;
-LBL_ERR:
- mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
- return err;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_exteuclid.c */
-
-/* Start: bn_mp_fread.c */
-#include <tommath_private.h>
-#ifdef BN_MP_FREAD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-#ifndef LTM_NO_FILE
-/* read a bigint from a file stream in ASCII */
-int mp_fread(mp_int *a, int radix, FILE *stream)
-{
- int err, ch, neg, y;
-
- /* clear a */
- mp_zero(a);
-
- /* if first digit is - then set negative */
- ch = fgetc(stream);
- if (ch == '-') {
- neg = MP_NEG;
- ch = fgetc(stream);
- } else {
- neg = MP_ZPOS;
- }
-
- for (;;) {
- /* find y in the radix map */
- for (y = 0; y < radix; y++) {
- if (mp_s_rmap[y] == ch) {
- break;
- }
- }
- if (y == radix) {
- break;
- }
-
- /* shift up and add */
- if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
- return err;
- }
- if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
- return err;
- }
-
- ch = fgetc(stream);
- }
- if (mp_cmp_d(a, 0) != MP_EQ) {
- a->sign = neg;
- }
-
- return MP_OKAY;
-}
-#endif
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_fread.c */
-
-/* Start: bn_mp_fwrite.c */
-#include <tommath_private.h>
-#ifdef BN_MP_FWRITE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-#ifndef LTM_NO_FILE
-int mp_fwrite(mp_int *a, int radix, FILE *stream)
-{
- char *buf;
- int err, len, x;
-
- if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) {
- return err;
- }
-
- buf = OPT_CAST(char) XMALLOC (len);
- if (buf == NULL) {
- return MP_MEM;
- }
-
- if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) {
- XFREE (buf);
- return err;
- }
-
- for (x = 0; x < len; x++) {
- if (fputc(buf[x], stream) == EOF) {
- XFREE (buf);
- return MP_VAL;
- }
- }
-
- XFREE (buf);
- return MP_OKAY;
-}
-#endif
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_fwrite.c */
-
-/* Start: bn_mp_gcd.c */
-#include <tommath_private.h>
-#ifdef BN_MP_GCD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* Greatest Common Divisor using the binary method */
-int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
-{
- mp_int u, v;
- int k, u_lsb, v_lsb, res;
-
- /* either zero than gcd is the largest */
- if (mp_iszero (a) == MP_YES) {
- return mp_abs (b, c);
- }
- if (mp_iszero (b) == MP_YES) {
- return mp_abs (a, c);
- }
-
- /* get copies of a and b we can modify */
- if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
- return res;
- }
-
- if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
- goto LBL_U;
- }
-
- /* must be positive for the remainder of the algorithm */
- u.sign = v.sign = MP_ZPOS;
-
- /* B1. Find the common power of two for u and v */
- u_lsb = mp_cnt_lsb(&u);
- v_lsb = mp_cnt_lsb(&v);
- k = MIN(u_lsb, v_lsb);
-
- if (k > 0) {
- /* divide the power of two out */
- if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
- goto LBL_V;
- }
-
- if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
- goto LBL_V;
- }
- }
-
- /* divide any remaining factors of two out */
- if (u_lsb != k) {
- if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
- goto LBL_V;
- }
- }
-
- if (v_lsb != k) {
- if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
- goto LBL_V;
- }
- }
-
- while (mp_iszero(&v) == MP_NO) {
- /* make sure v is the largest */
- if (mp_cmp_mag(&u, &v) == MP_GT) {
- /* swap u and v to make sure v is >= u */
- mp_exch(&u, &v);
- }
-
- /* subtract smallest from largest */
- if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
- goto LBL_V;
- }
-
- /* Divide out all factors of two */
- if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
- goto LBL_V;
- }
- }
-
- /* multiply by 2**k which we divided out at the beginning */
- if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
- goto LBL_V;
- }
- c->sign = MP_ZPOS;
- res = MP_OKAY;
-LBL_V:mp_clear (&u);
-LBL_U:mp_clear (&v);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_gcd.c */
-
-/* Start: bn_mp_get_int.c */
-#include <tommath_private.h>
-#ifdef BN_MP_GET_INT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* get the lower 32-bits of an mp_int */
-unsigned long mp_get_int(mp_int * a)
-{
- int i;
- mp_min_u32 res;
-
- if (a->used == 0) {
- return 0;
- }
-
- /* get number of digits of the lsb we have to read */
- i = MIN(a->used,(int)(((sizeof(unsigned long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;
-
- /* get most significant digit of result */
- res = DIGIT(a,i);
-
- while (--i >= 0) {
- res = (res << DIGIT_BIT) | DIGIT(a,i);
- }
-
- /* force result to 32-bits always so it is consistent on non 32-bit platforms */
- return res & 0xFFFFFFFFUL;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_get_int.c */
-
-/* Start: bn_mp_get_long.c */
-#include <tommath_private.h>
-#ifdef BN_MP_GET_LONG_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* get the lower unsigned long of an mp_int, platform dependent */
-unsigned long mp_get_long(mp_int * a)
-{
- int i;
- unsigned long res;
-
- if (a->used == 0) {
- return 0;
- }
-
- /* get number of digits of the lsb we have to read */
- i = MIN(a->used,(int)(((sizeof(unsigned long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;
-
- /* get most significant digit of result */
- res = DIGIT(a,i);
-
-#if (ULONG_MAX != 0xffffffffuL) || (DIGIT_BIT < 32)
- while (--i >= 0) {
- res = (res << DIGIT_BIT) | DIGIT(a,i);
- }
-#endif
- return res;
-}
-#endif
-
-/* End: bn_mp_get_long.c */
-
-/* Start: bn_mp_get_long_long.c */
-#include <tommath_private.h>
-#ifdef BN_MP_GET_LONG_LONG_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* get the lower unsigned long long of an mp_int, platform dependent */
-unsigned long long mp_get_long_long (mp_int * a)
-{
- int i;
- unsigned long long res;
-
- if (a->used == 0) {
- return 0;
- }
-
- /* get number of digits of the lsb we have to read */
- i = MIN(a->used,(int)(((sizeof(unsigned long long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;
-
- /* get most significant digit of result */
- res = DIGIT(a,i);
-
-#if DIGIT_BIT < 64
- while (--i >= 0) {
- res = (res << DIGIT_BIT) | DIGIT(a,i);
- }
-#endif
- return res;
-}
-#endif
-
-/* End: bn_mp_get_long_long.c */
-
-/* Start: bn_mp_grow.c */
-#include <tommath_private.h>
-#ifdef BN_MP_GROW_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* grow as required */
-int mp_grow (mp_int * a, int size)
-{
- int i;
- mp_digit *tmp;
-
- /* if the alloc size is smaller alloc more ram */
- if (a->alloc < size) {
- /* ensure there are always at least MP_PREC digits extra on top */
- size += (MP_PREC * 2) - (size % MP_PREC);
-
- /* reallocate the array a->dp
- *
- * We store the return in a temporary variable
- * in case the operation failed we don't want
- * to overwrite the dp member of a.
- */
- tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
- if (tmp == NULL) {
- /* reallocation failed but "a" is still valid [can be freed] */
- return MP_MEM;
- }
-
- /* reallocation succeeded so set a->dp */
- a->dp = tmp;
-
- /* zero excess digits */
- i = a->alloc;
- a->alloc = size;
- for (; i < a->alloc; i++) {
- a->dp[i] = 0;
- }
- }
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_grow.c */
-
-/* Start: bn_mp_import.c */
-#include <tommath_private.h>
-#ifdef BN_MP_IMPORT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* based on gmp's mpz_import.
- * see http://gmplib.org/manual/Integer-Import-and-Export.html
- */
-int mp_import(mp_int* rop, size_t count, int order, size_t size,
- int endian, size_t nails, const void* op) {
- int result;
- size_t odd_nails, nail_bytes, i, j;
- unsigned char odd_nail_mask;
-
- mp_zero(rop);
-
- if (endian == 0) {
- union {
- unsigned int i;
- char c[4];
- } lint;
- lint.i = 0x01020304;
-
- endian = (lint.c[0] == 4) ? -1 : 1;
- }
-
- odd_nails = (nails % 8);
- odd_nail_mask = 0xff;
- for (i = 0; i < odd_nails; ++i) {
- odd_nail_mask ^= (1 << (7 - i));
- }
- nail_bytes = nails / 8;
-
- for (i = 0; i < count; ++i) {
- for (j = 0; j < (size - nail_bytes); ++j) {
- unsigned char byte = *(
- (unsigned char*)op +
- (((order == 1) ? i : ((count - 1) - i)) * size) +
- ((endian == 1) ? (j + nail_bytes) : (((size - 1) - j) - nail_bytes))
- );
-
- if (
- (result = mp_mul_2d(rop, ((j == 0) ? (8 - odd_nails) : 8), rop)) != MP_OKAY) {
- return result;
- }
-
- rop->dp[0] |= (j == 0) ? (byte & odd_nail_mask) : byte;
- rop->used += 1;
- }
- }
-
- mp_clamp(rop);
-
- return MP_OKAY;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_import.c */
-
-/* Start: bn_mp_init.c */
-#include <tommath_private.h>
-#ifdef BN_MP_INIT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* init a new mp_int */
-int mp_init (mp_int * a)
-{
- int i;
-
- /* allocate memory required and clear it */
- a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
- if (a->dp == NULL) {
- return MP_MEM;
- }
-
- /* set the digits to zero */
- for (i = 0; i < MP_PREC; i++) {
- a->dp[i] = 0;
- }
-
- /* set the used to zero, allocated digits to the default precision
- * and sign to positive */
- a->used = 0;
- a->alloc = MP_PREC;
- a->sign = MP_ZPOS;
-
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_init.c */
-
-/* Start: bn_mp_init_copy.c */
-#include <tommath_private.h>
-#ifdef BN_MP_INIT_COPY_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* creates "a" then copies b into it */
-int mp_init_copy (mp_int * a, mp_int * b)
-{
- int res;
-
- if ((res = mp_init_size (a, b->used)) != MP_OKAY) {
- return res;
- }
-
- if((res = mp_copy (b, a)) != MP_OKAY) {
- mp_clear(a);
- }
-
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_init_copy.c */
-
-/* Start: bn_mp_init_multi.c */
-#include <tommath_private.h>
-#ifdef BN_MP_INIT_MULTI_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-#include <stdarg.h>
-
-int mp_init_multi(mp_int *mp, ...)
-{
- mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
- int n = 0; /* Number of ok inits */
- mp_int* cur_arg = mp;
- va_list args;
-
- va_start(args, mp); /* init args to next argument from caller */
- while (cur_arg != NULL) {
- if (mp_init(cur_arg) != MP_OKAY) {
- /* Oops - error! Back-track and mp_clear what we already
- succeeded in init-ing, then return error.
- */
- va_list clean_args;
-
- /* now start cleaning up */
- cur_arg = mp;
- va_start(clean_args, mp);
- while (n-- != 0) {
- mp_clear(cur_arg);
- cur_arg = va_arg(clean_args, mp_int*);
- }
- va_end(clean_args);
- res = MP_MEM;
- break;
- }
- n++;
- cur_arg = va_arg(args, mp_int*);
- }
- va_end(args);
- return res; /* Assumed ok, if error flagged above. */
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_init_multi.c */
-
-/* Start: bn_mp_init_set.c */
-#include <tommath_private.h>
-#ifdef BN_MP_INIT_SET_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* initialize and set a digit */
-int mp_init_set (mp_int * a, mp_digit b)
-{
- int err;
- if ((err = mp_init(a)) != MP_OKAY) {
- return err;
- }
- mp_set(a, b);
- return err;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_init_set.c */
-
-/* Start: bn_mp_init_set_int.c */
-#include <tommath_private.h>
-#ifdef BN_MP_INIT_SET_INT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* initialize and set a digit */
-int mp_init_set_int (mp_int * a, unsigned long b)
-{
- int err;
- if ((err = mp_init(a)) != MP_OKAY) {
- return err;
- }
- return mp_set_int(a, b);
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_init_set_int.c */
-
-/* Start: bn_mp_init_size.c */
-#include <tommath_private.h>
-#ifdef BN_MP_INIT_SIZE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* init an mp_init for a given size */
-int mp_init_size (mp_int * a, int size)
-{
- int x;
-
- /* pad size so there are always extra digits */
- size += (MP_PREC * 2) - (size % MP_PREC);
-
- /* alloc mem */
- a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
- if (a->dp == NULL) {
- return MP_MEM;
- }
-
- /* set the members */
- a->used = 0;
- a->alloc = size;
- a->sign = MP_ZPOS;
-
- /* zero the digits */
- for (x = 0; x < size; x++) {
- a->dp[x] = 0;
- }
-
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_init_size.c */
-
-/* Start: bn_mp_invmod.c */
-#include <tommath_private.h>
-#ifdef BN_MP_INVMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* hac 14.61, pp608 */
-int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
-{
- /* b cannot be negative */
- if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
- return MP_VAL;
- }
-
-#ifdef BN_FAST_MP_INVMOD_C
- /* if the modulus is odd we can use a faster routine instead */
- if ((mp_isodd(b) == MP_YES) && (mp_cmp_d(b, 1) != MP_EQ)) {
- return fast_mp_invmod (a, b, c);
- }
-#endif
-
-#ifdef BN_MP_INVMOD_SLOW_C
- return mp_invmod_slow(a, b, c);
-#else
- return MP_VAL;
-#endif
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_invmod.c */
-
-/* Start: bn_mp_invmod_slow.c */
-#include <tommath_private.h>
-#ifdef BN_MP_INVMOD_SLOW_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* hac 14.61, pp608 */
-int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
-{
- mp_int x, y, u, v, A, B, C, D;
- int res;
-
- /* b cannot be negative */
- if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
- return MP_VAL;
- }
-
- /* init temps */
- if ((res = mp_init_multi(&x, &y, &u, &v,
- &A, &B, &C, &D, NULL)) != MP_OKAY) {
- return res;
- }
-
- /* x = a, y = b */
- if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_copy (b, &y)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* 2. [modified] if x,y are both even then return an error! */
- if ((mp_iseven (&x) == MP_YES) && (mp_iseven (&y) == MP_YES)) {
- res = MP_VAL;
- goto LBL_ERR;
- }
-
- /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
- if ((res = mp_copy (&x, &u)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_copy (&y, &v)) != MP_OKAY) {
- goto LBL_ERR;
- }
- mp_set (&A, 1);
- mp_set (&D, 1);
-
-top:
- /* 4. while u is even do */
- while (mp_iseven (&u) == MP_YES) {
- /* 4.1 u = u/2 */
- if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* 4.2 if A or B is odd then */
- if ((mp_isodd (&A) == MP_YES) || (mp_isodd (&B) == MP_YES)) {
- /* A = (A+y)/2, B = (B-x)/2 */
- if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
- /* A = A/2, B = B/2 */
- if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
-
- /* 5. while v is even do */
- while (mp_iseven (&v) == MP_YES) {
- /* 5.1 v = v/2 */
- if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* 5.2 if C or D is odd then */
- if ((mp_isodd (&C) == MP_YES) || (mp_isodd (&D) == MP_YES)) {
- /* C = (C+y)/2, D = (D-x)/2 */
- if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
- /* C = C/2, D = D/2 */
- if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
-
- /* 6. if u >= v then */
- if (mp_cmp (&u, &v) != MP_LT) {
- /* u = u - v, A = A - C, B = B - D */
- if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
- goto LBL_ERR;
- }
- } else {
- /* v - v - u, C = C - A, D = D - B */
- if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
-
- /* if not zero goto step 4 */
- if (mp_iszero (&u) == MP_NO)
- goto top;
-
- /* now a = C, b = D, gcd == g*v */
-
- /* if v != 1 then there is no inverse */
- if (mp_cmp_d (&v, 1) != MP_EQ) {
- res = MP_VAL;
- goto LBL_ERR;
- }
-
- /* if its too low */
- while (mp_cmp_d(&C, 0) == MP_LT) {
- if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
-
- /* too big */
- while (mp_cmp_mag(&C, b) != MP_LT) {
- if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
-
- /* C is now the inverse */
- mp_exch (&C, c);
- res = MP_OKAY;
-LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_invmod_slow.c */
-
-/* Start: bn_mp_is_square.c */
-#include <tommath_private.h>
-#ifdef BN_MP_IS_SQUARE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* Check if remainders are possible squares - fast exclude non-squares */
-static const char rem_128[128] = {
- 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1
-};
-
-static const char rem_105[105] = {
- 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
- 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
- 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
- 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
- 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1,
- 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1
-};
-
-/* Store non-zero to ret if arg is square, and zero if not */
-int mp_is_square(mp_int *arg,int *ret)
-{
- int res;
- mp_digit c;
- mp_int t;
- unsigned long r;
-
- /* Default to Non-square :) */
- *ret = MP_NO;
-
- if (arg->sign == MP_NEG) {
- return MP_VAL;
- }
-
- /* digits used? (TSD) */
- if (arg->used == 0) {
- return MP_OKAY;
- }
-
- /* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
- if (rem_128[127 & DIGIT(arg,0)] == 1) {
- return MP_OKAY;
- }
-
- /* Next check mod 105 (3*5*7) */
- if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) {
- return res;
- }
- if (rem_105[c] == 1) {
- return MP_OKAY;
- }
-
-
- if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
- return res;
- }
- if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) {
- goto LBL_ERR;
- }
- r = mp_get_int(&t);
- /* Check for other prime modules, note it's not an ERROR but we must
- * free "t" so the easiest way is to goto LBL_ERR. We know that res
- * is already equal to MP_OKAY from the mp_mod call
- */
- if (((1L<<(r%11)) & 0x5C4L) != 0L) goto LBL_ERR;
- if (((1L<<(r%13)) & 0x9E4L) != 0L) goto LBL_ERR;
- if (((1L<<(r%17)) & 0x5CE8L) != 0L) goto LBL_ERR;
- if (((1L<<(r%19)) & 0x4F50CL) != 0L) goto LBL_ERR;
- if (((1L<<(r%23)) & 0x7ACCA0L) != 0L) goto LBL_ERR;
- if (((1L<<(r%29)) & 0xC2EDD0CL) != 0L) goto LBL_ERR;
- if (((1L<<(r%31)) & 0x6DE2B848L) != 0L) goto LBL_ERR;
-
- /* Final check - is sqr(sqrt(arg)) == arg ? */
- if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
-LBL_ERR:mp_clear(&t);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_is_square.c */
-
-/* Start: bn_mp_jacobi.c */
-#include <tommath_private.h>
-#ifdef BN_MP_JACOBI_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* computes the jacobi c = (a | n) (or Legendre if n is prime)
- * HAC pp. 73 Algorithm 2.149
- * HAC is wrong here, as the special case of (0 | 1) is not
- * handled correctly.
- */
-int mp_jacobi (mp_int * a, mp_int * n, int *c)
-{
- mp_int a1, p1;
- int k, s, r, res;
- mp_digit residue;
-
- /* if a < 0 return MP_VAL */
- if (mp_isneg(a) == MP_YES) {
- return MP_VAL;
- }
-
- /* if n <= 0 return MP_VAL */
- if (mp_cmp_d(n, 0) != MP_GT) {
- return MP_VAL;
- }
-
- /* step 1. handle case of a == 0 */
- if (mp_iszero (a) == MP_YES) {
- /* special case of a == 0 and n == 1 */
- if (mp_cmp_d (n, 1) == MP_EQ) {
- *c = 1;
- } else {
- *c = 0;
- }
- return MP_OKAY;
- }
-
- /* step 2. if a == 1, return 1 */
- if (mp_cmp_d (a, 1) == MP_EQ) {
- *c = 1;
- return MP_OKAY;
- }
-
- /* default */
- s = 0;
-
- /* step 3. write a = a1 * 2**k */
- if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
- return res;
- }
-
- if ((res = mp_init (&p1)) != MP_OKAY) {
- goto LBL_A1;
- }
-
- /* divide out larger power of two */
- k = mp_cnt_lsb(&a1);
- if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
- goto LBL_P1;
- }
-
- /* step 4. if e is even set s=1 */
- if ((k & 1) == 0) {
- s = 1;
- } else {
- /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
- residue = n->dp[0] & 7;
-
- if ((residue == 1) || (residue == 7)) {
- s = 1;
- } else if ((residue == 3) || (residue == 5)) {
- s = -1;
- }
- }
-
- /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
- if ( ((n->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
- s = -s;
- }
-
- /* if a1 == 1 we're done */
- if (mp_cmp_d (&a1, 1) == MP_EQ) {
- *c = s;
- } else {
- /* n1 = n mod a1 */
- if ((res = mp_mod (n, &a1, &p1)) != MP_OKAY) {
- goto LBL_P1;
- }
- if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
- goto LBL_P1;
- }
- *c = s * r;
- }
-
- /* done */
- res = MP_OKAY;
-LBL_P1:mp_clear (&p1);
-LBL_A1:mp_clear (&a1);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_jacobi.c */
-
-/* Start: bn_mp_karatsuba_mul.c */
-#include <tommath_private.h>
-#ifdef BN_MP_KARATSUBA_MUL_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* c = |a| * |b| using Karatsuba Multiplication using
- * three half size multiplications
- *
- * Let B represent the radix [e.g. 2**DIGIT_BIT] and
- * let n represent half of the number of digits in
- * the min(a,b)
- *
- * a = a1 * B**n + a0
- * b = b1 * B**n + b0
- *
- * Then, a * b =>
- a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
- *
- * Note that a1b1 and a0b0 are used twice and only need to be
- * computed once. So in total three half size (half # of
- * digit) multiplications are performed, a0b0, a1b1 and
- * (a1+b1)(a0+b0)
- *
- * Note that a multiplication of half the digits requires
- * 1/4th the number of single precision multiplications so in
- * total after one call 25% of the single precision multiplications
- * are saved. Note also that the call to mp_mul can end up back
- * in this function if the a0, a1, b0, or b1 are above the threshold.
- * This is known as divide-and-conquer and leads to the famous
- * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
- * the standard O(N**2) that the baseline/comba methods use.
- * Generally though the overhead of this method doesn't pay off
- * until a certain size (N ~ 80) is reached.
- */
-int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
-{
- mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
- int B, err;
-
- /* default the return code to an error */
- err = MP_MEM;
-
- /* min # of digits */
- B = MIN (a->used, b->used);
-
- /* now divide in two */
- B = B >> 1;
-
- /* init copy all the temps */
- if (mp_init_size (&x0, B) != MP_OKAY)
- goto LBL_ERR;
- if (mp_init_size (&x1, a->used - B) != MP_OKAY)
- goto X0;
- if (mp_init_size (&y0, B) != MP_OKAY)
- goto X1;
- if (mp_init_size (&y1, b->used - B) != MP_OKAY)
- goto Y0;
-
- /* init temps */
- if (mp_init_size (&t1, B * 2) != MP_OKAY)
- goto Y1;
- if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
- goto T1;
- if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
- goto X0Y0;
-
- /* now shift the digits */
- x0.used = y0.used = B;
- x1.used = a->used - B;
- y1.used = b->used - B;
-
- {
- int x;
- mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
-
- /* we copy the digits directly instead of using higher level functions
- * since we also need to shift the digits
- */
- tmpa = a->dp;
- tmpb = b->dp;
-
- tmpx = x0.dp;
- tmpy = y0.dp;
- for (x = 0; x < B; x++) {
- *tmpx++ = *tmpa++;
- *tmpy++ = *tmpb++;
- }
-
- tmpx = x1.dp;
- for (x = B; x < a->used; x++) {
- *tmpx++ = *tmpa++;
- }
-
- tmpy = y1.dp;
- for (x = B; x < b->used; x++) {
- *tmpy++ = *tmpb++;
- }
- }
-
- /* only need to clamp the lower words since by definition the
- * upper words x1/y1 must have a known number of digits
- */
- mp_clamp (&x0);
- mp_clamp (&y0);
-
- /* now calc the products x0y0 and x1y1 */
- /* after this x0 is no longer required, free temp [x0==t2]! */
- if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
- goto X1Y1; /* x0y0 = x0*y0 */
- if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
- goto X1Y1; /* x1y1 = x1*y1 */
-
- /* now calc x1+x0 and y1+y0 */
- if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
- goto X1Y1; /* t1 = x1 - x0 */
- if (s_mp_add (&y1, &y0, &x0) != MP_OKAY)
- goto X1Y1; /* t2 = y1 - y0 */
- if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
- goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */
-
- /* add x0y0 */
- if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
- goto X1Y1; /* t2 = x0y0 + x1y1 */
- if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY)
- goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
-
- /* shift by B */
- if (mp_lshd (&t1, B) != MP_OKAY)
- goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
- if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
- goto X1Y1; /* x1y1 = x1y1 << 2*B */
-
- if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
- goto X1Y1; /* t1 = x0y0 + t1 */
- if (mp_add (&t1, &x1y1, c) != MP_OKAY)
- goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
-
- /* Algorithm succeeded set the return code to MP_OKAY */
- err = MP_OKAY;
-
-X1Y1:mp_clear (&x1y1);
-X0Y0:mp_clear (&x0y0);
-T1:mp_clear (&t1);
-Y1:mp_clear (&y1);
-Y0:mp_clear (&y0);
-X1:mp_clear (&x1);
-X0:mp_clear (&x0);
-LBL_ERR:
- return err;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_karatsuba_mul.c */
-
-/* Start: bn_mp_karatsuba_sqr.c */
-#include <tommath_private.h>
-#ifdef BN_MP_KARATSUBA_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* Karatsuba squaring, computes b = a*a using three
- * half size squarings
- *
- * See comments of karatsuba_mul for details. It
- * is essentially the same algorithm but merely
- * tuned to perform recursive squarings.
- */
-int mp_karatsuba_sqr (mp_int * a, mp_int * b)
-{
- mp_int x0, x1, t1, t2, x0x0, x1x1;
- int B, err;
-
- err = MP_MEM;
-
- /* min # of digits */
- B = a->used;
-
- /* now divide in two */
- B = B >> 1;
-
- /* init copy all the temps */
- if (mp_init_size (&x0, B) != MP_OKAY)
- goto LBL_ERR;
- if (mp_init_size (&x1, a->used - B) != MP_OKAY)
- goto X0;
-
- /* init temps */
- if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
- goto X1;
- if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
- goto T1;
- if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
- goto T2;
- if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
- goto X0X0;
-
- {
- int x;
- mp_digit *dst, *src;
-
- src = a->dp;
-
- /* now shift the digits */
- dst = x0.dp;
- for (x = 0; x < B; x++) {
- *dst++ = *src++;
- }
-
- dst = x1.dp;
- for (x = B; x < a->used; x++) {
- *dst++ = *src++;
- }
- }
-
- x0.used = B;
- x1.used = a->used - B;
-
- mp_clamp (&x0);
-
- /* now calc the products x0*x0 and x1*x1 */
- if (mp_sqr (&x0, &x0x0) != MP_OKAY)
- goto X1X1; /* x0x0 = x0*x0 */
- if (mp_sqr (&x1, &x1x1) != MP_OKAY)
- goto X1X1; /* x1x1 = x1*x1 */
-
- /* now calc (x1+x0)**2 */
- if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
- goto X1X1; /* t1 = x1 - x0 */
- if (mp_sqr (&t1, &t1) != MP_OKAY)
- goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */
-
- /* add x0y0 */
- if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
- goto X1X1; /* t2 = x0x0 + x1x1 */
- if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY)
- goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */
-
- /* shift by B */
- if (mp_lshd (&t1, B) != MP_OKAY)
- goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
- if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
- goto X1X1; /* x1x1 = x1x1 << 2*B */
-
- if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
- goto X1X1; /* t1 = x0x0 + t1 */
- if (mp_add (&t1, &x1x1, b) != MP_OKAY)
- goto X1X1; /* t1 = x0x0 + t1 + x1x1 */
-
- err = MP_OKAY;
-
-X1X1:mp_clear (&x1x1);
-X0X0:mp_clear (&x0x0);
-T2:mp_clear (&t2);
-T1:mp_clear (&t1);
-X1:mp_clear (&x1);
-X0:mp_clear (&x0);
-LBL_ERR:
- return err;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_karatsuba_sqr.c */
-
-/* Start: bn_mp_lcm.c */
-#include <tommath_private.h>
-#ifdef BN_MP_LCM_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* computes least common multiple as |a*b|/(a, b) */
-int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
-{
- int res;
- mp_int t1, t2;
-
-
- if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) {
- return res;
- }
-
- /* t1 = get the GCD of the two inputs */
- if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
- goto LBL_T;
- }
-
- /* divide the smallest by the GCD */
- if (mp_cmp_mag(a, b) == MP_LT) {
- /* store quotient in t2 such that t2 * b is the LCM */
- if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
- goto LBL_T;
- }
- res = mp_mul(b, &t2, c);
- } else {
- /* store quotient in t2 such that t2 * a is the LCM */
- if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
- goto LBL_T;
- }
- res = mp_mul(a, &t2, c);
- }
-
- /* fix the sign to positive */
- c->sign = MP_ZPOS;
-
-LBL_T:
- mp_clear_multi (&t1, &t2, NULL);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_lcm.c */
-
-/* Start: bn_mp_lshd.c */
-#include <tommath_private.h>
-#ifdef BN_MP_LSHD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* shift left a certain amount of digits */
-int mp_lshd (mp_int * a, int b)
-{
- int x, res;
-
- /* if its less than zero return */
- if (b <= 0) {
- return MP_OKAY;
- }
-
- /* grow to fit the new digits */
- if (a->alloc < (a->used + b)) {
- if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
- return res;
- }
- }
-
- {
- mp_digit *top, *bottom;
-
- /* increment the used by the shift amount then copy upwards */
- a->used += b;
-
- /* top */
- top = a->dp + a->used - 1;
-
- /* base */
- bottom = (a->dp + a->used - 1) - b;
-
- /* much like mp_rshd this is implemented using a sliding window
- * except the window goes the otherway around. Copying from
- * the bottom to the top. see bn_mp_rshd.c for more info.
- */
- for (x = a->used - 1; x >= b; x--) {
- *top-- = *bottom--;
- }
-
- /* zero the lower digits */
- top = a->dp;
- for (x = 0; x < b; x++) {
- *top++ = 0;
- }
- }
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_lshd.c */
-
-/* Start: bn_mp_mod.c */
-#include <tommath_private.h>
-#ifdef BN_MP_MOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */
-int
-mp_mod (mp_int * a, mp_int * b, mp_int * c)
-{
- mp_int t;
- int res;
-
- if ((res = mp_init_size (&t, b->used)) != MP_OKAY) {
- return res;
- }
-
- if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
- mp_clear (&t);
- return res;
- }
-
- if ((mp_iszero(&t) != MP_NO) || (t.sign == b->sign)) {
- res = MP_OKAY;
- mp_exch (&t, c);
- } else {
- res = mp_add (b, &t, c);
- }
-
- mp_clear (&t);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_mod.c */
-
-/* Start: bn_mp_mod_2d.c */
-#include <tommath_private.h>
-#ifdef BN_MP_MOD_2D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* calc a value mod 2**b */
-int
-mp_mod_2d (mp_int * a, int b, mp_int * c)
-{
- int x, res;
-
- /* if b is <= 0 then zero the int */
- if (b <= 0) {
- mp_zero (c);
- return MP_OKAY;
- }
-
- /* if the modulus is larger than the value than return */
- if (b >= (int) (a->used * DIGIT_BIT)) {
- res = mp_copy (a, c);
- return res;
- }
-
- /* copy */
- if ((res = mp_copy (a, c)) != MP_OKAY) {
- return res;
- }
-
- /* zero digits above the last digit of the modulus */
- for (x = (b / DIGIT_BIT) + (((b % DIGIT_BIT) == 0) ? 0 : 1); x < c->used; x++) {
- c->dp[x] = 0;
- }
- /* clear the digit that is not completely outside/inside the modulus */
- c->dp[b / DIGIT_BIT] &=
- (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
- mp_clamp (c);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_mod_2d.c */
-
-/* Start: bn_mp_mod_d.c */
-#include <tommath_private.h>
-#ifdef BN_MP_MOD_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-int
-mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
-{
- return mp_div_d(a, b, NULL, c);
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_mod_d.c */
-
-/* Start: bn_mp_montgomery_calc_normalization.c */
-#include <tommath_private.h>
-#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/*
- * shifts with subtractions when the result is greater than b.
- *
- * The method is slightly modified to shift B unconditionally upto just under
- * the leading bit of b. This saves alot of multiple precision shifting.
- */
-int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
-{
- int x, bits, res;
-
- /* how many bits of last digit does b use */
- bits = mp_count_bits (b) % DIGIT_BIT;
-
- if (b->used > 1) {
- if ((res = mp_2expt (a, ((b->used - 1) * DIGIT_BIT) + bits - 1)) != MP_OKAY) {
- return res;
- }
- } else {
- mp_set(a, 1);
- bits = 1;
- }
-
-
- /* now compute C = A * B mod b */
- for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
- if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
- return res;
- }
- if (mp_cmp_mag (a, b) != MP_LT) {
- if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
- return res;
- }
- }
- }
-
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_montgomery_calc_normalization.c */
-
-/* Start: bn_mp_montgomery_reduce.c */
-#include <tommath_private.h>
-#ifdef BN_MP_MONTGOMERY_REDUCE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* computes xR**-1 == x (mod N) via Montgomery Reduction */
-int
-mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
-{
- int ix, res, digs;
- mp_digit mu;
-
- /* can the fast reduction [comba] method be used?
- *
- * Note that unlike in mul you're safely allowed *less*
- * than the available columns [255 per default] since carries
- * are fixed up in the inner loop.
- */
- digs = (n->used * 2) + 1;
- if ((digs < MP_WARRAY) &&
- (n->used <
- (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
- return fast_mp_montgomery_reduce (x, n, rho);
- }
-
- /* grow the input as required */
- if (x->alloc < digs) {
- if ((res = mp_grow (x, digs)) != MP_OKAY) {
- return res;
- }
- }
- x->used = digs;
-
- for (ix = 0; ix < n->used; ix++) {
- /* mu = ai * rho mod b
- *
- * The value of rho must be precalculated via
- * montgomery_setup() such that
- * it equals -1/n0 mod b this allows the
- * following inner loop to reduce the
- * input one digit at a time
- */
- mu = (mp_digit) (((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);
-
- /* a = a + mu * m * b**i */
- {
- int iy;
- mp_digit *tmpn, *tmpx, u;
- mp_word r;
-
- /* alias for digits of the modulus */
- tmpn = n->dp;
-
- /* alias for the digits of x [the input] */
- tmpx = x->dp + ix;
-
- /* set the carry to zero */
- u = 0;
-
- /* Multiply and add in place */
- for (iy = 0; iy < n->used; iy++) {
- /* compute product and sum */
- r = ((mp_word)mu * (mp_word)*tmpn++) +
- (mp_word) u + (mp_word) *tmpx;
-
- /* get carry */
- u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-
- /* fix digit */
- *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
- }
- /* At this point the ix'th digit of x should be zero */
-
-
- /* propagate carries upwards as required*/
- while (u != 0) {
- *tmpx += u;
- u = *tmpx >> DIGIT_BIT;
- *tmpx++ &= MP_MASK;
- }
- }
- }
-
- /* at this point the n.used'th least
- * significant digits of x are all zero
- * which means we can shift x to the
- * right by n.used digits and the
- * residue is unchanged.
- */
-
- /* x = x/b**n.used */
- mp_clamp(x);
- mp_rshd (x, n->used);
-
- /* if x >= n then x = x - n */
- if (mp_cmp_mag (x, n) != MP_LT) {
- return s_mp_sub (x, n, x);
- }
-
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_montgomery_reduce.c */
-
-/* Start: bn_mp_montgomery_setup.c */
-#include <tommath_private.h>
-#ifdef BN_MP_MONTGOMERY_SETUP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* setups the montgomery reduction stuff */
-int
-mp_montgomery_setup (mp_int * n, mp_digit * rho)
-{
- mp_digit x, b;
-
-/* fast inversion mod 2**k
- *
- * Based on the fact that
- *
- * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
- * => 2*X*A - X*X*A*A = 1
- * => 2*(1) - (1) = 1
- */
- b = n->dp[0];
-
- if ((b & 1) == 0) {
- return MP_VAL;
- }
-
- x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
- x *= 2 - (b * x); /* here x*a==1 mod 2**8 */
-#if !defined(MP_8BIT)
- x *= 2 - (b * x); /* here x*a==1 mod 2**16 */
-#endif
-#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
- x *= 2 - (b * x); /* here x*a==1 mod 2**32 */
-#endif
-#ifdef MP_64BIT
- x *= 2 - (b * x); /* here x*a==1 mod 2**64 */
-#endif
-
- /* rho = -1/m mod b */
- *rho = (mp_digit)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
-
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_montgomery_setup.c */
-
-/* Start: bn_mp_mul.c */
-#include <tommath_private.h>
-#ifdef BN_MP_MUL_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* high level multiplication (handles sign) */
-int mp_mul (mp_int * a, mp_int * b, mp_int * c)
-{
- int res, neg;
- neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
-
- /* use Toom-Cook? */
-#ifdef BN_MP_TOOM_MUL_C
- if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
- res = mp_toom_mul(a, b, c);
- } else
-#endif
-#ifdef BN_MP_KARATSUBA_MUL_C
- /* use Karatsuba? */
- if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
- res = mp_karatsuba_mul (a, b, c);
- } else
-#endif
- {
- /* can we use the fast multiplier?
- *
- * The fast multiplier can be used if the output will
- * have less than MP_WARRAY digits and the number of
- * digits won't affect carry propagation
- */
- int digs = a->used + b->used + 1;
-
-#ifdef BN_FAST_S_MP_MUL_DIGS_C
- if ((digs < MP_WARRAY) &&
- (MIN(a->used, b->used) <=
- (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
- res = fast_s_mp_mul_digs (a, b, c, digs);
- } else
-#endif
- {
-#ifdef BN_S_MP_MUL_DIGS_C
- res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
-#else
- res = MP_VAL;
-#endif
- }
- }
- c->sign = (c->used > 0) ? neg : MP_ZPOS;
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_mul.c */
-
-/* Start: bn_mp_mul_2.c */
-#include <tommath_private.h>
-#ifdef BN_MP_MUL_2_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* b = a*2 */
-int mp_mul_2(mp_int * a, mp_int * b)
-{
- int x, res, oldused;
-
- /* grow to accomodate result */
- if (b->alloc < (a->used + 1)) {
- if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
- return res;
- }
- }
-
- oldused = b->used;
- b->used = a->used;
-
- {
- mp_digit r, rr, *tmpa, *tmpb;
-
- /* alias for source */
- tmpa = a->dp;
-
- /* alias for dest */
- tmpb = b->dp;
-
- /* carry */
- r = 0;
- for (x = 0; x < a->used; x++) {
-
- /* get what will be the *next* carry bit from the
- * MSB of the current digit
- */
- rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
-
- /* now shift up this digit, add in the carry [from the previous] */
- *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
-
- /* copy the carry that would be from the source
- * digit into the next iteration
- */
- r = rr;
- }
-
- /* new leading digit? */
- if (r != 0) {
- /* add a MSB which is always 1 at this point */
- *tmpb = 1;
- ++(b->used);
- }
-
- /* now zero any excess digits on the destination
- * that we didn't write to
- */
- tmpb = b->dp + b->used;
- for (x = b->used; x < oldused; x++) {
- *tmpb++ = 0;
- }
- }
- b->sign = a->sign;
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_mul_2.c */
-
-/* Start: bn_mp_mul_2d.c */
-#include <tommath_private.h>
-#ifdef BN_MP_MUL_2D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* shift left by a certain bit count */
-int mp_mul_2d (mp_int * a, int b, mp_int * c)
-{
- mp_digit d;
- int res;
-
- /* copy */
- if (a != c) {
- if ((res = mp_copy (a, c)) != MP_OKAY) {
- return res;
- }
- }
-
- if (c->alloc < (int)(c->used + (b / DIGIT_BIT) + 1)) {
- if ((res = mp_grow (c, c->used + (b / DIGIT_BIT) + 1)) != MP_OKAY) {
- return res;
- }
- }
-
- /* shift by as many digits in the bit count */
- if (b >= (int)DIGIT_BIT) {
- if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
- return res;
- }
- }
-
- /* shift any bit count < DIGIT_BIT */
- d = (mp_digit) (b % DIGIT_BIT);
- if (d != 0) {
- mp_digit *tmpc, shift, mask, r, rr;
- int x;
-
- /* bitmask for carries */
- mask = (((mp_digit)1) << d) - 1;
-
- /* shift for msbs */
- shift = DIGIT_BIT - d;
-
- /* alias */
- tmpc = c->dp;
-
- /* carry */
- r = 0;
- for (x = 0; x < c->used; x++) {
- /* get the higher bits of the current word */
- rr = (*tmpc >> shift) & mask;
-
- /* shift the current word and OR in the carry */
- *tmpc = ((*tmpc << d) | r) & MP_MASK;
- ++tmpc;
-
- /* set the carry to the carry bits of the current word */
- r = rr;
- }
-
- /* set final carry */
- if (r != 0) {
- c->dp[(c->used)++] = r;
- }
- }
- mp_clamp (c);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_mul_2d.c */
-
-/* Start: bn_mp_mul_d.c */
-#include <tommath_private.h>
-#ifdef BN_MP_MUL_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* multiply by a digit */
-int
-mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
-{
- mp_digit u, *tmpa, *tmpc;
- mp_word r;
- int ix, res, olduse;
-
- /* make sure c is big enough to hold a*b */
- if (c->alloc < (a->used + 1)) {
- if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
- return res;
- }
- }
-
- /* get the original destinations used count */
- olduse = c->used;
-
- /* set the sign */
- c->sign = a->sign;
-
- /* alias for a->dp [source] */
- tmpa = a->dp;
-
- /* alias for c->dp [dest] */
- tmpc = c->dp;
-
- /* zero carry */
- u = 0;
-
- /* compute columns */
- for (ix = 0; ix < a->used; ix++) {
- /* compute product and carry sum for this term */
- r = (mp_word)u + ((mp_word)*tmpa++ * (mp_word)b);
-
- /* mask off higher bits to get a single digit */
- *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
-
- /* send carry into next iteration */
- u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
- }
-
- /* store final carry [if any] and increment ix offset */
- *tmpc++ = u;
- ++ix;
-
- /* now zero digits above the top */
- while (ix++ < olduse) {
- *tmpc++ = 0;
- }
-
- /* set used count */
- c->used = a->used + 1;
- mp_clamp(c);
-
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_mul_d.c */
-
-/* Start: bn_mp_mulmod.c */
-#include <tommath_private.h>
-#ifdef BN_MP_MULMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* d = a * b (mod c) */
-int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
- int res;
- mp_int t;
-
- if ((res = mp_init_size (&t, c->used)) != MP_OKAY) {
- return res;
- }
-
- if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
- mp_clear (&t);
- return res;
- }
- res = mp_mod (&t, c, d);
- mp_clear (&t);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_mulmod.c */
-
-/* Start: bn_mp_n_root.c */
-#include <tommath_private.h>
-#ifdef BN_MP_N_ROOT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* wrapper function for mp_n_root_ex()
- * computes c = (a)**(1/b) such that (c)**b <= a and (c+1)**b > a
- */
-int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
-{
- return mp_n_root_ex(a, b, c, 0);
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_n_root.c */
-
-/* Start: bn_mp_n_root_ex.c */
-#include <tommath_private.h>
-#ifdef BN_MP_N_ROOT_EX_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* find the n'th root of an integer
- *
- * Result found such that (c)**b <= a and (c+1)**b > a
- *
- * This algorithm uses Newton's approximation
- * x[i+1] = x[i] - f(x[i])/f'(x[i])
- * which will find the root in log(N) time where
- * each step involves a fair bit. This is not meant to
- * find huge roots [square and cube, etc].
- */
-int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
-{
- mp_int t1, t2, t3;
- int res, neg;
-
- /* input must be positive if b is even */
- if (((b & 1) == 0) && (a->sign == MP_NEG)) {
- return MP_VAL;
- }
-
- if ((res = mp_init (&t1)) != MP_OKAY) {
- return res;
- }
-
- if ((res = mp_init (&t2)) != MP_OKAY) {
- goto LBL_T1;
- }
-
- if ((res = mp_init (&t3)) != MP_OKAY) {
- goto LBL_T2;
- }
-
- /* if a is negative fudge the sign but keep track */
- neg = a->sign;
- a->sign = MP_ZPOS;
-
- /* t2 = 2 */
- mp_set (&t2, 2);
-
- do {
- /* t1 = t2 */
- if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
- goto LBL_T3;
- }
-
- /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
-
- /* t3 = t1**(b-1) */
- if ((res = mp_expt_d_ex (&t1, b - 1, &t3, fast)) != MP_OKAY) {
- goto LBL_T3;
- }
-
- /* numerator */
- /* t2 = t1**b */
- if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
- goto LBL_T3;
- }
-
- /* t2 = t1**b - a */
- if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
- goto LBL_T3;
- }
-
- /* denominator */
- /* t3 = t1**(b-1) * b */
- if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
- goto LBL_T3;
- }
-
- /* t3 = (t1**b - a)/(b * t1**(b-1)) */
- if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
- goto LBL_T3;
- }
-
- if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
- goto LBL_T3;
- }
- } while (mp_cmp (&t1, &t2) != MP_EQ);
-
- /* result can be off by a few so check */
- for (;;) {
- if ((res = mp_expt_d_ex (&t1, b, &t2, fast)) != MP_OKAY) {
- goto LBL_T3;
- }
-
- if (mp_cmp (&t2, a) == MP_GT) {
- if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
- goto LBL_T3;
- }
- } else {
- break;
- }
- }
-
- /* reset the sign of a first */
- a->sign = neg;
-
- /* set the result */
- mp_exch (&t1, c);
-
- /* set the sign of the result */
- c->sign = neg;
-
- res = MP_OKAY;
-
-LBL_T3:mp_clear (&t3);
-LBL_T2:mp_clear (&t2);
-LBL_T1:mp_clear (&t1);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_n_root_ex.c */
-
-/* Start: bn_mp_neg.c */
-#include <tommath_private.h>
-#ifdef BN_MP_NEG_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* b = -a */
-int mp_neg (mp_int * a, mp_int * b)
-{
- int res;
- if (a != b) {
- if ((res = mp_copy (a, b)) != MP_OKAY) {
- return res;
- }
- }
-
- if (mp_iszero(b) != MP_YES) {
- b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
- } else {
- b->sign = MP_ZPOS;
- }
-
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_neg.c */
-
-/* Start: bn_mp_or.c */
-#include <tommath_private.h>
-#ifdef BN_MP_OR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* OR two ints together */
-int mp_or (mp_int * a, mp_int * b, mp_int * c)
-{
- int res, ix, px;
- mp_int t, *x;
-
- if (a->used > b->used) {
- if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
- return res;
- }
- px = b->used;
- x = b;
- } else {
- if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
- return res;
- }
- px = a->used;
- x = a;
- }
-
- for (ix = 0; ix < px; ix++) {
- t.dp[ix] |= x->dp[ix];
- }
- mp_clamp (&t);
- mp_exch (c, &t);
- mp_clear (&t);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_or.c */
-
-/* Start: bn_mp_prime_fermat.c */
-#include <tommath_private.h>
-#ifdef BN_MP_PRIME_FERMAT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* performs one Fermat test.
- *
- * If "a" were prime then b**a == b (mod a) since the order of
- * the multiplicative sub-group would be phi(a) = a-1. That means
- * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
- *
- * Sets result to 1 if the congruence holds, or zero otherwise.
- */
-int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
-{
- mp_int t;
- int err;
-
- /* default to composite */
- *result = MP_NO;
-
- /* ensure b > 1 */
- if (mp_cmp_d(b, 1) != MP_GT) {
- return MP_VAL;
- }
-
- /* init t */
- if ((err = mp_init (&t)) != MP_OKAY) {
- return err;
- }
-
- /* compute t = b**a mod a */
- if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) {
- goto LBL_T;
- }
-
- /* is it equal to b? */
- if (mp_cmp (&t, b) == MP_EQ) {
- *result = MP_YES;
- }
-
- err = MP_OKAY;
-LBL_T:mp_clear (&t);
- return err;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_prime_fermat.c */
-
-/* Start: bn_mp_prime_is_divisible.c */
-#include <tommath_private.h>
-#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* determines if an integers is divisible by one
- * of the first PRIME_SIZE primes or not
- *
- * sets result to 0 if not, 1 if yes
- */
-int mp_prime_is_divisible (mp_int * a, int *result)
-{
- int err, ix;
- mp_digit res;
-
- /* default to not */
- *result = MP_NO;
-
- for (ix = 0; ix < PRIME_SIZE; ix++) {
- /* what is a mod LBL_prime_tab[ix] */
- if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) {
- return err;
- }
-
- /* is the residue zero? */
- if (res == 0) {
- *result = MP_YES;
- return MP_OKAY;
- }
- }
-
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_prime_is_divisible.c */
-
-/* Start: bn_mp_prime_is_prime.c */
-#include <tommath_private.h>
-#ifdef BN_MP_PRIME_IS_PRIME_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* performs a variable number of rounds of Miller-Rabin
- *
- * Probability of error after t rounds is no more than
-
- *
- * Sets result to 1 if probably prime, 0 otherwise
- */
-int mp_prime_is_prime (mp_int * a, int t, int *result)
-{
- mp_int b;
- int ix, err, res;
-
- /* default to no */
- *result = MP_NO;
-
- /* valid value of t? */
- if ((t <= 0) || (t > PRIME_SIZE)) {
- return MP_VAL;
- }
-
- /* is the input equal to one of the primes in the table? */
- for (ix = 0; ix < PRIME_SIZE; ix++) {
- if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
- *result = 1;
- return MP_OKAY;
- }
- }
-
- /* first perform trial division */
- if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
- return err;
- }
-
- /* return if it was trivially divisible */
- if (res == MP_YES) {
- return MP_OKAY;
- }
-
- /* now perform the miller-rabin rounds */
- if ((err = mp_init (&b)) != MP_OKAY) {
- return err;
- }
-
- for (ix = 0; ix < t; ix++) {
- /* set the prime */
- mp_set (&b, ltm_prime_tab[ix]);
-
- if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
- goto LBL_B;
- }
-
- if (res == MP_NO) {
- goto LBL_B;
- }
- }
-
- /* passed the test */
- *result = MP_YES;
-LBL_B:mp_clear (&b);
- return err;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_prime_is_prime.c */
-
-/* Start: bn_mp_prime_miller_rabin.c */
-#include <tommath_private.h>
-#ifdef BN_MP_PRIME_MILLER_RABIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* Miller-Rabin test of "a" to the base of "b" as described in
- * HAC pp. 139 Algorithm 4.24
- *
- * Sets result to 0 if definitely composite or 1 if probably prime.
- * Randomly the chance of error is no more than 1/4 and often
- * very much lower.
- */
-int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
-{
- mp_int n1, y, r;
- int s, j, err;
-
- /* default */
- *result = MP_NO;
-
- /* ensure b > 1 */
- if (mp_cmp_d(b, 1) != MP_GT) {
- return MP_VAL;
- }
-
- /* get n1 = a - 1 */
- if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
- return err;
- }
- if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
- goto LBL_N1;
- }
-
- /* set 2**s * r = n1 */
- if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
- goto LBL_N1;
- }
-
- /* count the number of least significant bits
- * which are zero
- */
- s = mp_cnt_lsb(&r);
-
- /* now divide n - 1 by 2**s */
- if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
- goto LBL_R;
- }
-
- /* compute y = b**r mod a */
- if ((err = mp_init (&y)) != MP_OKAY) {
- goto LBL_R;
- }
- if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
- goto LBL_Y;
- }
-
- /* if y != 1 and y != n1 do */
- if ((mp_cmp_d (&y, 1) != MP_EQ) && (mp_cmp (&y, &n1) != MP_EQ)) {
- j = 1;
- /* while j <= s-1 and y != n1 */
- while ((j <= (s - 1)) && (mp_cmp (&y, &n1) != MP_EQ)) {
- if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
- goto LBL_Y;
- }
-
- /* if y == 1 then composite */
- if (mp_cmp_d (&y, 1) == MP_EQ) {
- goto LBL_Y;
- }
-
- ++j;
- }
-
- /* if y != n1 then composite */
- if (mp_cmp (&y, &n1) != MP_EQ) {
- goto LBL_Y;
- }
- }
-
- /* probably prime now */
- *result = MP_YES;
-LBL_Y:mp_clear (&y);
-LBL_R:mp_clear (&r);
-LBL_N1:mp_clear (&n1);
- return err;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_prime_miller_rabin.c */
-
-/* Start: bn_mp_prime_next_prime.c */
-#include <tommath_private.h>
-#ifdef BN_MP_PRIME_NEXT_PRIME_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* finds the next prime after the number "a" using "t" trials
- * of Miller-Rabin.
- *
- * bbs_style = 1 means the prime must be congruent to 3 mod 4
- */
-int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
-{
- int err, res = MP_NO, x, y;
- mp_digit res_tab[PRIME_SIZE], step, kstep;
- mp_int b;
-
- /* ensure t is valid */
- if ((t <= 0) || (t > PRIME_SIZE)) {
- return MP_VAL;
- }
-
- /* force positive */
- a->sign = MP_ZPOS;
-
- /* simple algo if a is less than the largest prime in the table */
- if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) {
- /* find which prime it is bigger than */
- for (x = PRIME_SIZE - 2; x >= 0; x--) {
- if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) {
- if (bbs_style == 1) {
- /* ok we found a prime smaller or
- * equal [so the next is larger]
- *
- * however, the prime must be
- * congruent to 3 mod 4
- */
- if ((ltm_prime_tab[x + 1] & 3) != 3) {
- /* scan upwards for a prime congruent to 3 mod 4 */
- for (y = x + 1; y < PRIME_SIZE; y++) {
- if ((ltm_prime_tab[y] & 3) == 3) {
- mp_set(a, ltm_prime_tab[y]);
- return MP_OKAY;
- }
- }
- }
- } else {
- mp_set(a, ltm_prime_tab[x + 1]);
- return MP_OKAY;
- }
- }
- }
- /* at this point a maybe 1 */
- if (mp_cmp_d(a, 1) == MP_EQ) {
- mp_set(a, 2);
- return MP_OKAY;
- }
- /* fall through to the sieve */
- }
-
- /* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
- if (bbs_style == 1) {
- kstep = 4;
- } else {
- kstep = 2;
- }
-
- /* at this point we will use a combination of a sieve and Miller-Rabin */
-
- if (bbs_style == 1) {
- /* if a mod 4 != 3 subtract the correct value to make it so */
- if ((a->dp[0] & 3) != 3) {
- if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
- }
- } else {
- if (mp_iseven(a) == MP_YES) {
- /* force odd */
- if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
- return err;
- }
- }
- }
-
- /* generate the restable */
- for (x = 1; x < PRIME_SIZE; x++) {
- if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) {
- return err;
- }
- }
-
- /* init temp used for Miller-Rabin Testing */
- if ((err = mp_init(&b)) != MP_OKAY) {
- return err;
- }
-
- for (;;) {
- /* skip to the next non-trivially divisible candidate */
- step = 0;
- do {
- /* y == 1 if any residue was zero [e.g. cannot be prime] */
- y = 0;
-
- /* increase step to next candidate */
- step += kstep;
-
- /* compute the new residue without using division */
- for (x = 1; x < PRIME_SIZE; x++) {
- /* add the step to each residue */
- res_tab[x] += kstep;
-
- /* subtract the modulus [instead of using division] */
- if (res_tab[x] >= ltm_prime_tab[x]) {
- res_tab[x] -= ltm_prime_tab[x];
- }
-
- /* set flag if zero */
- if (res_tab[x] == 0) {
- y = 1;
- }
- }
- } while ((y == 1) && (step < ((((mp_digit)1) << DIGIT_BIT) - kstep)));
-
- /* add the step */
- if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* if didn't pass sieve and step == MAX then skip test */
- if ((y == 1) && (step >= ((((mp_digit)1) << DIGIT_BIT) - kstep))) {
- continue;
- }
-
- /* is this prime? */
- for (x = 0; x < t; x++) {
- mp_set(&b, ltm_prime_tab[x]);
- if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if (res == MP_NO) {
- break;
- }
- }
-
- if (res == MP_YES) {
- break;
- }
- }
-
- err = MP_OKAY;
-LBL_ERR:
- mp_clear(&b);
- return err;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_prime_next_prime.c */
-
-/* Start: bn_mp_prime_rabin_miller_trials.c */
-#include <tommath_private.h>
-#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-
-static const struct {
- int k, t;
-} sizes[] = {
-{ 128, 28 },
-{ 256, 16 },
-{ 384, 10 },
-{ 512, 7 },
-{ 640, 6 },
-{ 768, 5 },
-{ 896, 4 },
-{ 1024, 4 }
-};
-
-/* returns # of RM trials required for a given bit size */
-int mp_prime_rabin_miller_trials(int size)
-{
- int x;
-
- for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
- if (sizes[x].k == size) {
- return sizes[x].t;
- } else if (sizes[x].k > size) {
- return (x == 0) ? sizes[0].t : sizes[x - 1].t;
- }
- }
- return sizes[x-1].t + 1;
-}
-
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_prime_rabin_miller_trials.c */
-
-/* Start: bn_mp_prime_random_ex.c */
-#include <tommath_private.h>
-#ifdef BN_MP_PRIME_RANDOM_EX_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* makes a truly random prime of a given size (bits),
- *
- * Flags are as follows:
- *
- * LTM_PRIME_BBS - make prime congruent to 3 mod 4
- * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
- * LTM_PRIME_2MSB_ON - make the 2nd highest bit one
- *
- * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
- * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
- * so it can be NULL
- *
- */
-
-/* This is possibly the mother of all prime generation functions, muahahahahaha! */
-int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
-{
- unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
- int res, err, bsize, maskOR_msb_offset;
-
- /* sanity check the input */
- if ((size <= 1) || (t <= 0)) {
- return MP_VAL;
- }
-
- /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
- if ((flags & LTM_PRIME_SAFE) != 0) {
- flags |= LTM_PRIME_BBS;
- }
-
- /* calc the byte size */
- bsize = (size>>3) + ((size&7)?1:0);
-
- /* we need a buffer of bsize bytes */
- tmp = OPT_CAST(unsigned char) XMALLOC(bsize);
- if (tmp == NULL) {
- return MP_MEM;
- }
-
- /* calc the maskAND value for the MSbyte*/
- maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7)));
-
- /* calc the maskOR_msb */
- maskOR_msb = 0;
- maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
- if ((flags & LTM_PRIME_2MSB_ON) != 0) {
- maskOR_msb |= 0x80 >> ((9 - size) & 7);
- }
-
- /* get the maskOR_lsb */
- maskOR_lsb = 1;
- if ((flags & LTM_PRIME_BBS) != 0) {
- maskOR_lsb |= 3;
- }
-
- do {
- /* read the bytes */
- if (cb(tmp, bsize, dat) != bsize) {
- err = MP_VAL;
- goto error;
- }
-
- /* work over the MSbyte */
- tmp[0] &= maskAND;
- tmp[0] |= 1 << ((size - 1) & 7);
-
- /* mix in the maskORs */
- tmp[maskOR_msb_offset] |= maskOR_msb;
- tmp[bsize-1] |= maskOR_lsb;
-
- /* read it in */
- if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY) { goto error; }
-
- /* is it prime? */
- if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
- if (res == MP_NO) {
- continue;
- }
-
- if ((flags & LTM_PRIME_SAFE) != 0) {
- /* see if (a-1)/2 is prime */
- if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) { goto error; }
- if ((err = mp_div_2(a, a)) != MP_OKAY) { goto error; }
-
- /* is it prime? */
- if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
- }
- } while (res == MP_NO);
-
- if ((flags & LTM_PRIME_SAFE) != 0) {
- /* restore a to the original value */
- if ((err = mp_mul_2(a, a)) != MP_OKAY) { goto error; }
- if ((err = mp_add_d(a, 1, a)) != MP_OKAY) { goto error; }
- }
-
- err = MP_OKAY;
-error:
- XFREE(tmp);
- return err;
-}
-
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_prime_random_ex.c */
-
-/* Start: bn_mp_radix_size.c */
-#include <tommath_private.h>
-#ifdef BN_MP_RADIX_SIZE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* returns size of ASCII reprensentation */
-int mp_radix_size (mp_int * a, int radix, int *size)
-{
- int res, digs;
- mp_int t;
- mp_digit d;
-
- *size = 0;
-
- /* make sure the radix is in range */
- if ((radix < 2) || (radix > 64)) {
- return MP_VAL;
- }
-
- if (mp_iszero(a) == MP_YES) {
- *size = 2;
- return MP_OKAY;
- }
-
- /* special case for binary */
- if (radix == 2) {
- *size = mp_count_bits (a) + ((a->sign == MP_NEG) ? 1 : 0) + 1;
- return MP_OKAY;
- }
-
- /* digs is the digit count */
- digs = 0;
-
- /* if it's negative add one for the sign */
- if (a->sign == MP_NEG) {
- ++digs;
- }
-
- /* init a copy of the input */
- if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
- return res;
- }
-
- /* force temp to positive */
- t.sign = MP_ZPOS;
-
- /* fetch out all of the digits */
- while (mp_iszero (&t) == MP_NO) {
- if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
- mp_clear (&t);
- return res;
- }
- ++digs;
- }
- mp_clear (&t);
-
- /* return digs + 1, the 1 is for the NULL byte that would be required. */
- *size = digs + 1;
- return MP_OKAY;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_radix_size.c */
-
-/* Start: bn_mp_radix_smap.c */
-#include <tommath_private.h>
-#ifdef BN_MP_RADIX_SMAP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* chars used in radix conversions */
-const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_radix_smap.c */
-
-/* Start: bn_mp_rand.c */
-#include <tommath_private.h>
-#ifdef BN_MP_RAND_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-#if MP_GEN_RANDOM_MAX == 0xffffffff
- #define MP_GEN_RANDOM_SHIFT 32
-#elif MP_GEN_RANDOM_MAX == 32767
- /* SHRT_MAX */
- #define MP_GEN_RANDOM_SHIFT 15
-#elif MP_GEN_RANDOM_MAX == 2147483647
- /* INT_MAX */
- #define MP_GEN_RANDOM_SHIFT 31
-#elif !defined(MP_GEN_RANDOM_SHIFT)
-#error Thou shalt define their own valid MP_GEN_RANDOM_SHIFT
-#endif
-
-/* makes a pseudo-random int of a given size */
-static mp_digit s_gen_random(void)
-{
- mp_digit d = 0, msk = 0;
- do {
- d <<= MP_GEN_RANDOM_SHIFT;
- d |= ((mp_digit) MP_GEN_RANDOM());
- msk <<= MP_GEN_RANDOM_SHIFT;
- msk |= (MP_MASK & MP_GEN_RANDOM_MAX);
- } while ((MP_MASK & msk) != MP_MASK);
- d &= MP_MASK;
- return d;
-}
-
-int
-mp_rand (mp_int * a, int digits)
-{
- int res;
- mp_digit d;
-
- mp_zero (a);
- if (digits <= 0) {
- return MP_OKAY;
- }
-
- /* first place a random non-zero digit */
- do {
- d = s_gen_random();
- } while (d == 0);
-
- if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
- return res;
- }
-
- while (--digits > 0) {
- if ((res = mp_lshd (a, 1)) != MP_OKAY) {
- return res;
- }
-
- if ((res = mp_add_d (a, s_gen_random(), a)) != MP_OKAY) {
- return res;
- }
- }
-
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_rand.c */
-
-/* Start: bn_mp_read_radix.c */
-#include <tommath_private.h>
-#ifdef BN_MP_READ_RADIX_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* read a string [ASCII] in a given radix */
-int mp_read_radix (mp_int * a, const char *str, int radix)
-{
- int y, res, neg;
- char ch;
-
- /* zero the digit bignum */
- mp_zero(a);
-
- /* make sure the radix is ok */
- if ((radix < 2) || (radix > 64)) {
- return MP_VAL;
- }
-
- /* if the leading digit is a
- * minus set the sign to negative.
- */
- if (*str == '-') {
- ++str;
- neg = MP_NEG;
- } else {
- neg = MP_ZPOS;
- }
-
- /* set the integer to the default of zero */
- mp_zero (a);
-
- /* process each digit of the string */
- while (*str != '\0') {
- /* if the radix <= 36 the conversion is case insensitive
- * this allows numbers like 1AB and 1ab to represent the same value
- * [e.g. in hex]
- */
- ch = (radix <= 36) ? (char)toupper((int)*str) : *str;
- for (y = 0; y < 64; y++) {
- if (ch == mp_s_rmap[y]) {
- break;
- }
- }
-
- /* if the char was found in the map
- * and is less than the given radix add it
- * to the number, otherwise exit the loop.
- */
- if (y < radix) {
- if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
- return res;
- }
- if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
- return res;
- }
- } else {
- break;
- }
- ++str;
- }
-
- /* set the sign only if a != 0 */
- if (mp_iszero(a) != MP_YES) {
- a->sign = neg;
- }
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_read_radix.c */
-
-/* Start: bn_mp_read_signed_bin.c */
-#include <tommath_private.h>
-#ifdef BN_MP_READ_SIGNED_BIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* read signed bin, big endian, first byte is 0==positive or 1==negative */
-int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
-{
- int res;
-
- /* read magnitude */
- if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) {
- return res;
- }
-
- /* first byte is 0 for positive, non-zero for negative */
- if (b[0] == 0) {
- a->sign = MP_ZPOS;
- } else {
- a->sign = MP_NEG;
- }
-
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_read_signed_bin.c */
-
-/* Start: bn_mp_read_unsigned_bin.c */
-#include <tommath_private.h>
-#ifdef BN_MP_READ_UNSIGNED_BIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* reads a unsigned char array, assumes the msb is stored first [big endian] */
-int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
-{
- int res;
-
- /* make sure there are at least two digits */
- if (a->alloc < 2) {
- if ((res = mp_grow(a, 2)) != MP_OKAY) {
- return res;
- }
- }
-
- /* zero the int */
- mp_zero (a);
-
- /* read the bytes in */
- while (c-- > 0) {
- if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
- return res;
- }
-
-#ifndef MP_8BIT
- a->dp[0] |= *b++;
- a->used += 1;
-#else
- a->dp[0] = (*b & MP_MASK);
- a->dp[1] |= ((*b++ >> 7U) & 1);
- a->used += 2;
-#endif
- }
- mp_clamp (a);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_read_unsigned_bin.c */
-
-/* Start: bn_mp_reduce.c */
-#include <tommath_private.h>
-#ifdef BN_MP_REDUCE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* reduces x mod m, assumes 0 < x < m**2, mu is
- * precomputed via mp_reduce_setup.
- * From HAC pp.604 Algorithm 14.42
- */
-int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
-{
- mp_int q;
- int res, um = m->used;
-
- /* q = x */
- if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
- return res;
- }
-
- /* q1 = x / b**(k-1) */
- mp_rshd (&q, um - 1);
-
- /* according to HAC this optimization is ok */
- if (((mp_digit) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
- if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
- goto CLEANUP;
- }
- } else {
-#ifdef BN_S_MP_MUL_HIGH_DIGS_C
- if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
- goto CLEANUP;
- }
-#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
- if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
- goto CLEANUP;
- }
-#else
- {
- res = MP_VAL;
- goto CLEANUP;
- }
-#endif
- }
-
- /* q3 = q2 / b**(k+1) */
- mp_rshd (&q, um + 1);
-
- /* x = x mod b**(k+1), quick (no division) */
- if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
- goto CLEANUP;
- }
-
- /* q = q * m mod b**(k+1), quick (no division) */
- if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
- goto CLEANUP;
- }
-
- /* x = x - q */
- if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
- goto CLEANUP;
- }
-
- /* If x < 0, add b**(k+1) to it */
- if (mp_cmp_d (x, 0) == MP_LT) {
- mp_set (&q, 1);
- if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
- goto CLEANUP;
- if ((res = mp_add (x, &q, x)) != MP_OKAY)
- goto CLEANUP;
- }
-
- /* Back off if it's too big */
- while (mp_cmp (x, m) != MP_LT) {
- if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
- goto CLEANUP;
- }
- }
-
-CLEANUP:
- mp_clear (&q);
-
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_reduce.c */
-
-/* Start: bn_mp_reduce_2k.c */
-#include <tommath_private.h>
-#ifdef BN_MP_REDUCE_2K_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* reduces a modulo n where n is of the form 2**p - d */
-int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
-{
- mp_int q;
- int p, res;
-
- if ((res = mp_init(&q)) != MP_OKAY) {
- return res;
- }
-
- p = mp_count_bits(n);
-top:
- /* q = a/2**p, a = a mod 2**p */
- if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if (d != 1) {
- /* q = q * d */
- if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
- goto LBL_ERR;
- }
- }
-
- /* a = a + q */
- if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if (mp_cmp_mag(a, n) != MP_LT) {
- if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
- goto LBL_ERR;
- }
- goto top;
- }
-
-LBL_ERR:
- mp_clear(&q);
- return res;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_reduce_2k.c */
-
-/* Start: bn_mp_reduce_2k_l.c */
-#include <tommath_private.h>
-#ifdef BN_MP_REDUCE_2K_L_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* reduces a modulo n where n is of the form 2**p - d
- This differs from reduce_2k since "d" can be larger
- than a single digit.
-*/
-int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
-{
- mp_int q;
- int p, res;
-
- if ((res = mp_init(&q)) != MP_OKAY) {
- return res;
- }
-
- p = mp_count_bits(n);
-top:
- /* q = a/2**p, a = a mod 2**p */
- if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* q = q * d */
- if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* a = a + q */
- if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if (mp_cmp_mag(a, n) != MP_LT) {
- if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
- goto LBL_ERR;
- }
- goto top;
- }
-
-LBL_ERR:
- mp_clear(&q);
- return res;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_reduce_2k_l.c */
-
-/* Start: bn_mp_reduce_2k_setup.c */
-#include <tommath_private.h>
-#ifdef BN_MP_REDUCE_2K_SETUP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* determines the setup value */
-int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
-{
- int res, p;
- mp_int tmp;
-
- if ((res = mp_init(&tmp)) != MP_OKAY) {
- return res;
- }
-
- p = mp_count_bits(a);
- if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
- mp_clear(&tmp);
- return res;
- }
-
- if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
- mp_clear(&tmp);
- return res;
- }
-
- *d = tmp.dp[0];
- mp_clear(&tmp);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_reduce_2k_setup.c */
-
-/* Start: bn_mp_reduce_2k_setup_l.c */
-#include <tommath_private.h>
-#ifdef BN_MP_REDUCE_2K_SETUP_L_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* determines the setup value */
-int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
-{
- int res;
- mp_int tmp;
-
- if ((res = mp_init(&tmp)) != MP_OKAY) {
- return res;
- }
-
- if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
-LBL_ERR:
- mp_clear(&tmp);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_reduce_2k_setup_l.c */
-
-/* Start: bn_mp_reduce_is_2k.c */
-#include <tommath_private.h>
-#ifdef BN_MP_REDUCE_IS_2K_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* determines if mp_reduce_2k can be used */
-int mp_reduce_is_2k(mp_int *a)
-{
- int ix, iy, iw;
- mp_digit iz;
-
- if (a->used == 0) {
- return MP_NO;
- } else if (a->used == 1) {
- return MP_YES;
- } else if (a->used > 1) {
- iy = mp_count_bits(a);
- iz = 1;
- iw = 1;
-
- /* Test every bit from the second digit up, must be 1 */
- for (ix = DIGIT_BIT; ix < iy; ix++) {
- if ((a->dp[iw] & iz) == 0) {
- return MP_NO;
- }
- iz <<= 1;
- if (iz > (mp_digit)MP_MASK) {
- ++iw;
- iz = 1;
- }
- }
- }
- return MP_YES;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_reduce_is_2k.c */
-
-/* Start: bn_mp_reduce_is_2k_l.c */
-#include <tommath_private.h>
-#ifdef BN_MP_REDUCE_IS_2K_L_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* determines if reduce_2k_l can be used */
-int mp_reduce_is_2k_l(mp_int *a)
-{
- int ix, iy;
-
- if (a->used == 0) {
- return MP_NO;
- } else if (a->used == 1) {
- return MP_YES;
- } else if (a->used > 1) {
- /* if more than half of the digits are -1 we're sold */
- for (iy = ix = 0; ix < a->used; ix++) {
- if (a->dp[ix] == MP_MASK) {
- ++iy;
- }
- }
- return (iy >= (a->used/2)) ? MP_YES : MP_NO;
-
- }
- return MP_NO;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_reduce_is_2k_l.c */
-
-/* Start: bn_mp_reduce_setup.c */
-#include <tommath_private.h>
-#ifdef BN_MP_REDUCE_SETUP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* pre-calculate the value required for Barrett reduction
- * For a given modulus "b" it calulates the value required in "a"
- */
-int mp_reduce_setup (mp_int * a, mp_int * b)
-{
- int res;
-
- if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
- return res;
- }
- return mp_div (a, b, a, NULL);
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_reduce_setup.c */
-
-/* Start: bn_mp_rshd.c */
-#include <tommath_private.h>
-#ifdef BN_MP_RSHD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* shift right a certain amount of digits */
-void mp_rshd (mp_int * a, int b)
-{
- int x;
-
- /* if b <= 0 then ignore it */
- if (b <= 0) {
- return;
- }
-
- /* if b > used then simply zero it and return */
- if (a->used <= b) {
- mp_zero (a);
- return;
- }
-
- {
- mp_digit *bottom, *top;
-
- /* shift the digits down */
-
- /* bottom */
- bottom = a->dp;
-
- /* top [offset into digits] */
- top = a->dp + b;
-
- /* this is implemented as a sliding window where
- * the window is b-digits long and digits from
- * the top of the window are copied to the bottom
- *
- * e.g.
-
- b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
- /\ | ---->
- \-------------------/ ---->
- */
- for (x = 0; x < (a->used - b); x++) {
- *bottom++ = *top++;
- }
-
- /* zero the top digits */
- for (; x < a->used; x++) {
- *bottom++ = 0;
- }
- }
-
- /* remove excess digits */
- a->used -= b;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_rshd.c */
-
-/* Start: bn_mp_set.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SET_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* set to a digit */
-void mp_set (mp_int * a, mp_digit b)
-{
- mp_zero (a);
- a->dp[0] = b & MP_MASK;
- a->used = (a->dp[0] != 0) ? 1 : 0;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_set.c */
-
-/* Start: bn_mp_set_int.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SET_INT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* set a 32-bit const */
-int mp_set_int (mp_int * a, unsigned long b)
-{
- int x, res;
-
- mp_zero (a);
-
- /* set four bits at a time */
- for (x = 0; x < 8; x++) {
- /* shift the number up four bits */
- if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) {
- return res;
- }
-
- /* OR in the top four bits of the source */
- a->dp[0] |= (b >> 28) & 15;
-
- /* shift the source up to the next four bits */
- b <<= 4;
-
- /* ensure that digits are not clamped off */
- a->used += 1;
- }
- mp_clamp (a);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_set_int.c */
-
-/* Start: bn_mp_set_long.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SET_LONG_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* set a platform dependent unsigned long int */
-MP_SET_XLONG(mp_set_long, unsigned long)
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_set_long.c */
-
-/* Start: bn_mp_set_long_long.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SET_LONG_LONG_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* set a platform dependent unsigned long long int */
-MP_SET_XLONG(mp_set_long_long, unsigned long long)
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_set_long_long.c */
-
-/* Start: bn_mp_shrink.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SHRINK_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* shrink a bignum */
-int mp_shrink (mp_int * a)
-{
- mp_digit *tmp;
- int used = 1;
-
- if(a->used > 0) {
- used = a->used;
- }
-
- if (a->alloc != used) {
- if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * used)) == NULL) {
- return MP_MEM;
- }
- a->dp = tmp;
- a->alloc = used;
- }
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_shrink.c */
-
-/* Start: bn_mp_signed_bin_size.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SIGNED_BIN_SIZE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* get the size for an signed equivalent */
-int mp_signed_bin_size (mp_int * a)
-{
- return 1 + mp_unsigned_bin_size (a);
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_signed_bin_size.c */
-
-/* Start: bn_mp_sqr.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* computes b = a*a */
-int
-mp_sqr (mp_int * a, mp_int * b)
-{
- int res;
-
-#ifdef BN_MP_TOOM_SQR_C
- /* use Toom-Cook? */
- if (a->used >= TOOM_SQR_CUTOFF) {
- res = mp_toom_sqr(a, b);
- /* Karatsuba? */
- } else
-#endif
-#ifdef BN_MP_KARATSUBA_SQR_C
- if (a->used >= KARATSUBA_SQR_CUTOFF) {
- res = mp_karatsuba_sqr (a, b);
- } else
-#endif
- {
-#ifdef BN_FAST_S_MP_SQR_C
- /* can we use the fast comba multiplier? */
- if ((((a->used * 2) + 1) < MP_WARRAY) &&
- (a->used <
- (1 << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) - 1)))) {
- res = fast_s_mp_sqr (a, b);
- } else
-#endif
- {
-#ifdef BN_S_MP_SQR_C
- res = s_mp_sqr (a, b);
-#else
- res = MP_VAL;
-#endif
- }
- }
- b->sign = MP_ZPOS;
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_sqr.c */
-
-/* Start: bn_mp_sqrmod.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SQRMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* c = a * a (mod b) */
-int
-mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
-{
- int res;
- mp_int t;
-
- if ((res = mp_init (&t)) != MP_OKAY) {
- return res;
- }
-
- if ((res = mp_sqr (a, &t)) != MP_OKAY) {
- mp_clear (&t);
- return res;
- }
- res = mp_mod (&t, b, c);
- mp_clear (&t);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_sqrmod.c */
-
-/* Start: bn_mp_sqrt.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SQRT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* this function is less generic than mp_n_root, simpler and faster */
-int mp_sqrt(mp_int *arg, mp_int *ret)
-{
- int res;
- mp_int t1,t2;
-
- /* must be positive */
- if (arg->sign == MP_NEG) {
- return MP_VAL;
- }
-
- /* easy out */
- if (mp_iszero(arg) == MP_YES) {
- mp_zero(ret);
- return MP_OKAY;
- }
-
- if ((res = mp_init_copy(&t1, arg)) != MP_OKAY) {
- return res;
- }
-
- if ((res = mp_init(&t2)) != MP_OKAY) {
- goto E2;
- }
-
- /* First approx. (not very bad for large arg) */
- mp_rshd (&t1,t1.used/2);
-
- /* t1 > 0 */
- if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
- goto E1;
- }
- if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
- goto E1;
- }
- if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
- goto E1;
- }
- /* And now t1 > sqrt(arg) */
- do {
- if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
- goto E1;
- }
- if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
- goto E1;
- }
- if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
- goto E1;
- }
- /* t1 >= sqrt(arg) >= t2 at this point */
- } while (mp_cmp_mag(&t1,&t2) == MP_GT);
-
- mp_exch(&t1,ret);
-
-E1: mp_clear(&t2);
-E2: mp_clear(&t1);
- return res;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_sqrt.c */
-
-/* Start: bn_mp_sqrtmod_prime.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SQRTMOD_PRIME_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- */
-
-/* Tonelli-Shanks algorithm
- * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
- * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
- *
- */
-
-int mp_sqrtmod_prime(mp_int *n, mp_int *prime, mp_int *ret)
-{
- int res, legendre;
- mp_int t1, C, Q, S, Z, M, T, R, two;
- mp_digit i;
-
- /* first handle the simple cases */
- if (mp_cmp_d(n, 0) == MP_EQ) {
- mp_zero(ret);
- return MP_OKAY;
- }
- if (mp_cmp_d(prime, 2) == MP_EQ) return MP_VAL; /* prime must be odd */
- if ((res = mp_jacobi(n, prime, &legendre)) != MP_OKAY) return res;
- if (legendre == -1) return MP_VAL; /* quadratic non-residue mod prime */
-
- if ((res = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) {
- return res;
- }
-
- /* SPECIAL CASE: if prime mod 4 == 3
- * compute directly: res = n^(prime+1)/4 mod prime
- * Handbook of Applied Cryptography algorithm 3.36
- */
- if ((res = mp_mod_d(prime, 4, &i)) != MP_OKAY) goto cleanup;
- if (i == 3) {
- if ((res = mp_add_d(prime, 1, &t1)) != MP_OKAY) goto cleanup;
- if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
- if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
- if ((res = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY) goto cleanup;
- res = MP_OKAY;
- goto cleanup;
- }
-
- /* NOW: Tonelli-Shanks algorithm */
-
- /* factor out powers of 2 from prime-1, defining Q and S as: prime-1 = Q*2^S */
- if ((res = mp_copy(prime, &Q)) != MP_OKAY) goto cleanup;
- if ((res = mp_sub_d(&Q, 1, &Q)) != MP_OKAY) goto cleanup;
- /* Q = prime - 1 */
- mp_zero(&S);
- /* S = 0 */
- while (mp_iseven(&Q) != MP_NO) {
- if ((res = mp_div_2(&Q, &Q)) != MP_OKAY) goto cleanup;
- /* Q = Q / 2 */
- if ((res = mp_add_d(&S, 1, &S)) != MP_OKAY) goto cleanup;
- /* S = S + 1 */
- }
-
- /* find a Z such that the Legendre symbol (Z|prime) == -1 */
- if ((res = mp_set_int(&Z, 2)) != MP_OKAY) goto cleanup;
- /* Z = 2 */
- while(1) {
- if ((res = mp_jacobi(&Z, prime, &legendre)) != MP_OKAY) goto cleanup;
- if (legendre == -1) break;
- if ((res = mp_add_d(&Z, 1, &Z)) != MP_OKAY) goto cleanup;
- /* Z = Z + 1 */
- }
-
- if ((res = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY) goto cleanup;
- /* C = Z ^ Q mod prime */
- if ((res = mp_add_d(&Q, 1, &t1)) != MP_OKAY) goto cleanup;
- if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
- /* t1 = (Q + 1) / 2 */
- if ((res = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY) goto cleanup;
- /* R = n ^ ((Q + 1) / 2) mod prime */
- if ((res = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY) goto cleanup;
- /* T = n ^ Q mod prime */
- if ((res = mp_copy(&S, &M)) != MP_OKAY) goto cleanup;
- /* M = S */
- if ((res = mp_set_int(&two, 2)) != MP_OKAY) goto cleanup;
-
- res = MP_VAL;
- while (1) {
- if ((res = mp_copy(&T, &t1)) != MP_OKAY) goto cleanup;
- i = 0;
- while (1) {
- if (mp_cmp_d(&t1, 1) == MP_EQ) break;
- if ((res = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup;
- i++;
- }
- if (i == 0) {
- if ((res = mp_copy(&R, ret)) != MP_OKAY) goto cleanup;
- res = MP_OKAY;
- goto cleanup;
- }
- if ((res = mp_sub_d(&M, i, &t1)) != MP_OKAY) goto cleanup;
- if ((res = mp_sub_d(&t1, 1, &t1)) != MP_OKAY) goto cleanup;
- if ((res = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY) goto cleanup;
- /* t1 = 2 ^ (M - i - 1) */
- if ((res = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY) goto cleanup;
- /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */
- if ((res = mp_sqrmod(&t1, prime, &C)) != MP_OKAY) goto cleanup;
- /* C = (t1 * t1) mod prime */
- if ((res = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY) goto cleanup;
- /* R = (R * t1) mod prime */
- if ((res = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY) goto cleanup;
- /* T = (T * C) mod prime */
- mp_set(&M, i);
- /* M = i */
- }
-
-cleanup:
- mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
- return res;
-}
-
-#endif
-
-/* End: bn_mp_sqrtmod_prime.c */
-
-/* Start: bn_mp_sub.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SUB_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* high level subtraction (handles signs) */
-int
-mp_sub (mp_int * a, mp_int * b, mp_int * c)
-{
- int sa, sb, res;
-
- sa = a->sign;
- sb = b->sign;
-
- if (sa != sb) {
- /* subtract a negative from a positive, OR */
- /* subtract a positive from a negative. */
- /* In either case, ADD their magnitudes, */
- /* and use the sign of the first number. */
- c->sign = sa;
- res = s_mp_add (a, b, c);
- } else {
- /* subtract a positive from a positive, OR */
- /* subtract a negative from a negative. */
- /* First, take the difference between their */
- /* magnitudes, then... */
- if (mp_cmp_mag (a, b) != MP_LT) {
- /* Copy the sign from the first */
- c->sign = sa;
- /* The first has a larger or equal magnitude */
- res = s_mp_sub (a, b, c);
- } else {
- /* The result has the *opposite* sign from */
- /* the first number. */
- c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
- /* The second has a larger magnitude */
- res = s_mp_sub (b, a, c);
- }
- }
- return res;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_sub.c */
-
-/* Start: bn_mp_sub_d.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SUB_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* single digit subtraction */
-int
-mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
-{
- mp_digit *tmpa, *tmpc, mu;
- int res, ix, oldused;
-
- /* grow c as required */
- if (c->alloc < (a->used + 1)) {
- if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
- return res;
- }
- }
-
- /* if a is negative just do an unsigned
- * addition [with fudged signs]
- */
- if (a->sign == MP_NEG) {
- a->sign = MP_ZPOS;
- res = mp_add_d(a, b, c);
- a->sign = c->sign = MP_NEG;
-
- /* clamp */
- mp_clamp(c);
-
- return res;
- }
-
- /* setup regs */
- oldused = c->used;
- tmpa = a->dp;
- tmpc = c->dp;
-
- /* if a <= b simply fix the single digit */
- if (((a->used == 1) && (a->dp[0] <= b)) || (a->used == 0)) {
- if (a->used == 1) {
- *tmpc++ = b - *tmpa;
- } else {
- *tmpc++ = b;
- }
- ix = 1;
-
- /* negative/1digit */
- c->sign = MP_NEG;
- c->used = 1;
- } else {
- /* positive/size */
- c->sign = MP_ZPOS;
- c->used = a->used;
-
- /* subtract first digit */
- *tmpc = *tmpa++ - b;
- mu = *tmpc >> ((sizeof(mp_digit) * CHAR_BIT) - 1);
- *tmpc++ &= MP_MASK;
-
- /* handle rest of the digits */
- for (ix = 1; ix < a->used; ix++) {
- *tmpc = *tmpa++ - mu;
- mu = *tmpc >> ((sizeof(mp_digit) * CHAR_BIT) - 1);
- *tmpc++ &= MP_MASK;
- }
- }
-
- /* zero excess digits */
- while (ix++ < oldused) {
- *tmpc++ = 0;
- }
- mp_clamp(c);
- return MP_OKAY;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_sub_d.c */
-
-/* Start: bn_mp_submod.c */
-#include <tommath_private.h>
-#ifdef BN_MP_SUBMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* d = a - b (mod c) */
-int
-mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
- int res;
- mp_int t;
-
-
- if ((res = mp_init (&t)) != MP_OKAY) {
- return res;
- }
-
- if ((res = mp_sub (a, b, &t)) != MP_OKAY) {
- mp_clear (&t);
- return res;
- }
- res = mp_mod (&t, c, d);
- mp_clear (&t);
- return res;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_submod.c */
-
-/* Start: bn_mp_to_signed_bin.c */
-#include <tommath_private.h>
-#ifdef BN_MP_TO_SIGNED_BIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* store in signed [big endian] format */
-int mp_to_signed_bin (mp_int * a, unsigned char *b)
-{
- int res;
-
- if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) {
- return res;
- }
- b[0] = (a->sign == MP_ZPOS) ? (unsigned char)0 : (unsigned char)1;
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_to_signed_bin.c */
-
-/* Start: bn_mp_to_signed_bin_n.c */
-#include <tommath_private.h>
-#ifdef BN_MP_TO_SIGNED_BIN_N_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* store in signed [big endian] format */
-int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
-{
- if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
- return MP_VAL;
- }
- *outlen = mp_signed_bin_size(a);
- return mp_to_signed_bin(a, b);
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_to_signed_bin_n.c */
-
-/* Start: bn_mp_to_unsigned_bin.c */
-#include <tommath_private.h>
-#ifdef BN_MP_TO_UNSIGNED_BIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* store in unsigned [big endian] format */
-int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
-{
- int x, res;
- mp_int t;
-
- if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
- return res;
- }
-
- x = 0;
- while (mp_iszero (&t) == MP_NO) {
-#ifndef MP_8BIT
- b[x++] = (unsigned char) (t.dp[0] & 255);
-#else
- b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
-#endif
- if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
- mp_clear (&t);
- return res;
- }
- }
- bn_reverse (b, x);
- mp_clear (&t);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_to_unsigned_bin.c */
-
-/* Start: bn_mp_to_unsigned_bin_n.c */
-#include <tommath_private.h>
-#ifdef BN_MP_TO_UNSIGNED_BIN_N_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* store in unsigned [big endian] format */
-int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
-{
- if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
- return MP_VAL;
- }
- *outlen = mp_unsigned_bin_size(a);
- return mp_to_unsigned_bin(a, b);
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_to_unsigned_bin_n.c */
-
-/* Start: bn_mp_toom_mul.c */
-#include <tommath_private.h>
-#ifdef BN_MP_TOOM_MUL_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* multiplication using the Toom-Cook 3-way algorithm
- *
- * Much more complicated than Karatsuba but has a lower
- * asymptotic running time of O(N**1.464). This algorithm is
- * only particularly useful on VERY large inputs
- * (we're talking 1000s of digits here...).
-*/
-int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
-{
- mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
- int res, B;
-
- /* init temps */
- if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
- &a0, &a1, &a2, &b0, &b1,
- &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
- return res;
- }
-
- /* B */
- B = MIN(a->used, b->used) / 3;
-
- /* a = a2 * B**2 + a1 * B + a0 */
- if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_copy(a, &a1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- mp_rshd(&a1, B);
- if ((res = mp_mod_2d(&a1, DIGIT_BIT * B, &a1)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_copy(a, &a2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- mp_rshd(&a2, B*2);
-
- /* b = b2 * B**2 + b1 * B + b0 */
- if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_copy(b, &b1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- mp_rshd(&b1, B);
- (void)mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
-
- if ((res = mp_copy(b, &b2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- mp_rshd(&b2, B*2);
-
- /* w0 = a0*b0 */
- if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* w4 = a2 * b2 */
- if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
- if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
- if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
-
- /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
- if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* now solve the matrix
-
- 0 0 0 0 1
- 1 2 4 8 16
- 1 1 1 1 1
- 16 8 4 2 1
- 1 0 0 0 0
-
- using 12 subtractions, 4 shifts,
- 2 small divisions and 1 small multiplication
- */
-
- /* r1 - r4 */
- if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r3 - r0 */
- if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r1/2 */
- if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r3/2 */
- if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r2 - r0 - r4 */
- if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r1 - r2 */
- if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r3 - r2 */
- if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r1 - 8r0 */
- if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r3 - 8r4 */
- if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* 3r2 - r1 - r3 */
- if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r1 - r2 */
- if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r3 - r2 */
- if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r1/3 */
- if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r3/3 */
- if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* at this point shift W[n] by B*n */
- if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
-LBL_ERR:
- mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
- &a0, &a1, &a2, &b0, &b1,
- &b2, &tmp1, &tmp2, NULL);
- return res;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_toom_mul.c */
-
-/* Start: bn_mp_toom_sqr.c */
-#include <tommath_private.h>
-#ifdef BN_MP_TOOM_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* squaring using Toom-Cook 3-way algorithm */
-int
-mp_toom_sqr(mp_int *a, mp_int *b)
-{
- mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
- int res, B;
-
- /* init temps */
- if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) {
- return res;
- }
-
- /* B */
- B = a->used / 3;
-
- /* a = a2 * B**2 + a1 * B + a0 */
- if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_copy(a, &a1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- mp_rshd(&a1, B);
- if ((res = mp_mod_2d(&a1, DIGIT_BIT * B, &a1)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_copy(a, &a2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- mp_rshd(&a2, B*2);
-
- /* w0 = a0*a0 */
- if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* w4 = a2 * a2 */
- if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* w1 = (a2 + 2(a1 + 2a0))**2 */
- if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* w3 = (a0 + 2(a1 + 2a2))**2 */
- if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_sqr(&tmp1, &w3)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
-
- /* w2 = (a2 + a1 + a0)**2 */
- if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sqr(&tmp1, &w2)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* now solve the matrix
-
- 0 0 0 0 1
- 1 2 4 8 16
- 1 1 1 1 1
- 16 8 4 2 1
- 1 0 0 0 0
-
- using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
- */
-
- /* r1 - r4 */
- if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r3 - r0 */
- if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r1/2 */
- if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r3/2 */
- if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r2 - r0 - r4 */
- if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r1 - r2 */
- if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r3 - r2 */
- if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r1 - 8r0 */
- if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r3 - 8r4 */
- if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* 3r2 - r1 - r3 */
- if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r1 - r2 */
- if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r3 - r2 */
- if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r1/3 */
- if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
- goto LBL_ERR;
- }
- /* r3/3 */
- if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- /* at this point shift W[n] by B*n */
- if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
- if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
- goto LBL_ERR;
- }
- if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {
- goto LBL_ERR;
- }
-
-LBL_ERR:
- mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
- return res;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_toom_sqr.c */
-
-/* Start: bn_mp_toradix.c */
-#include <tommath_private.h>
-#ifdef BN_MP_TORADIX_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* stores a bignum as a ASCII string in a given radix (2..64) */
-int mp_toradix (mp_int * a, char *str, int radix)
-{
- int res, digs;
- mp_int t;
- mp_digit d;
- char *_s = str;
-
- /* check range of the radix */
- if ((radix < 2) || (radix > 64)) {
- return MP_VAL;
- }
-
- /* quick out if its zero */
- if (mp_iszero(a) == MP_YES) {
- *str++ = '0';
- *str = '\0';
- return MP_OKAY;
- }
-
- if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
- return res;
- }
-
- /* if it is negative output a - */
- if (t.sign == MP_NEG) {
- ++_s;
- *str++ = '-';
- t.sign = MP_ZPOS;
- }
-
- digs = 0;
- while (mp_iszero (&t) == MP_NO) {
- if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
- mp_clear (&t);
- return res;
- }
- *str++ = mp_s_rmap[d];
- ++digs;
- }
-
- /* reverse the digits of the string. In this case _s points
- * to the first digit [exluding the sign] of the number]
- */
- bn_reverse ((unsigned char *)_s, digs);
-
- /* append a NULL so the string is properly terminated */
- *str = '\0';
-
- mp_clear (&t);
- return MP_OKAY;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_toradix.c */
-
-/* Start: bn_mp_toradix_n.c */
-#include <tommath_private.h>
-#ifdef BN_MP_TORADIX_N_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* stores a bignum as a ASCII string in a given radix (2..64)
- *
- * Stores upto maxlen-1 chars and always a NULL byte
- */
-int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
-{
- int res, digs;
- mp_int t;
- mp_digit d;
- char *_s = str;
-
- /* check range of the maxlen, radix */
- if ((maxlen < 2) || (radix < 2) || (radix > 64)) {
- return MP_VAL;
- }
-
- /* quick out if its zero */
- if (mp_iszero(a) == MP_YES) {
- *str++ = '0';
- *str = '\0';
- return MP_OKAY;
- }
-
- if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
- return res;
- }
-
- /* if it is negative output a - */
- if (t.sign == MP_NEG) {
- /* we have to reverse our digits later... but not the - sign!! */
- ++_s;
-
- /* store the flag and mark the number as positive */
- *str++ = '-';
- t.sign = MP_ZPOS;
-
- /* subtract a char */
- --maxlen;
- }
-
- digs = 0;
- while (mp_iszero (&t) == MP_NO) {
- if (--maxlen < 1) {
- /* no more room */
- break;
- }
- if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
- mp_clear (&t);
- return res;
- }
- *str++ = mp_s_rmap[d];
- ++digs;
- }
-
- /* reverse the digits of the string. In this case _s points
- * to the first digit [exluding the sign] of the number
- */
- bn_reverse ((unsigned char *)_s, digs);
-
- /* append a NULL so the string is properly terminated */
- *str = '\0';
-
- mp_clear (&t);
- return MP_OKAY;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_toradix_n.c */
-
-/* Start: bn_mp_unsigned_bin_size.c */
-#include <tommath_private.h>
-#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* get the size for an unsigned equivalent */
-int mp_unsigned_bin_size (mp_int * a)
-{
- int size = mp_count_bits (a);
- return (size / 8) + (((size & 7) != 0) ? 1 : 0);
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_unsigned_bin_size.c */
-
-/* Start: bn_mp_xor.c */
-#include <tommath_private.h>
-#ifdef BN_MP_XOR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* XOR two ints together */
-int
-mp_xor (mp_int * a, mp_int * b, mp_int * c)
-{
- int res, ix, px;
- mp_int t, *x;
-
- if (a->used > b->used) {
- if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
- return res;
- }
- px = b->used;
- x = b;
- } else {
- if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
- return res;
- }
- px = a->used;
- x = a;
- }
-
- for (ix = 0; ix < px; ix++) {
- t.dp[ix] ^= x->dp[ix];
- }
- mp_clamp (&t);
- mp_exch (c, &t);
- mp_clear (&t);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_xor.c */
-
-/* Start: bn_mp_zero.c */
-#include <tommath_private.h>
-#ifdef BN_MP_ZERO_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* set to zero */
-void mp_zero (mp_int * a)
-{
- int n;
- mp_digit *tmp;
-
- a->sign = MP_ZPOS;
- a->used = 0;
-
- tmp = a->dp;
- for (n = 0; n < a->alloc; n++) {
- *tmp++ = 0;
- }
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_mp_zero.c */
-
-/* Start: bn_prime_tab.c */
-#include <tommath_private.h>
-#ifdef BN_PRIME_TAB_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-const mp_digit ltm_prime_tab[] = {
- 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
- 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
- 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
- 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
-#ifndef MP_8BIT
- 0x0083,
- 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
- 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
- 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
- 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
-
- 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
- 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
- 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
- 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
- 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
- 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
- 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
- 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
-
- 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
- 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
- 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
- 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
- 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
- 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
- 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
- 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
-
- 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
- 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
- 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
- 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
- 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
- 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
- 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
- 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
-#endif
-};
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_prime_tab.c */
-
-/* Start: bn_reverse.c */
-#include <tommath_private.h>
-#ifdef BN_REVERSE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* reverse an array, used for radix code */
-void
-bn_reverse (unsigned char *s, int len)
-{
- int ix, iy;
- unsigned char t;
-
- ix = 0;
- iy = len - 1;
- while (ix < iy) {
- t = s[ix];
- s[ix] = s[iy];
- s[iy] = t;
- ++ix;
- --iy;
- }
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_reverse.c */
-
-/* Start: bn_s_mp_add.c */
-#include <tommath_private.h>
-#ifdef BN_S_MP_ADD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* low level addition, based on HAC pp.594, Algorithm 14.7 */
-int
-s_mp_add (mp_int * a, mp_int * b, mp_int * c)
-{
- mp_int *x;
- int olduse, res, min, max;
-
- /* find sizes, we let |a| <= |b| which means we have to sort
- * them. "x" will point to the input with the most digits
- */
- if (a->used > b->used) {
- min = b->used;
- max = a->used;
- x = a;
- } else {
- min = a->used;
- max = b->used;
- x = b;
- }
-
- /* init result */
- if (c->alloc < (max + 1)) {
- if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
- return res;
- }
- }
-
- /* get old used digit count and set new one */
- olduse = c->used;
- c->used = max + 1;
-
- {
- mp_digit u, *tmpa, *tmpb, *tmpc;
- int i;
-
- /* alias for digit pointers */
-
- /* first input */
- tmpa = a->dp;
-
- /* second input */
- tmpb = b->dp;
-
- /* destination */
- tmpc = c->dp;
-
- /* zero the carry */
- u = 0;
- for (i = 0; i < min; i++) {
- /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
- *tmpc = *tmpa++ + *tmpb++ + u;
-
- /* U = carry bit of T[i] */
- u = *tmpc >> ((mp_digit)DIGIT_BIT);
-
- /* take away carry bit from T[i] */
- *tmpc++ &= MP_MASK;
- }
-
- /* now copy higher words if any, that is in A+B
- * if A or B has more digits add those in
- */
- if (min != max) {
- for (; i < max; i++) {
- /* T[i] = X[i] + U */
- *tmpc = x->dp[i] + u;
-
- /* U = carry bit of T[i] */
- u = *tmpc >> ((mp_digit)DIGIT_BIT);
-
- /* take away carry bit from T[i] */
- *tmpc++ &= MP_MASK;
- }
- }
-
- /* add carry */
- *tmpc++ = u;
-
- /* clear digits above oldused */
- for (i = c->used; i < olduse; i++) {
- *tmpc++ = 0;
- }
- }
-
- mp_clamp (c);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_s_mp_add.c */
-
-/* Start: bn_s_mp_exptmod.c */
-#include <tommath_private.h>
-#ifdef BN_S_MP_EXPTMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-#ifdef MP_LOW_MEM
- #define TAB_SIZE 32
-#else
- #define TAB_SIZE 256
-#endif
-
-int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
-{
- mp_int M[TAB_SIZE], res, mu;
- mp_digit buf;
- int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
- int (*redux)(mp_int*,mp_int*,mp_int*);
-
- /* find window size */
- x = mp_count_bits (X);
- if (x <= 7) {
- winsize = 2;
- } else if (x <= 36) {
- winsize = 3;
- } else if (x <= 140) {
- winsize = 4;
- } else if (x <= 450) {
- winsize = 5;
- } else if (x <= 1303) {
- winsize = 6;
- } else if (x <= 3529) {
- winsize = 7;
- } else {
- winsize = 8;
- }
-
-#ifdef MP_LOW_MEM
- if (winsize > 5) {
- winsize = 5;
- }
-#endif
-
- /* init M array */
- /* init first cell */
- if ((err = mp_init(&M[1])) != MP_OKAY) {
- return err;
- }
-
- /* now init the second half of the array */
- for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
- if ((err = mp_init(&M[x])) != MP_OKAY) {
- for (y = 1<<(winsize-1); y < x; y++) {
- mp_clear (&M[y]);
- }
- mp_clear(&M[1]);
- return err;
- }
- }
-
- /* create mu, used for Barrett reduction */
- if ((err = mp_init (&mu)) != MP_OKAY) {
- goto LBL_M;
- }
-
- if (redmode == 0) {
- if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
- goto LBL_MU;
- }
- redux = mp_reduce;
- } else {
- if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
- goto LBL_MU;
- }
- redux = mp_reduce_2k_l;
- }
-
- /* create M table
- *
- * The M table contains powers of the base,
- * e.g. M[x] = G**x mod P
- *
- * The first half of the table is not
- * computed though accept for M[0] and M[1]
- */
- if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
- goto LBL_MU;
- }
-
- /* compute the value at M[1<<(winsize-1)] by squaring
- * M[1] (winsize-1) times
- */
- if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
- goto LBL_MU;
- }
-
- for (x = 0; x < (winsize - 1); x++) {
- /* square it */
- if ((err = mp_sqr (&M[1 << (winsize - 1)],
- &M[1 << (winsize - 1)])) != MP_OKAY) {
- goto LBL_MU;
- }
-
- /* reduce modulo P */
- if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
- goto LBL_MU;
- }
- }
-
- /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
- * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
- */
- for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
- if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
- goto LBL_MU;
- }
- if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
- goto LBL_MU;
- }
- }
-
- /* setup result */
- if ((err = mp_init (&res)) != MP_OKAY) {
- goto LBL_MU;
- }
- mp_set (&res, 1);
-
- /* set initial mode and bit cnt */
- mode = 0;
- bitcnt = 1;
- buf = 0;
- digidx = X->used - 1;
- bitcpy = 0;
- bitbuf = 0;
-
- for (;;) {
- /* grab next digit as required */
- if (--bitcnt == 0) {
- /* if digidx == -1 we are out of digits */
- if (digidx == -1) {
- break;
- }
- /* read next digit and reset the bitcnt */
- buf = X->dp[digidx--];
- bitcnt = (int) DIGIT_BIT;
- }
-
- /* grab the next msb from the exponent */
- y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
- buf <<= (mp_digit)1;
-
- /* if the bit is zero and mode == 0 then we ignore it
- * These represent the leading zero bits before the first 1 bit
- * in the exponent. Technically this opt is not required but it
- * does lower the # of trivial squaring/reductions used
- */
- if ((mode == 0) && (y == 0)) {
- continue;
- }
-
- /* if the bit is zero and mode == 1 then we square */
- if ((mode == 1) && (y == 0)) {
- if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
- goto LBL_RES;
- }
- if ((err = redux (&res, P, &mu)) != MP_OKAY) {
- goto LBL_RES;
- }
- continue;
- }
-
- /* else we add it to the window */
- bitbuf |= (y << (winsize - ++bitcpy));
- mode = 2;
-
- if (bitcpy == winsize) {
- /* ok window is filled so square as required and multiply */
- /* square first */
- for (x = 0; x < winsize; x++) {
- if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
- goto LBL_RES;
- }
- if ((err = redux (&res, P, &mu)) != MP_OKAY) {
- goto LBL_RES;
- }
- }
-
- /* then multiply */
- if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
- goto LBL_RES;
- }
- if ((err = redux (&res, P, &mu)) != MP_OKAY) {
- goto LBL_RES;
- }
-
- /* empty window and reset */
- bitcpy = 0;
- bitbuf = 0;
- mode = 1;
- }
- }
-
- /* if bits remain then square/multiply */
- if ((mode == 2) && (bitcpy > 0)) {
- /* square then multiply if the bit is set */
- for (x = 0; x < bitcpy; x++) {
- if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
- goto LBL_RES;
- }
- if ((err = redux (&res, P, &mu)) != MP_OKAY) {
- goto LBL_RES;
- }
-
- bitbuf <<= 1;
- if ((bitbuf & (1 << winsize)) != 0) {
- /* then multiply */
- if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
- goto LBL_RES;
- }
- if ((err = redux (&res, P, &mu)) != MP_OKAY) {
- goto LBL_RES;
- }
- }
- }
- }
-
- mp_exch (&res, Y);
- err = MP_OKAY;
-LBL_RES:mp_clear (&res);
-LBL_MU:mp_clear (&mu);
-LBL_M:
- mp_clear(&M[1]);
- for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
- mp_clear (&M[x]);
- }
- return err;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_s_mp_exptmod.c */
-
-/* Start: bn_s_mp_mul_digs.c */
-#include <tommath_private.h>
-#ifdef BN_S_MP_MUL_DIGS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* multiplies |a| * |b| and only computes upto digs digits of result
- * HAC pp. 595, Algorithm 14.12 Modified so you can control how
- * many digits of output are created.
- */
-int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
- mp_int t;
- int res, pa, pb, ix, iy;
- mp_digit u;
- mp_word r;
- mp_digit tmpx, *tmpt, *tmpy;
-
- /* can we use the fast multiplier? */
- if (((digs) < MP_WARRAY) &&
- (MIN (a->used, b->used) <
- (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
- return fast_s_mp_mul_digs (a, b, c, digs);
- }
-
- if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
- return res;
- }
- t.used = digs;
-
- /* compute the digits of the product directly */
- pa = a->used;
- for (ix = 0; ix < pa; ix++) {
- /* set the carry to zero */
- u = 0;
-
- /* limit ourselves to making digs digits of output */
- pb = MIN (b->used, digs - ix);
-
- /* setup some aliases */
- /* copy of the digit from a used within the nested loop */
- tmpx = a->dp[ix];
-
- /* an alias for the destination shifted ix places */
- tmpt = t.dp + ix;
-
- /* an alias for the digits of b */
- tmpy = b->dp;
-
- /* compute the columns of the output and propagate the carry */
- for (iy = 0; iy < pb; iy++) {
- /* compute the column as a mp_word */
- r = (mp_word)*tmpt +
- ((mp_word)tmpx * (mp_word)*tmpy++) +
- (mp_word)u;
-
- /* the new column is the lower part of the result */
- *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-
- /* get the carry word from the result */
- u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
- }
- /* set carry if it is placed below digs */
- if ((ix + iy) < digs) {
- *tmpt = u;
- }
- }
-
- mp_clamp (&t);
- mp_exch (&t, c);
-
- mp_clear (&t);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_s_mp_mul_digs.c */
-
-/* Start: bn_s_mp_mul_high_digs.c */
-#include <tommath_private.h>
-#ifdef BN_S_MP_MUL_HIGH_DIGS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* multiplies |a| * |b| and does not compute the lower digs digits
- * [meant to get the higher part of the product]
- */
-int
-s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
- mp_int t;
- int res, pa, pb, ix, iy;
- mp_digit u;
- mp_word r;
- mp_digit tmpx, *tmpt, *tmpy;
-
- /* can we use the fast multiplier? */
-#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
- if (((a->used + b->used + 1) < MP_WARRAY)
- && (MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
- return fast_s_mp_mul_high_digs (a, b, c, digs);
- }
-#endif
-
- if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
- return res;
- }
- t.used = a->used + b->used + 1;
-
- pa = a->used;
- pb = b->used;
- for (ix = 0; ix < pa; ix++) {
- /* clear the carry */
- u = 0;
-
- /* left hand side of A[ix] * B[iy] */
- tmpx = a->dp[ix];
-
- /* alias to the address of where the digits will be stored */
- tmpt = &(t.dp[digs]);
-
- /* alias for where to read the right hand side from */
- tmpy = b->dp + (digs - ix);
-
- for (iy = digs - ix; iy < pb; iy++) {
- /* calculate the double precision result */
- r = (mp_word)*tmpt +
- ((mp_word)tmpx * (mp_word)*tmpy++) +
- (mp_word)u;
-
- /* get the lower part */
- *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-
- /* carry the carry */
- u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
- }
- *tmpt = u;
- }
- mp_clamp (&t);
- mp_exch (&t, c);
- mp_clear (&t);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_s_mp_mul_high_digs.c */
-
-/* Start: bn_s_mp_sqr.c */
-#include <tommath_private.h>
-#ifdef BN_S_MP_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
-int s_mp_sqr (mp_int * a, mp_int * b)
-{
- mp_int t;
- int res, ix, iy, pa;
- mp_word r;
- mp_digit u, tmpx, *tmpt;
-
- pa = a->used;
- if ((res = mp_init_size (&t, (2 * pa) + 1)) != MP_OKAY) {
- return res;
- }
-
- /* default used is maximum possible size */
- t.used = (2 * pa) + 1;
-
- for (ix = 0; ix < pa; ix++) {
- /* first calculate the digit at 2*ix */
- /* calculate double precision result */
- r = (mp_word)t.dp[2*ix] +
- ((mp_word)a->dp[ix] * (mp_word)a->dp[ix]);
-
- /* store lower part in result */
- t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
-
- /* get the carry */
- u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-
- /* left hand side of A[ix] * A[iy] */
- tmpx = a->dp[ix];
-
- /* alias for where to store the results */
- tmpt = t.dp + ((2 * ix) + 1);
-
- for (iy = ix + 1; iy < pa; iy++) {
- /* first calculate the product */
- r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
-
- /* now calculate the double precision result, note we use
- * addition instead of *2 since it's easier to optimize
- */
- r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
-
- /* store lower part */
- *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-
- /* get carry */
- u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
- }
- /* propagate upwards */
- while (u != ((mp_digit) 0)) {
- r = ((mp_word) *tmpt) + ((mp_word) u);
- *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
- u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
- }
- }
-
- mp_clamp (&t);
- mp_exch (&t, b);
- mp_clear (&t);
- return MP_OKAY;
-}
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_s_mp_sqr.c */
-
-/* Start: bn_s_mp_sub.c */
-#include <tommath_private.h>
-#ifdef BN_S_MP_SUB_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
-int
-s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
-{
- int olduse, res, min, max;
-
- /* find sizes */
- min = b->used;
- max = a->used;
-
- /* init result */
- if (c->alloc < max) {
- if ((res = mp_grow (c, max)) != MP_OKAY) {
- return res;
- }
- }
- olduse = c->used;
- c->used = max;
-
- {
- mp_digit u, *tmpa, *tmpb, *tmpc;
- int i;
-
- /* alias for digit pointers */
- tmpa = a->dp;
- tmpb = b->dp;
- tmpc = c->dp;
-
- /* set carry to zero */
- u = 0;
- for (i = 0; i < min; i++) {
- /* T[i] = A[i] - B[i] - U */
- *tmpc = (*tmpa++ - *tmpb++) - u;
-
- /* U = carry bit of T[i]
- * Note this saves performing an AND operation since
- * if a carry does occur it will propagate all the way to the
- * MSB. As a result a single shift is enough to get the carry
- */
- u = *tmpc >> ((mp_digit)((CHAR_BIT * sizeof(mp_digit)) - 1));
-
- /* Clear carry from T[i] */
- *tmpc++ &= MP_MASK;
- }
-
- /* now copy higher words if any, e.g. if A has more digits than B */
- for (; i < max; i++) {
- /* T[i] = A[i] - U */
- *tmpc = *tmpa++ - u;
-
- /* U = carry bit of T[i] */
- u = *tmpc >> ((mp_digit)((CHAR_BIT * sizeof(mp_digit)) - 1));
-
- /* Clear carry from T[i] */
- *tmpc++ &= MP_MASK;
- }
-
- /* clear digits above used (since we may not have grown result above) */
- for (i = c->used; i < olduse; i++) {
- *tmpc++ = 0;
- }
- }
-
- mp_clamp (c);
- return MP_OKAY;
-}
-
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bn_s_mp_sub.c */
-
-/* Start: bncore.c */
-#include <tommath_private.h>
-#ifdef BNCORE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
- */
-
-/* Known optimal configurations
-
- CPU /Compiler /MUL CUTOFF/SQR CUTOFF
--------------------------------------------------------------
- Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-)
- AMD Athlon64 /GCC v3.4.4 / 80/ 120/LTM 0.35
-
-*/
-
-int KARATSUBA_MUL_CUTOFF = 80, /* Min. number of digits before Karatsuba multiplication is used. */
- KARATSUBA_SQR_CUTOFF = 120, /* Min. number of digits before Karatsuba squaring is used. */
-
- TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */
- TOOM_SQR_CUTOFF = 400;
-#endif
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
-
-/* End: bncore.c */
-
-
-/* EOF */