Edit
kc3-lang/libtommath/pre_gen
Tom St Denis
- mpi.c
-
/* File Generated Automatically by gen.pl */ /* Start: bncore.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* configured for a AMD Duron Morgan core with etc/tune.c */ int KARATSUBA_MUL_CUTOFF = 73, /* Min. number of digits before Karatsuba multiplication is used. */ KARATSUBA_SQR_CUTOFF = 121, /* Min. number of digits before Karatsuba squaring is used. */ MONTGOMERY_EXPT_CUTOFF = 128; /* max. number of digits that montgomery reductions will help for */ /* End: bncore.c */ /* Start: bn_fast_mp_invmod.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* computes the modular inverse via binary extended euclidean algorithm, * that is c = 1/a mod b * * Based on mp_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; if ((res = mp_init (&x)) != MP_OKAY) { goto __ERR; } if ((res = mp_init (&y)) != MP_OKAY) { goto __X; } if ((res = mp_init (&u)) != MP_OKAY) { goto __Y; } if ((res = mp_init (&v)) != MP_OKAY) { goto __U; } if ((res = mp_init (&B)) != MP_OKAY) { goto __V; } if ((res = mp_init (&D)) != MP_OKAY) { goto __B; } /* x == modulus, y == value to invert */ if ((res = mp_copy (b, &x)) != MP_OKAY) { goto __D; } if ((res = mp_copy (a, &y)) != MP_OKAY) { goto __D; } if ((res = mp_abs (&y, &y)) != MP_OKAY) { goto __D; } /* 2. [modified] if x,y are both even then return an error! * * That is if gcd(x,y) = 2 * k then obviously there is no inverse. */ if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) { res = MP_VAL; goto __D; } /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ if ((res = mp_copy (&x, &u)) != MP_OKAY) { goto __D; } if ((res = mp_copy (&y, &v)) != MP_OKAY) { goto __D; } mp_set (&D, 1); top: /* 4. while u is even do */ while (mp_iseven (&u) == 1) { /* 4.1 u = u/2 */ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { goto __D; } /* 4.2 if A or B is odd then */ if (mp_iseven (&B) == 0) { if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { goto __D; } } /* A = A/2, B = B/2 */ if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { goto __D; } } /* 5. while v is even do */ while (mp_iseven (&v) == 1) { /* 5.1 v = v/2 */ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { goto __D; } /* 5.2 if C,D are even then */ if (mp_iseven (&D) == 0) { /* C = (C+y)/2, D = (D-x)/2 */ if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { goto __D; } } /* C = C/2, D = D/2 */ if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { goto __D; } } /* 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 __D; } if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { goto __D; } } else { /* v - v - u, C = C - A, D = D - B */ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { goto __D; } if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { goto __D; } } /* if not zero goto step 4 */ if (mp_iszero (&u) == 0) { 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 __D; } /* b is now the inverse */ neg = a->sign; while (D.sign == MP_NEG) { if ((res = mp_add (&D, b, &D)) != MP_OKAY) { goto __D; } } mp_exch (&D, c); c->sign = neg; res = MP_OKAY; __D:mp_clear (&D); __B:mp_clear (&B); __V:mp_clear (&v); __U:mp_clear (&u); __Y:mp_clear (&y); __X:mp_clear (&x); __ERR: return res; } /* End: bn_fast_mp_invmod.c */ /* Start: bn_fast_mp_montgomery_reduce.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* computes xR^-1 == x (mod N) via Montgomery Reduction * * This is an optimized implementation of mp_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 * a, mp_int * m, mp_digit mp) { int ix, res, olduse; mp_word W[512]; /* get old used count */ olduse = a->used; /* grow a as required */ if (a->alloc < m->used + 1) { if ((res = mp_grow (a, m->used + 1)) != MP_OKAY) { return res; } } { register mp_word *_W; register mp_digit *tmpa; _W = W; tmpa = a->dp; /* copy the digits of a */ for (ix = 0; ix < a->used; ix++) { *_W++ = *tmpa++; } /* zero the high words */ for (; ix < m->used * 2 + 1; ix++) { *_W++ = 0; } } for (ix = 0; ix < m->used; ix++) { /* ui = 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) */ register mp_digit ui; ui = (((mp_digit) (W[ix] & MP_MASK)) * mp) & MP_MASK; /* a = a + ui * 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 */ { register int iy; register mp_digit *tmpx; register mp_word *_W; /* alias for the digits of the modulus */ tmpx = m->dp; /* Alias for the columns set by an offset of ix */ _W = W + ix; /* inner loop */ for (iy = 0; iy < m->used; iy++) { *_W++ += ((mp_word) ui) * ((mp_word) * tmpx++); } } /* now fix carry for next digit, W[ix+1] */ W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT); } { register mp_digit *tmpa; register mp_word *_W, *_W1; /* nox fix rest of carries */ _W1 = W + ix; _W = W + ++ix; for (; ix <= m->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 */ tmpa = a->dp; _W = W + m->used; for (ix = 0; ix < m->used + 1; ix++) { *tmpa++ = *_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++) { *tmpa++ = 0; } } /* set the max used and clamp */ a->used = m->used + 1; mp_clamp (a); /* if A >= m then A = A - m */ if (mp_cmp_mag (a, m) != MP_LT) { return s_mp_sub (a, m, a); } return MP_OKAY; } /* End: bn_fast_mp_montgomery_reduce.c */ /* Start: bn_fast_s_mp_mul_digs.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; mp_word W[512]; /* grow the destination as required */ if (c->alloc < digs) { if ((res = mp_grow (c, digs)) != MP_OKAY) { return res; } } /* clear temp buf (the columns) */ memset (W, 0, sizeof (mp_word) * digs); /* calculate the columns */ pa = a->used; for (ix = 0; ix < pa; ix++) { /* this multiplier has been modified to allow you to control how many digits * of output are produced. So at most we want to make upto "digs" digits * of output. * * this adds products to distinct columns (at ix+iy) of W * note that each step through the loop is not dependent on * the previous which means the compiler can easily unroll * the loop without scheduling problems */ { register mp_digit tmpx, *tmpy; register mp_word *_W; register int iy, pb; /* alias for the the word on the left e.g. A[ix] * A[iy] */ tmpx = a->dp[ix]; /* alias for the right side */ tmpy = b->dp; /* alias for the columns, each step through the loop adds a new term to each column */ _W = W + ix; /* the number of digits is limited by their placement. E.g. we avoid multiplying digits that will end up above the # of digits of precision requested */ pb = MIN (b->used, digs - ix); for (iy = 0; iy < pb; iy++) { *_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++); } } } /* setup dest */ olduse = c->used; c->used = digs; { register mp_digit *tmpc; /* At this point W[] contains the sums of each column. To get the * correct result we must take the extra bits from each column and * carry them down * * Note that while this adds extra code to the multiplier it saves time * since the carry propagation is removed from the above nested loop. * This has the effect of reducing the work from N*(N+N*c)==N^2 + c*N^2 to * N^2 + N*c where c is the cost of the shifting. On very small numbers * this is slower but on most cryptographic size numbers it is faster. */ tmpc = c->dp; for (ix = 1; ix < digs; ix++) { W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT)); *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); } *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK)); /* clear unused */ for (; ix < olduse; ix++) { *tmpc++ = 0; } } mp_clamp (c); return MP_OKAY; } /* End: bn_fast_s_mp_mul_digs.c */ /* Start: bn_fast_s_mp_mul_high_digs.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* this is a modified version of fast_s_mp_mul_digs that only produces * output digits *above* digs. See the comments for fast_s_mp_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 oldused, newused, res, pa, pb, ix; mp_word W[512]; /* calculate size of product and allocate more space if required */ newused = a->used + b->used + 1; if (c->alloc < newused) { if ((res = mp_grow (c, newused)) != MP_OKAY) { return res; } } /* like the other comba method we compute the columns first */ pa = a->used; pb = b->used; memset (W + digs, 0, (pa + pb + 1 - digs) * sizeof (mp_word)); for (ix = 0; ix < pa; ix++) { { register mp_digit tmpx, *tmpy; register int iy; register mp_word *_W; /* work todo, that is we only calculate digits that are at "digs" or above */ iy = digs - ix; /* copy of word on the left of A[ix] * B[iy] */ tmpx = a->dp[ix]; /* alias for right side */ tmpy = b->dp + iy; /* alias for the columns of output. Offset to be equal to or above the * smallest digit place requested */ _W = &(W[digs]); /* compute column products for digits above the minimum */ for (; iy < pb; iy++) { *_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++); } } } /* setup dest */ oldused = c->used; c->used = newused; /* now convert the array W downto what we need */ for (ix = digs + 1; ix < newused; ix++) { W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT)); c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); } c->dp[(pa + pb + 1) - 1] = (mp_digit) (W[(pa + pb + 1) - 1] & ((mp_word) MP_MASK)); for (; ix < oldused; ix++) { c->dp[ix] = 0; } mp_clamp (c); return MP_OKAY; } /* End: bn_fast_s_mp_mul_high_digs.c */ /* Start: bn_fast_s_mp_sqr.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* fast squaring * * This is the comba method where the columns of the product are computed first * then the carries are computed. This has the effect of making a very simple * inner loop that is executed the most * * W2 represents the outer products and W the inner. * * A further optimizations is made because the inner products are of the form * "A * B * 2". The *2 part does not need to be computed until the end which is * good because 64-bit shifts are slow! * * Based on Algorithm 14.16 on pp.597 of HAC. * */ int fast_s_mp_sqr (mp_int * a, mp_int * b) { int olduse, newused, res, ix, pa; mp_word W2[512], W[512]; /* calculate size of product and allocate as required */ pa = a->used; newused = pa + pa + 1; if (b->alloc < newused) { if ((res = mp_grow (b, newused)) != MP_OKAY) { return res; } } /* zero temp buffer (columns) * Note that there are two buffers. Since squaring requires * a outter and inner product and the inner product requires * computing a product and doubling it (a relatively expensive * op to perform n^2 times if you don't have to) the inner and * outer products are computed in different buffers. This way * the inner product can be doubled using n doublings instead of * n^2 */ memset (W, 0, newused * sizeof (mp_word)); memset (W2, 0, newused * sizeof (mp_word)); /* note optimization * values in W2 are only written in even locations which means * we can collapse the array to 256 words [and fixup the memset above] * provided we also fix up the summations below. Ideally * the fixup loop should be unrolled twice to handle the even/odd * cases, and then a final step to handle odd cases [e.g. newused == odd] * * This will not only save ~8*256 = 2KB of stack but lower the number of * operations required to finally fix up the columns */ /* This computes the inner product. To simplify the inner N^2 loop * the multiplication by two is done afterwards in the N loop. */ for (ix = 0; ix < pa; ix++) { /* compute the outer product * * Note that every outer product is computed * for a particular column only once which means that * there is no need todo a double precision addition */ W2[ix + ix] = ((mp_word) a->dp[ix]) * ((mp_word) a->dp[ix]); { register mp_digit tmpx, *tmpy; register mp_word *_W; register int iy; /* copy of left side */ tmpx = a->dp[ix]; /* alias for right side */ tmpy = a->dp + (ix + 1); /* the column to store the result in */ _W = W + (ix + ix + 1); /* inner products */ for (iy = ix + 1; iy < pa; iy++) { *_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++); } } } /* setup dest */ olduse = b->used; b->used = newused; /* double first value, since the inner products are half of what they should be */ W[0] += W[0] + W2[0]; /* now compute digits */ { register mp_digit *tmpb; tmpb = b->dp; for (ix = 1; ix < newused; ix++) { /* double/add next digit */ W[ix] += W[ix] + W2[ix]; W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT)); *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); } *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK)); /* clear high */ for (; ix < olduse; ix++) { *tmpb++ = 0; } } mp_clamp (b); return MP_OKAY; } /* End: bn_fast_s_mp_sqr.c */ /* Start: bn_mp_2expt.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; mp_zero (a); if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) { return res; } a->used = b / DIGIT_BIT + 1; a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT); return MP_OKAY; } /* End: bn_mp_2expt.c */ /* Start: bn_mp_abs.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* b = |a| * * Simple function copies the input and fixes the sign to positive */ int mp_abs (mp_int * a, mp_int * b) { int res; if ((res = mp_copy (a, b)) != MP_OKAY) { return res; } b->sign = MP_ZPOS; return MP_OKAY; } /* End: bn_mp_abs.c */ /* Start: bn_mp_add.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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 four cases */ if (sa == MP_ZPOS && sb == MP_ZPOS) { /* both positive */ res = s_mp_add (a, b, c); c->sign = MP_ZPOS; } else if (sa == MP_ZPOS && sb == MP_NEG) { /* a + -b == a - b, but if b>a then we do it as -(b-a) */ if (mp_cmp_mag (a, b) == MP_LT) { res = s_mp_sub (b, a, c); c->sign = MP_NEG; } else { res = s_mp_sub (a, b, c); c->sign = MP_ZPOS; } } else if (sa == MP_NEG && sb == MP_ZPOS) { /* -a + b == b - a, but if a>b then we do it as -(a-b) */ if (mp_cmp_mag (a, b) == MP_GT) { res = s_mp_sub (a, b, c); c->sign = MP_NEG; } else { res = s_mp_sub (b, a, c); c->sign = MP_ZPOS; } } else { /* -a + -b == -(a + b) */ res = s_mp_add (a, b, c); c->sign = MP_NEG; } return res; } /* End: bn_mp_add.c */ /* Start: bn_mp_addmod.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; } /* End: bn_mp_addmod.c */ /* Start: bn_mp_add_d.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* single digit addition */ int mp_add_d (mp_int * a, mp_digit b, mp_int * c) { mp_int t; int res; if ((res = mp_init (&t)) != MP_OKAY) { return res; } mp_set (&t, b); res = mp_add (a, &t, c); mp_clear (&t); return res; } /* End: bn_mp_add_d.c */ /* Start: bn_mp_and.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; } /* End: bn_mp_and.c */ /* Start: bn_mp_clamp.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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) { while (a->used > 0 && a->dp[a->used - 1] == 0) --(a->used); if (a->used == 0) { a->sign = MP_ZPOS; } } /* End: bn_mp_clamp.c */ /* Start: bn_mp_clear.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* clear one (frees) */ void mp_clear (mp_int * a) { if (a->dp != NULL) { /* first zero the digits */ memset (a->dp, 0, sizeof (mp_digit) * a->used); /* free ram */ free (a->dp); /* reset members to make debugging easier */ a->dp = NULL; a->alloc = a->used = 0; } } /* End: bn_mp_clear.c */ /* Start: bn_mp_cmp.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* compare two ints (signed)*/ int mp_cmp (mp_int * a, mp_int * b) { /* compare based on sign */ if (a->sign == MP_NEG && b->sign == MP_ZPOS) { return MP_LT; } else if (a->sign == MP_ZPOS && b->sign == MP_NEG) { return MP_GT; } return mp_cmp_mag (a, b); } /* End: bn_mp_cmp.c */ /* Start: bn_mp_cmp_d.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* compare a digit */ int mp_cmp_d (mp_int * a, mp_digit b) { if (a->sign == MP_NEG) { return MP_LT; } if (a->used > 1) { return MP_GT; } if (a->dp[0] > b) { return MP_GT; } else if (a->dp[0] < b) { return MP_LT; } else { return MP_EQ; } } /* End: bn_mp_cmp_d.c */ /* Start: bn_mp_cmp_mag.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* compare maginitude of two ints (unsigned) */ int mp_cmp_mag (mp_int * a, mp_int * b) { int n; /* compare based on # of non-zero digits */ if (a->used > b->used) { return MP_GT; } else if (a->used < b->used) { return MP_LT; } /* compare based on digits */ for (n = a->used - 1; n >= 0; n--) { if (a->dp[n] > b->dp[n]) { return MP_GT; } else if (a->dp[n] < b->dp[n]) { return MP_LT; } } return MP_EQ; } /* End: bn_mp_cmp_mag.c */ /* Start: bn_mp_copy.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* copy, b = a */ int mp_copy (mp_int * a, mp_int * b) { int res, n; /* if dst == src do nothing */ if (a == b || a->dp == b->dp) { return MP_OKAY; } /* grow dest */ if ((res = mp_grow (b, a->used)) != MP_OKAY) { return res; } /* zero b and copy the parameters over */ b->used = a->used; b->sign = a->sign; { register mp_digit *tmpa, *tmpb; tmpa = a->dp; tmpb = b->dp; /* copy all the digits */ for (n = 0; n < a->used; n++) { *tmpb++ = *tmpa++; } /* clear high digits */ for (; n < b->alloc; n++) { *tmpb++ = 0; } } return MP_OKAY; } /* End: bn_mp_copy.c */ /* Start: bn_mp_count_bits.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* returns the number of bits in an int */ int mp_count_bits (mp_int * a) { int r; mp_digit q; if (a->used == 0) { return 0; } r = (a->used - 1) * DIGIT_BIT; q = a->dp[a->used - 1]; while (q > ((mp_digit) 0)) { ++r; q >>= ((mp_digit) 1); } return r; } /* End: bn_mp_count_bits.c */ /* Start: bn_mp_div.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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) == 1) { 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 __Q; } if ((res = mp_init (&t2)) != MP_OKAY) { goto __T1; } if ((res = mp_init_copy (&x, a)) != MP_OKAY) { goto __T2; } if ((res = mp_init_copy (&y, b)) != MP_OKAY) { goto __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 = 0; while ((y.dp[y.used - 1] & (((mp_digit) 1) << (DIGIT_BIT - 1))) == ((mp_digit) 0)) { ++norm; if ((res = mp_mul_2 (&x, &x)) != MP_OKAY) { goto __Y; } if ((res = mp_mul_2 (&y, &y)) != MP_OKAY) { goto __Y; } } /* 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; /* step 2. 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 __Y; } while (mp_cmp (&x, &y) != MP_LT) { ++(q.dp[n - t]); if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) { goto __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] = ((1UL << DIGIT_BIT) - 1UL); } 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)); } /* step 3.2 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 __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 (&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 __Y; } if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { goto __Y; } if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) { goto __Y; } /* step 3.4 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 __Y; } if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { goto __Y; } if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) { goto __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 = a->sign; if (c != NULL) { mp_clamp (&q); mp_exch (&q, c); c->sign = neg; } if (d != NULL) { mp_div_2d (&x, norm, &x, NULL); mp_exch (&x, d); } res = MP_OKAY; __Y:mp_clear (&y); __X:mp_clear (&x); __T2:mp_clear (&t2); __T1:mp_clear (&t1); __Q:mp_clear (&q); return res; } /* End: bn_mp_div.c */ /* Start: bn_mp_div_2.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; { register mp_digit r, rr, *tmpa, *tmpb; tmpa = a->dp + b->used - 1; tmpb = b->dp + b->used - 1; r = 0; for (x = b->used - 1; x >= 0; x--) { rr = *tmpa & 1; *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1)); r = rr; } tmpb = b->dp + b->used; for (x = b->used; x < oldused; x++) { *tmpb++ = 0; } } b->sign = a->sign; mp_clamp (b); return MP_OKAY; } /* End: bn_mp_div_2.c */ /* Start: bn_mp_div_2d.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* shift right by a certain bit count (store quotient in c, 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; mp_int t; /* 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; } if ((res = mp_init (&t)) != MP_OKAY) { return res; } /* get the remainder */ if (d != NULL) { if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) { mp_clear (&t); return res; } } /* copy */ if ((res = mp_copy (a, c)) != MP_OKAY) { mp_clear (&t); return res; } /* shift by as many digits in the bit count */ if (b >= DIGIT_BIT) { mp_rshd (c, b / DIGIT_BIT); } /* shift any bit count < DIGIT_BIT */ D = (mp_digit) (b % DIGIT_BIT); if (D != 0) { r = 0; for (x = c->used - 1; x >= 0; x--) { /* get the lower bits of this word in a temp */ rr = c->dp[x] & ((mp_digit) ((1U << D) - 1U)); /* shift the current word and mix in the carry bits from the previous word */ c->dp[x] = (c->dp[x] >> D) | (r << (DIGIT_BIT - D)); /* set the carry to the carry bits of the current word found above */ r = rr; } } mp_clamp (c); res = MP_OKAY; if (d != NULL) { mp_exch (&t, d); } mp_clear (&t); return MP_OKAY; } /* End: bn_mp_div_2d.c */ /* Start: bn_mp_div_d.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* single digit division */ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d) { mp_int t, t2; int res; if ((res = mp_init (&t)) != MP_OKAY) { return res; } if ((res = mp_init (&t2)) != MP_OKAY) { mp_clear (&t); return res; } mp_set (&t, b); res = mp_div (a, &t, c, &t2); if (d != NULL) { *d = t2.dp[0]; } mp_clear (&t); mp_clear (&t2); return res; } /* End: bn_mp_div_d.c */ /* Start: bn_mp_dr_reduce.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* reduce "a" in place modulo "b" using the Diminished Radix algorithm. * * Based on algorithm from the paper * * "Generating Efficient Primes for Discrete Log Cryptosystems" * Chae Hoon Lim, Pil Loong Lee, * POSTECH Information Research Laboratories * * The modulus must be of a special format [see manual] */ int mp_dr_reduce (mp_int * a, mp_int * b, mp_digit mp) { int err, i, j, k; mp_word r; mp_digit mu, *tmpj, *tmpi; /* k = digits in modulus */ k = b->used; /* ensure that "a" has at least 2k digits */ if (a->alloc < k + k) { if ((err = mp_grow (a, k + k)) != MP_OKAY) { return err; } } /* alias for a->dp[i] */ tmpi = a->dp + k + k - 1; /* for (i = 2k - 1; i >= k; i = i - 1) * * This is the main loop of the reduction. Note that at the end * the words above position k are not zeroed as expected. The end * result is that the digits from 0 to k-1 are the residue. So * we have to clear those afterwards. */ for (i = k + k - 1; i >= k; i = i - 1) { /* x[i - 1 : i - k] += x[i]*mp */ /* x[i] * mp */ r = ((mp_word) *tmpi--) * ((mp_word) mp); /* now add r to x[i-1:i-k] * * First add it to the first digit x[i-k] then form the carry * then enter the main loop */ j = i - k; /* alias for a->dp[j] */ tmpj = a->dp + j; /* add digit */ *tmpj += (mp_digit)(r & MP_MASK); /* this is the carry */ mu = (r >> ((mp_word) DIGIT_BIT)) + (*tmpj >> DIGIT_BIT); /* clear carry from a->dp[j] */ *tmpj++ &= MP_MASK; /* now add rest of the digits * * Note this is basically a simple single digit addition to * a larger multiple digit number. This is optimized somewhat * because the propagation of carries is not likely to move * more than a few digits. * */ for (++j; mu != 0 && j <= (i - 1); ++j) { *tmpj += mu; mu = *tmpj >> DIGIT_BIT; *tmpj++ &= MP_MASK; } /* if final carry */ if (mu != 0) { /* add mp to this to correct */ j = i - k; tmpj = a->dp + j; *tmpj += mp; mu = *tmpj >> DIGIT_BIT; *tmpj++ &= MP_MASK; /* now handle carries */ for (++j; mu != 0 && j <= (i - 1); j++) { *tmpj += mu; mu = *tmpj >> DIGIT_BIT; *tmpj++ &= MP_MASK; } } } /* zero words above k */ tmpi = a->dp + k; for (i = k; i < a->used; i++) { *tmpi++ = 0; } /* clamp, sub and return */ mp_clamp (a); if (mp_cmp_mag (a, b) != MP_LT) { return s_mp_sub (a, b, a); } return MP_OKAY; } /* 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; } for (ix = 1; ix < a->used; ix++) { if (a->dp[ix] != MP_MASK) { return 0; } } return 1; } /* determines the setup value */ void mp_dr_setup(mp_int *a, mp_digit *d) { *d = (1 << DIGIT_BIT) - a->dp[0]; } /* End: bn_mp_dr_reduce.c */ /* Start: bn_mp_exch.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> void mp_exch (mp_int * a, mp_int * b) { mp_int t; t = *a; *a = *b; *b = t; } /* End: bn_mp_exch.c */ /* Start: bn_mp_exptmod.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> static int f_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y); /* 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; dr = mp_dr_is_modulus(P); /* if the modulus is odd use the fast method */ if (((mp_isodd (P) == 1 && P->used < MONTGOMERY_EXPT_CUTOFF) || dr == 1) && P->used > 4) { return mp_exptmod_fast (G, X, P, Y, dr); } else { return f_mp_exptmod (G, X, P, Y); } } static int f_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y) { mp_int M[256], res, mu; mp_digit buf; int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; /* 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; } /* init G array */ for (x = 0; x < (1 << winsize); x++) { if ((err = mp_init_size (&M[x], 1)) != MP_OKAY) { for (y = 0; y < x; y++) { mp_clear (&M[y]); } return err; } } /* create mu, used for Barrett reduction */ if ((err = mp_init (&mu)) != MP_OKAY) { goto __M; } if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) { goto __MU; } /* create M table * * The M table contains powers of the input 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 __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 __MU; } for (x = 0; x < (winsize - 1); x++) { if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) { goto __MU; } if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) { goto __MU; } } /* 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 __MU; } if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) { goto __MU; } } /* setup result */ if ((err = mp_init (&res)) != MP_OKAY) { goto __MU; } mp_set (&res, 1); /* set initial mode and bit cnt */ mode = 0; bitcnt = 0; buf = 0; digidx = X->used - 1; bitcpy = bitbuf = 0; bitcnt = 1; for (;;) { /* grab next digit as required */ if (--bitcnt == 0) { if (digidx == -1) { break; } buf = X->dp[digidx--]; bitcnt = (int) DIGIT_BIT; } /* grab the next msb from the exponent */ y = (buf >> (DIGIT_BIT - 1)) & 1; buf <<= 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 __RES; } if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { goto __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 multiply */ /* square first */ for (x = 0; x < winsize; x++) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { goto __RES; } if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { goto __RES; } } /* then multiply */ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) { goto __MU; } if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { goto __MU; } /* empty window and reset */ bitcpy = 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 __RES; } if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { goto __RES; } bitbuf <<= 1; if ((bitbuf & (1 << winsize)) != 0) { /* then multiply */ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) { goto __RES; } if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { goto __RES; } } } } mp_exch (&res, Y); err = MP_OKAY; __RES:mp_clear (&res); __MU:mp_clear (&mu); __M: for (x = 0; x < (1 << winsize); x++) { mp_clear (&M[x]); } return err; } /* End: bn_mp_exptmod.c */ /* Start: bn_mp_exptmod_fast.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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 reduction */ int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) { mp_int M[256], res; mp_digit buf, mp; int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; 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; } /* init G array */ for (x = 0; x < (1 << winsize); x++) { if ((err = mp_init (&M[x])) != MP_OKAY) { for (y = 0; y < x; y++) { mp_clear (&M[y]); } return err; } } if (redmode == 0) { /* now setup montgomery */ if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) { goto __M; } redux = mp_montgomery_reduce; } else { /* setup DR reduction */ mp_dr_setup(P, &mp); redux = mp_dr_reduce; } /* setup result */ if ((err = mp_init (&res)) != MP_OKAY) { goto __RES; } /* create M table * * The M table contains powers of the input 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 (redmode == 0) { /* now we need R mod m */ if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) { goto __RES; } /* now set M[1] to G * R mod m */ if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) { goto __RES; } } else { mp_set(&res, 1); if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) { goto __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 __RES; } for (x = 0; x < (winsize - 1); x++) { if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) { goto __RES; } if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) { goto __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 __RES; } if ((err = redux (&M[x], P, mp)) != MP_OKAY) { goto __RES; } } /* set initial mode and bit cnt */ mode = 0; bitcnt = 0; buf = 0; digidx = X->used - 1; bitcpy = bitbuf = 0; bitcnt = 1; for (;;) { /* grab next digit as required */ if (--bitcnt == 0) { if (digidx == -1) { break; } buf = X->dp[digidx--]; bitcnt = (int) DIGIT_BIT; } /* grab the next msb from the exponent */ y = (buf >> (DIGIT_BIT - 1)) & 1; buf <<= 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 __RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { goto __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 multiply */ /* square first */ for (x = 0; x < winsize; x++) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { goto __RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { goto __RES; } } /* then multiply */ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) { goto __RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { goto __RES; } /* empty window and reset */ bitcpy = 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 __RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { goto __RES; } bitbuf <<= 1; if ((bitbuf & (1 << winsize)) != 0) { /* then multiply */ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) { goto __RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { goto __RES; } } } } if (redmode == 0) { /* fixup result */ if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) { goto __RES; } } mp_exch (&res, Y); err = MP_OKAY; __RES:mp_clear (&res); __M: for (x = 0; x < (1 << winsize); x++) { mp_clear (&M[x]); } return err; } /* End: bn_mp_exptmod_fast.c */ /* Start: bn_mp_expt_d.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> int mp_expt_d (mp_int * a, mp_digit b, mp_int * c) { int res, x; mp_int g; if ((res = mp_init_copy (&g, a)) != MP_OKAY) { return res; } /* set initial result */ mp_set (c, 1); for (x = 0; x < (int) DIGIT_BIT; x++) { if ((res = mp_sqr (c, c)) != MP_OKAY) { mp_clear (&g); return res; } if ((b & (mp_digit) (1 << (DIGIT_BIT - 1))) != 0) { if ((res = mp_mul (c, &g, c)) != MP_OKAY) { mp_clear (&g); return res; } } b <<= 1; } mp_clear (&g); return MP_OKAY; } /* End: bn_mp_expt_d.c */ /* Start: bn_mp_gcd.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* Greatest Common Divisor using the binary method [Algorithm B, page 338, vol2 of TAOCP] */ int mp_gcd (mp_int * a, mp_int * b, mp_int * c) { mp_int u, v, t; int k, res, neg; /* either zero than gcd is the largest */ if (mp_iszero (a) == 1 && mp_iszero (b) == 0) { return mp_copy (b, c); } if (mp_iszero (a) == 0 && mp_iszero (b) == 1) { return mp_copy (a, c); } if (mp_iszero (a) == 1 && mp_iszero (b) == 1) { mp_set (c, 1); return MP_OKAY; } /* if both are negative they share (-1) as a common divisor */ neg = (a->sign == b->sign) ? a->sign : MP_ZPOS; if ((res = mp_init_copy (&u, a)) != MP_OKAY) { return res; } if ((res = mp_init_copy (&v, b)) != MP_OKAY) { goto __U; } /* must be positive for the remainder of the algorithm */ u.sign = v.sign = MP_ZPOS; if ((res = mp_init (&t)) != MP_OKAY) { goto __V; } /* B1. Find power of two */ k = 0; while ((u.dp[0] & 1) == 0 && (v.dp[0] & 1) == 0) { ++k; if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { goto __T; } if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { goto __T; } } /* B2. Initialize */ if ((u.dp[0] & 1) == 1) { if ((res = mp_copy (&v, &t)) != MP_OKAY) { goto __T; } t.sign = MP_NEG; } else { if ((res = mp_copy (&u, &t)) != MP_OKAY) { goto __T; } } do { /* B3 (and B4). Halve t, if even */ while (t.used != 0 && (t.dp[0] & 1) == 0) { if ((res = mp_div_2 (&t, &t)) != MP_OKAY) { goto __T; } } /* B5. if t>0 then u=t otherwise v=-t */ if (t.used != 0 && t.sign != MP_NEG) { if ((res = mp_copy (&t, &u)) != MP_OKAY) { goto __T; } } else { if ((res = mp_copy (&t, &v)) != MP_OKAY) { goto __T; } v.sign = (v.sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; } /* B6. t = u - v, if t != 0 loop otherwise terminate */ if ((res = mp_sub (&u, &v, &t)) != MP_OKAY) { goto __T; } } while (t.used != 0); if ((res = mp_mul_2d (&u, k, &u)) != MP_OKAY) { goto __T; } mp_exch (&u, c); c->sign = neg; res = MP_OKAY; __T:mp_clear (&t); __V:mp_clear (&u); __U:mp_clear (&v); return res; } /* End: bn_mp_gcd.c */ /* Start: bn_mp_grow.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* grow as required */ int mp_grow (mp_int * a, int size) { int i, n; /* if the alloc size is smaller alloc more ram */ if (a->alloc < size) { size += (MP_PREC * 2) - (size & (MP_PREC - 1)); /* ensure there are always at least MP_PREC digits extra on top */ a->dp = OPT_CAST realloc (a->dp, sizeof (mp_digit) * size); if (a->dp == NULL) { return MP_MEM; } n = a->alloc; a->alloc = size; for (i = n; i < a->alloc; i++) { a->dp[i] = 0; } } return MP_OKAY; } /* End: bn_mp_grow.c */ /* Start: bn_mp_init.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* init a new bigint */ int mp_init (mp_int * a) { /* allocate ram required and clear it */ a->dp = OPT_CAST calloc (sizeof (mp_digit), MP_PREC); if (a->dp == NULL) { return MP_MEM; } /* set the used to zero, allocated digit to the default precision * and sign to positive */ a->used = 0; a->alloc = MP_PREC; a->sign = MP_ZPOS; return MP_OKAY; } /* End: bn_mp_init.c */ /* Start: bn_mp_init_copy.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* creates "a" then copies b into it */ int mp_init_copy (mp_int * a, mp_int * b) { int res; if ((res = mp_init (a)) != MP_OKAY) { return res; } return mp_copy (b, a); } /* End: bn_mp_init_copy.c */ /* Start: bn_mp_init_size.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* init a mp_init and grow it to a given size */ int mp_init_size (mp_int * a, int size) { /* pad up so there are at least 16 zero digits */ size += (MP_PREC * 2) - (size & (MP_PREC - 1)); /* ensure there are always at least 16 digits extra on top */ a->dp = OPT_CAST calloc (sizeof (mp_digit), size); if (a->dp == NULL) { return MP_MEM; } a->used = 0; a->alloc = size; a->sign = MP_ZPOS; return MP_OKAY; } /* End: bn_mp_init_size.c */ /* Start: bn_mp_invmod.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> int mp_invmod (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) { return MP_VAL; } /* if the modulus is odd we can use a faster routine instead */ if (mp_iseven (b) == 0) { return fast_mp_invmod (a, b, c); } if ((res = mp_init (&x)) != MP_OKAY) { goto __ERR; } if ((res = mp_init (&y)) != MP_OKAY) { goto __X; } if ((res = mp_init (&u)) != MP_OKAY) { goto __Y; } if ((res = mp_init (&v)) != MP_OKAY) { goto __U; } if ((res = mp_init (&A)) != MP_OKAY) { goto __V; } if ((res = mp_init (&B)) != MP_OKAY) { goto __A; } if ((res = mp_init (&C)) != MP_OKAY) { goto __B; } if ((res = mp_init (&D)) != MP_OKAY) { goto __C; } /* x = a, y = b */ if ((res = mp_copy (a, &x)) != MP_OKAY) { goto __D; } if ((res = mp_copy (b, &y)) != MP_OKAY) { goto __D; } if ((res = mp_abs (&x, &x)) != MP_OKAY) { goto __D; } /* 2. [modified] if x,y are both even then return an error! */ if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) { res = MP_VAL; goto __D; } /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ if ((res = mp_copy (&x, &u)) != MP_OKAY) { goto __D; } if ((res = mp_copy (&y, &v)) != MP_OKAY) { goto __D; } mp_set (&A, 1); mp_set (&D, 1); top: /* 4. while u is even do */ while (mp_iseven (&u) == 1) { /* 4.1 u = u/2 */ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { goto __D; } /* 4.2 if A or B is odd then */ if (mp_iseven (&A) == 0 || mp_iseven (&B) == 0) { /* A = (A+y)/2, B = (B-x)/2 */ if ((res = mp_add (&A, &y, &A)) != MP_OKAY) { goto __D; } if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { goto __D; } } /* A = A/2, B = B/2 */ if ((res = mp_div_2 (&A, &A)) != MP_OKAY) { goto __D; } if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { goto __D; } } /* 5. while v is even do */ while (mp_iseven (&v) == 1) { /* 5.1 v = v/2 */ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { goto __D; } /* 5.2 if C,D are even then */ if (mp_iseven (&C) == 0 || mp_iseven (&D) == 0) { /* C = (C+y)/2, D = (D-x)/2 */ if ((res = mp_add (&C, &y, &C)) != MP_OKAY) { goto __D; } if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { goto __D; } } /* C = C/2, D = D/2 */ if ((res = mp_div_2 (&C, &C)) != MP_OKAY) { goto __D; } if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { goto __D; } } /* 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 __D; } if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) { goto __D; } if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { goto __D; } } else { /* v - v - u, C = C - A, D = D - B */ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { goto __D; } if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) { goto __D; } if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { goto __D; } } /* if not zero goto step 4 */ if (mp_iszero (&u) == 0) 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 __D; } /* a is now the inverse */ mp_exch (&C, c); res = MP_OKAY; __D:mp_clear (&D); __C:mp_clear (&C); __B:mp_clear (&B); __A:mp_clear (&A); __V:mp_clear (&v); __U:mp_clear (&u); __Y:mp_clear (&y); __X:mp_clear (&x); __ERR: return res; } /* End: bn_mp_invmod.c */ /* Start: bn_mp_jacobi.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* computes the jacobi c = (a | n) (or Legendre if b is prime) * HAC pp. 73 Algorithm 2.149 */ int mp_jacobi (mp_int * a, mp_int * n, int *c) { mp_int a1, n1, e; int s, r, res; mp_digit residue; /* step 1. if a == 0, return 0 */ if (mp_iszero (a) == 1) { *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^e */ if ((res = mp_init_copy (&a1, a)) != MP_OKAY) { return res; } if ((res = mp_init (&n1)) != MP_OKAY) { goto __A1; } if ((res = mp_init (&e)) != MP_OKAY) { goto __N1; } while (mp_iseven (&a1) == 1) { if ((res = mp_add_d (&e, 1, &e)) != MP_OKAY) { goto __E; } if ((res = mp_div_2 (&a1, &a1)) != MP_OKAY) { goto __E; } } /* step 4. if e is even set s=1 */ if (mp_iseven (&e) == 1) { s = 1; } else { /* else set s=1 if n = 1/7 (mod 8) or s=-1 if n = 3/5 (mod 8) */ if ((res = mp_mod_d (n, 8, &residue)) != MP_OKAY) { goto __E; } if (residue == 1 || residue == 7) { s = 1; } else if (residue == 3 || residue == 5) { s = -1; } } /* step 5. if n == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */ if ((res = mp_mod_d (n, 4, &residue)) != MP_OKAY) { goto __E; } if (residue == 3) { if ((res = mp_mod_d (&a1, 4, &residue)) != MP_OKAY) { goto __E; } if (residue == 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, &n1)) != MP_OKAY) { goto __E; } if ((res = mp_jacobi (&n1, &a1, &r)) != MP_OKAY) { goto __E; } *c = s * r; } /* done */ res = MP_OKAY; __E:mp_clear (&e); __N1:mp_clear (&n1); __A1:mp_clear (&a1); return res; } /* End: bn_mp_jacobi.c */ /* Start: bn_mp_karatsuba_mul.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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 - b1)(a0 - 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, t2, x0y0, x1y1; int B, err; err = MP_MEM; /* min # of digits */ B = MIN (a->used, b->used); /* now divide in two */ B = B / 2; /* init copy all the temps */ if (mp_init_size (&x0, B) != MP_OKAY) goto 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 (&t2, B * 2) != MP_OKAY) goto T1; if (mp_init_size (&x0y0, B * 2) != MP_OKAY) goto T2; if (mp_init_size (&x1y1, B * 2) != MP_OKAY) goto X0Y0; /* now shift the digits */ x0.sign = x1.sign = a->sign; y0.sign = y1.sign = b->sign; x0.used = y0.used = B; x1.used = a->used - B; y1.used = b->used - B; { register int x; register 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 */ 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 (mp_sub (&x1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = x1 - x0 */ if (mp_sub (&y1, &y0, &t2) != MP_OKAY) goto X1Y1; /* t2 = y1 - y0 */ if (mp_mul (&t1, &t2, &t1) != MP_OKAY) goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */ /* add x0y0 */ if (mp_add (&x0y0, &x1y1, &t2) != MP_OKAY) goto X1Y1; /* t2 = x0y0 + x1y1 */ if (mp_sub (&t2, &t1, &t1) != MP_OKAY) goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */ /* 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 */ err = MP_OKAY; X1Y1:mp_clear (&x1y1); X0Y0:mp_clear (&x0y0); T2:mp_clear (&t2); T1:mp_clear (&t1); Y1:mp_clear (&y1); Y0:mp_clear (&y0); X1:mp_clear (&x1); X0:mp_clear (&x0); ERR: return err; } /* End: bn_mp_karatsuba_mul.c */ /* Start: bn_mp_karatsuba_sqr.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* Karatsuba squaring, computes b = a*a using three half size squarings * * See comments of mp_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 / 2; /* init copy all the temps */ if (mp_init_size (&x0, B) != MP_OKAY) goto 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; { register int x; register 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 and y1-y0 */ if (mp_sub (&x1, &x0, &t1) != MP_OKAY) goto X1X1; /* t1 = x1 - x0 */ if (mp_sqr (&t1, &t1) != MP_OKAY) goto X1X1; /* t1 = (x1 - x0) * (y1 - y0) */ /* add x0y0 */ if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY) goto X1X1; /* t2 = x0y0 + x1y1 */ if (mp_sub (&t2, &t1, &t1) != MP_OKAY) goto X1X1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */ /* shift by B */ if (mp_lshd (&t1, B) != MP_OKAY) goto X1X1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */ if (mp_lshd (&x1x1, B * 2) != MP_OKAY) goto X1X1; /* x1y1 = x1y1 << 2*B */ if (mp_add (&x0x0, &t1, &t1) != MP_OKAY) goto X1X1; /* t1 = x0y0 + t1 */ if (mp_add (&t1, &x1x1, b) != MP_OKAY) goto X1X1; /* t1 = x0y0 + t1 + x1y1 */ 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); ERR: return err; } /* End: bn_mp_karatsuba_sqr.c */ /* Start: bn_mp_lcm.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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 t; if ((res = mp_init (&t)) != MP_OKAY) { return res; } if ((res = mp_mul (a, b, &t)) != MP_OKAY) { mp_clear (&t); return res; } if ((res = mp_gcd (a, b, c)) != MP_OKAY) { mp_clear (&t); return res; } res = mp_div (&t, c, c, NULL); mp_clear (&t); return res; } /* End: bn_mp_lcm.c */ /* Start: bn_mp_lshd.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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 ((res = mp_grow (a, a->used + b)) != MP_OKAY) { return res; } { register mp_digit *tmpa, *tmpaa; /* increment the used by the shift amount than copy upwards */ a->used += b; /* top */ tmpa = a->dp + a->used - 1; /* base */ tmpaa = 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--) { *tmpa-- = *tmpaa--; } /* zero the lower digits */ tmpa = a->dp; for (x = 0; x < b; x++) { *tmpa++ = 0; } } return MP_OKAY; } /* End: bn_mp_lshd.c */ /* Start: bn_mp_mod.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* c = a mod b, 0 <= c < b */ int mp_mod (mp_int * a, mp_int * b, mp_int * c) { mp_int t; int res; if ((res = mp_init (&t)) != MP_OKAY) { return res; } if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) { mp_clear (&t); return res; } if (t.sign == MP_NEG) { res = mp_add (b, &t, c); } else { res = MP_OKAY; mp_exch (&t, c); } mp_clear (&t); return res; } /* End: bn_mp_mod.c */ /* Start: bn_mp_mod_2d.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; } /* End: bn_mp_mod_2d.c */ /* Start: bn_mp_mod_d.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> int mp_mod_d (mp_int * a, mp_digit b, mp_digit * c) { mp_int t, t2; int res; if ((res = mp_init (&t)) != MP_OKAY) { return res; } if ((res = mp_init (&t2)) != MP_OKAY) { mp_clear (&t); return res; } mp_set (&t, b); mp_div (a, &t, NULL, &t2); if (t2.sign == MP_NEG) { if ((res = mp_add_d (&t2, b, &t2)) != MP_OKAY) { mp_clear (&t); mp_clear (&t2); return res; } } *c = t2.dp[0]; mp_clear (&t); mp_clear (&t2); return MP_OKAY; } /* End: bn_mp_mod_d.c */ /* Start: bn_mp_montgomery_calc_normalization.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* calculates a = B^n mod b for Montgomery reduction * Where B is the base [e.g. 2^DIGIT_BIT]. * B^n mod b is computed by first computing * A = B^(n-1) which doesn't require a reduction but a simple OR. * then C = A * B = B^n is computed by performing upto DIGIT_BIT * 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; /* compute A = B^(n-1) * 2^(bits-1) */ if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { return res; } /* now compute C = A * B mod b */ for (x = bits - 1; x < 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; } /* End: bn_mp_montgomery_calc_normalization.c */ /* Start: bn_mp_montgomery_reduce.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* computes xR^-1 == x (mod N) via Montgomery Reduction */ int mp_montgomery_reduce (mp_int * a, mp_int * m, mp_digit mp) { int ix, res, digs; mp_digit ui; digs = m->used * 2 + 1; if ((digs < 512) && digs < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { return fast_mp_montgomery_reduce (a, m, mp); } if (a->alloc < m->used * 2 + 1) { if ((res = mp_grow (a, m->used * 2 + 1)) != MP_OKAY) { return res; } } a->used = m->used * 2 + 1; for (ix = 0; ix < m->used; ix++) { /* ui = ai * m' mod b */ ui = (a->dp[ix] * mp) & MP_MASK; /* a = a + ui * m * b^i */ { register int iy; register mp_digit *tmpx, *tmpy, mu; register mp_word r; /* aliases */ tmpx = m->dp; tmpy = a->dp + ix; mu = 0; for (iy = 0; iy < m->used; iy++) { r = ((mp_word) ui) * ((mp_word) * tmpx++) + ((mp_word) mu) + ((mp_word) * tmpy); mu = (r >> ((mp_word) DIGIT_BIT)); *tmpy++ = (r & ((mp_word) MP_MASK)); } /* propagate carries */ while (mu) { *tmpy += mu; mu = (*tmpy >> DIGIT_BIT) & 1; *tmpy++ &= MP_MASK; } } } /* A = A/b^n */ mp_rshd (a, m->used); /* if A >= m then A = A - m */ if (mp_cmp_mag (a, m) != MP_LT) { return s_mp_sub (a, m, a); } return MP_OKAY; } /* End: bn_mp_montgomery_reduce.c */ /* Start: bn_mp_montgomery_setup.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* setups the montgomery reduction stuff */ int mp_montgomery_setup (mp_int * a, mp_digit * mp) { unsigned long x, b; /* fast inversion mod 2^32 * * 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 = a->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 */ x *= 2 - b * x; /* here x*a==1 mod 2^16; each step doubles the nb of bits */ x *= 2 - b * x; /* here x*a==1 mod 2^32 */ /* t = -1/m mod b */ *mp = ((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - (x & MP_MASK); return MP_OKAY; } /* End: bn_mp_montgomery_setup.c */ /* Start: bn_mp_mul.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; if (MIN (a->used, b->used) > KARATSUBA_MUL_CUTOFF) { res = mp_karatsuba_mul (a, b, c); } else { /* can we use the fast multiplier? * * The fast multiplier can be used if the output will have less than * 512 digits and the number of digits won't affect carry propagation */ int digs = a->used + b->used + 1; if ((digs < 512) && digs < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { res = fast_s_mp_mul_digs (a, b, c, digs); } else { res = s_mp_mul (a, b, c); } } c->sign = neg; return res; } /* End: bn_mp_mul.c */ /* Start: bn_mp_mulmod.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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 (&t)) != 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; } /* End: bn_mp_mulmod.c */ /* Start: bn_mp_mul_2.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* b = a*2 */ int mp_mul_2 (mp_int * a, mp_int * b) { int x, res, oldused; /* Optimization: should copy and shift at the same time */ if (b->alloc < a->used) { if ((res = mp_grow (b, a->used)) != MP_OKAY) { return res; } } oldused = b->used; b->used = a->used; /* shift any bit count < DIGIT_BIT */ { register mp_digit r, rr, *tmpa, *tmpb; r = 0; tmpa = a->dp; tmpb = b->dp; for (x = 0; x < b->used; x++) { rr = *tmpa >> (DIGIT_BIT - 1); *tmpb++ = ((*tmpa++ << 1) | r) & MP_MASK; r = rr; } /* new leading digit? */ if (r != 0) { if (b->alloc == b->used) { if ((res = mp_grow (b, b->used + 1)) != MP_OKAY) { return res; } /* after the grow *tmpb is no longer valid so we have to reset it! * (this bug took me about 17 minutes to find...!) */ tmpb = b->dp + b->used; } /* add a MSB of 1 */ *tmpb = 1; ++b->used; } tmpb = b->dp + b->used; for (x = b->used; x < oldused; x++) { *tmpb++ = 0; } } b->sign = a->sign; return MP_OKAY; } /* End: bn_mp_mul_2.c */ /* Start: bn_mp_mul_2d.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* shift left by a certain bit count */ int mp_mul_2d (mp_int * a, int b, mp_int * c) { mp_digit d, r, rr; int x, res; /* copy */ if ((res = mp_copy (a, c)) != MP_OKAY) { return res; } 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 >= DIGIT_BIT) { if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) { return res; } } c->used = c->alloc; /* shift any bit count < DIGIT_BIT */ d = (mp_digit) (b % DIGIT_BIT); if (d != 0) { r = 0; for (x = 0; x < c->used; x++) { /* get the higher bits of the current word */ rr = (c->dp[x] >> (DIGIT_BIT - d)) & ((mp_digit) ((1U << d) - 1U)); /* shift the current word and OR in the carry */ c->dp[x] = ((c->dp[x] << d) | r) & MP_MASK; /* set the carry to the carry bits of the current word */ r = rr; } } mp_clamp (c); return MP_OKAY; } /* End: bn_mp_mul_2d.c */ /* Start: bn_mp_mul_d.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* multiply by a digit */ int mp_mul_d (mp_int * a, mp_digit b, mp_int * c) { int res, pa, olduse; pa = a->used; if (c->alloc < pa + 1) { if ((res = mp_grow (c, pa + 1)) != MP_OKAY) { return res; } } olduse = c->used; c->used = pa + 1; { register mp_digit u, *tmpa, *tmpc; register mp_word r; register int ix; tmpc = c->dp + c->used; for (ix = c->used; ix < olduse; ix++) { *tmpc++ = 0; } tmpa = a->dp; tmpc = c->dp; u = 0; for (ix = 0; ix < pa; ix++) { r = ((mp_word) u) + ((mp_word) * tmpa++) * ((mp_word) b); *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK)); u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); } *tmpc = u; } mp_clamp (c); return MP_OKAY; } /* End: bn_mp_mul_d.c */ /* Start: bn_mp_neg.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* b = -a */ int mp_neg (mp_int * a, mp_int * b) { int res; if ((res = mp_copy (a, b)) != MP_OKAY) { return res; } b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; return MP_OKAY; } /* End: bn_mp_neg.c */ /* Start: bn_mp_n_root.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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 at most]. */ int mp_n_root (mp_int * a, mp_digit b, mp_int * c) { 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 __T1; } if ((res = mp_init (&t3)) != MP_OKAY) { goto __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 __T3; } /* t2 = t1 - ((t1^b - a) / (b * t1^(b-1))) */ if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) { /* t3 = t1^(b-1) */ goto __T3; } /* numerator */ if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) { /* t2 = t1^b */ goto __T3; } if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) { /* t2 = t1^b - a */ goto __T3; } if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) { /* t3 = t1^(b-1) * b */ goto __T3; } if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) { /* t3 = (t1^b - a)/(b * t1^(b-1)) */ goto __T3; } if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) { goto __T3; } } while (mp_cmp (&t1, &t2) != MP_EQ); /* result can be off by a few so check */ for (;;) { if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) { goto __T3; } if (mp_cmp (&t2, a) == MP_GT) { if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) { goto __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; __T3:mp_clear (&t3); __T2:mp_clear (&t2); __T1:mp_clear (&t1); return res; } /* End: bn_mp_n_root.c */ /* Start: bn_mp_or.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; } /* End: bn_mp_or.c */ /* Start: bn_mp_prime_fermat.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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 fail */ *result = 0; /* 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 __T; } /* is it equal to b? */ if (mp_cmp (&t, b) == MP_EQ) { *result = 1; } err = MP_OKAY; __T:mp_clear (&t); return err; } /* End: bn_mp_prime_fermat.c */ /* Start: bn_mp_prime_is_divisible.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* determines if an integers is divisible by one of the first 256 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 = 0; for (ix = 0; ix < 256; ix++) { /* is it equal to the prime? */ if (mp_cmp_d (a, __prime_tab[ix]) == MP_EQ) { *result = 1; return MP_OKAY; } /* what is a mod __prime_tab[ix] */ if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) { return err; } /* is the residue zero? */ if (res == 0) { *result = 1; return MP_OKAY; } } return MP_OKAY; } /* End: bn_mp_prime_is_divisible.c */ /* Start: bn_mp_prime_is_prime.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* performs a variable number of rounds of Miller-Rabin * * Probability of error after t rounds is no more than * (1/4)^t when 1 <= t <= 256 * * 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 = 0; /* valid value of t? */ if (t < 1 || t > 256) { return MP_VAL; } /* first perform trial division */ if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) { return err; } if (res == 1) { 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, __prime_tab[ix]); if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) { goto __B; } if (res == 0) { goto __B; } } /* passed the test */ *result = 1; __B:mp_clear (&b); return err; } /* End: bn_mp_prime_is_prime.c */ /* Start: bn_mp_prime_miller_rabin.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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 = 0; /* 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 __N1; } /* set 2^s * r = n1 */ if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) { goto __N1; } s = 0; while (mp_iseven (&r) == 1) { ++s; if ((err = mp_div_2 (&r, &r)) != MP_OKAY) { goto __R; } } /* compute y = b^r mod a */ if ((err = mp_init (&y)) != MP_OKAY) { goto __R; } if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) { goto __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 __Y; } /* if y == 1 then composite */ if (mp_cmp_d (&y, 1) == MP_EQ) { goto __Y; } ++j; } /* if y != n1 then composite */ if (mp_cmp (&y, &n1) != MP_EQ) { goto __Y; } } /* probably prime now */ *result = 1; __Y:mp_clear (&y); __R:mp_clear (&r); __N1:mp_clear (&n1); return err; } /* End: bn_mp_prime_miller_rabin.c */ /* Start: bn_mp_prime_next_prime.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* finds the next prime after the number "a" using "t" trials * of Miller-Rabin. */ int mp_prime_next_prime(mp_int *a, int t) { int err, res; if (mp_iseven(a) == 1) { /* force odd */ if ((err = mp_add_d(a, 1, a)) != MP_OKAY) { return err; } } else { /* force to next number */ if ((err = mp_add_d(a, 2, a)) != MP_OKAY) { return err; } } for (;;) { /* is this prime? */ if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { return err; } if (res == 1) { break; } /* add two, next candidate */ if ((err = mp_add_d(a, 2, a)) != MP_OKAY) { return err; } } return MP_OKAY; } /* End: bn_mp_prime_next_prime.c */ /* Start: bn_mp_rand.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* makes a pseudo-random int of a given size */ 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 = ((mp_digit) abs (rand ())); } 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, ((mp_digit) abs (rand ())), a)) != MP_OKAY) { return res; } } return MP_OKAY; } /* End: bn_mp_rand.c */ /* Start: bn_mp_read_signed_bin.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* read signed bin, big endian, first byte is 0==positive or 1==negative */ int mp_read_signed_bin (mp_int * a, unsigned char *b, int c) { int res; if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) { return res; } a->sign = ((b[0] == (unsigned char) 0) ? MP_ZPOS : MP_NEG); return MP_OKAY; } /* End: bn_mp_read_signed_bin.c */ /* Start: bn_mp_read_unsigned_bin.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* reads a unsigned char array, assumes the msb is stored first [big endian] */ int mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c) { int res; mp_zero (a); while (c-- > 0) { if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) { return res; } if (DIGIT_BIT != 7) { a->dp[0] |= *b++; a->used += 1; } else { a->dp[0] = (*b & MP_MASK); a->dp[1] |= ((*b++ >> 7U) & 1); a->used += 2; } } mp_clamp (a); return MP_OKAY; } /* End: bn_mp_read_unsigned_bin.c */ /* Start: bn_mp_reduce.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; } res = mp_div (a, b, a, NULL); return res; } /* 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; if ((res = mp_init_copy (&q, x)) != MP_OKAY) { return res; } mp_rshd (&q, um - 1); /* q1 = x / b^(k-1) */ /* according to HAC this is optimization is ok */ if (((unsigned long) m->used) > (1UL << (unsigned long) (DIGIT_BIT - 1UL))) { if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) { goto CLEANUP; } } else { if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { goto CLEANUP; } } mp_rshd (&q, um + 1); /* q3 = q2 / b^(k+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) break; } CLEANUP: mp_clear (&q); return res; } /* End: bn_mp_reduce.c */ /* Start: bn_mp_rshd.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; } { register mp_digit *tmpa, *tmpaa; /* shift the digits down */ /* base */ tmpa = a->dp; /* offset into digits */ tmpaa = 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++) { *tmpa++ = *tmpaa++; } /* zero the top digits */ for (; x < a->used; x++) { *tmpa++ = 0; } } mp_clamp (a); } /* End: bn_mp_rshd.c */ /* Start: bn_mp_set.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; } /* End: bn_mp_set.c */ /* Start: bn_mp_set_int.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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, simplest solution to the what if DIGIT_BIT==7 case */ 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 += 32 / DIGIT_BIT + 1; } mp_clamp (a); return MP_OKAY; } /* End: bn_mp_set_int.c */ /* Start: bn_mp_shrink.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* shrink a bignum */ int mp_shrink (mp_int * a) { if (a->alloc != a->used) { if ((a->dp = OPT_CAST realloc (a->dp, sizeof (mp_digit) * a->used)) == NULL) { return MP_MEM; } a->alloc = a->used; } return MP_OKAY; } /* End: bn_mp_shrink.c */ /* Start: bn_mp_signed_bin_size.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* get the size for an signed equivalent */ int mp_signed_bin_size (mp_int * a) { return 1 + mp_unsigned_bin_size (a); } /* End: bn_mp_signed_bin_size.c */ /* Start: bn_mp_sqr.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* computes b = a*a */ int mp_sqr (mp_int * a, mp_int * b) { int res; if (a->used > KARATSUBA_SQR_CUTOFF) { res = mp_karatsuba_sqr (a, b); } else { /* can we use the fast multiplier? */ if (((a->used * 2 + 1) < 512) && a->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT) - 1))) { res = fast_s_mp_sqr (a, b); } else { res = s_mp_sqr (a, b); } } b->sign = MP_ZPOS; return res; } /* End: bn_mp_sqr.c */ /* Start: bn_mp_sqrmod.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; } /* End: bn_mp_sqrmod.c */ /* Start: bn_mp_sub.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; /* handle four cases */ if (sa == MP_ZPOS && sb == MP_ZPOS) { /* both positive, a - b, but if b>a then we do -(b - a) */ if (mp_cmp_mag (a, b) == MP_LT) { /* b>a */ res = s_mp_sub (b, a, c); c->sign = MP_NEG; } else { res = s_mp_sub (a, b, c); c->sign = MP_ZPOS; } } else if (sa == MP_ZPOS && sb == MP_NEG) { /* a - -b == a + b */ res = s_mp_add (a, b, c); c->sign = MP_ZPOS; } else if (sa == MP_NEG && sb == MP_ZPOS) { /* -a - b == -(a + b) */ res = s_mp_add (a, b, c); c->sign = MP_NEG; } else { /* -a - -b == b - a, but if a>b == -(a - b) */ if (mp_cmp_mag (a, b) == MP_GT) { res = s_mp_sub (a, b, c); c->sign = MP_NEG; } else { res = s_mp_sub (b, a, c); c->sign = MP_ZPOS; } } return res; } /* End: bn_mp_sub.c */ /* Start: bn_mp_submod.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; } /* End: bn_mp_submod.c */ /* Start: bn_mp_sub_d.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* single digit subtraction */ int mp_sub_d (mp_int * a, mp_digit b, mp_int * c) { mp_int t; int res; if ((res = mp_init (&t)) != MP_OKAY) { return res; } mp_set (&t, b); res = mp_sub (a, &t, c); mp_clear (&t); return res; } /* End: bn_mp_sub_d.c */ /* Start: bn_mp_to_signed_bin.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1); return MP_OKAY; } /* End: bn_mp_to_signed_bin.c */ /* Start: bn_mp_to_unsigned_bin.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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) == 0) { if (DIGIT_BIT != 7) { b[x++] = (unsigned char) (t.dp[0] & 255); } else { b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7)); } 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; } /* End: bn_mp_to_unsigned_bin.c */ /* Start: bn_mp_unsigned_bin_size.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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)); } /* End: bn_mp_unsigned_bin_size.c */ /* Start: bn_mp_xor.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; } /* End: bn_mp_xor.c */ /* Start: bn_mp_zero.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* set to zero */ void mp_zero (mp_int * a) { a->sign = MP_ZPOS; a->used = 0; memset (a->dp, 0, sizeof (mp_digit) * a->alloc); } /* End: bn_mp_zero.c */ /* Start: bn_prime_tab.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> const mp_digit __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, 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 }; /* End: bn_prime_tab.c */ /* Start: bn_radix.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* chars used in radix conversions */ static const char *s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; /* read a string [ASCII] in a given radix */ int mp_read_radix (mp_int * a, char *str, int radix) { int y, res, neg; char ch; if (radix < 2 || radix > 64) { return MP_VAL; } if (*str == '-') { ++str; neg = MP_NEG; } else { neg = MP_ZPOS; } mp_zero (a); while (*str) { ch = (char) ((radix < 36) ? toupper (*str) : *str); for (y = 0; y < 64; y++) { if (ch == s_rmap[y]) { break; } } 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; } a->sign = neg; return MP_OKAY; } /* 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; if (radix < 2 || radix > 64) { return MP_VAL; } if ((res = mp_init_copy (&t, a)) != MP_OKAY) { return res; } if (t.sign == MP_NEG) { ++_s; *str++ = '-'; t.sign = MP_ZPOS; } digs = 0; while (mp_iszero (&t) == 0) { if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { mp_clear (&t); return res; } *str++ = s_rmap[d]; ++digs; } bn_reverse ((unsigned char *)_s, digs); *str++ = '\0'; mp_clear (&t); return MP_OKAY; } /* returns size of ASCII reprensentation */ int mp_radix_size (mp_int * a, int radix) { int res, digs; mp_int t; mp_digit d; /* special case for binary */ if (radix == 2) { return mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1; } if (radix < 2 || radix > 64) { return 0; } if ((res = mp_init_copy (&t, a)) != MP_OKAY) { return 0; } digs = 0; if (t.sign == MP_NEG) { ++digs; t.sign = MP_ZPOS; } while (mp_iszero (&t) == 0) { if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { mp_clear (&t); return 0; } ++digs; } mp_clear (&t); return digs + 1; } /* End: bn_radix.c */ /* Start: bn_reverse.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; } } /* End: bn_reverse.c */ /* Start: bn_s_mp_add.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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 if (a->used < b->used) { min = a->used; max = b->used; x = b; } else { min = max = a->used; x = NULL; } /* init result */ if (c->alloc < max + 1) { if ((res = mp_grow (c, max + 1)) != MP_OKAY) { return res; } } olduse = c->used; c->used = max + 1; /* add digits from lower part */ /* set the carry to zero */ { register mp_digit u, *tmpa, *tmpb, *tmpc; register int i; /* alias for digit pointers */ /* first input */ tmpa = a->dp; /* second input */ tmpb = b->dp; /* destination */ tmpc = c->dp; 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 >> 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 >> DIGIT_BIT; /* take away carry bit from T[i] */ *tmpc++ &= MP_MASK; } } /* add carry */ *tmpc++ = u; /* 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; } /* End: bn_s_mp_add.c */ /* Start: bn_s_mp_mul_digs.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; 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 */ tmpx = a->dp[ix]; tmpt = &(t.dp[ix]); 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)); } if (ix + iy < digs) *tmpt = u; } mp_clamp (&t); mp_exch (&t, c); mp_clear (&t); return MP_OKAY; } /* End: bn_s_mp_mul_digs.c */ /* Start: bn_s_mp_mul_high_digs.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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? */ if (((a->used + b->used + 1) < 512) && MAX (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { return fast_s_mp_mul_high_digs (a, b, c, digs); } 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; } /* End: bn_s_mp_mul_high_digs.c */ /* Start: bn_s_mp_sqr.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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, u; mp_digit tmpx, *tmpt; pa = a->used; if ((res = mp_init_size (&t, pa + pa + 1)) != MP_OKAY) { return res; } t.used = pa + pa + 1; for (ix = 0; ix < pa; ix++) { /* first calculate the digit at 2*ix */ /* calculate double precision result */ r = ((mp_word) t.dp[ix + 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 = (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[ix + 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 its 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 = (r >> ((mp_word) DIGIT_BIT)); } r = ((mp_word) * tmpt) + u; *tmpt = (mp_digit) (r & ((mp_word) MP_MASK)); u = (r >> ((mp_word) DIGIT_BIT)); /* propagate upwards */ ++tmpt; while (u != ((mp_word) 0)) { r = ((mp_word) * tmpt) + ((mp_word) 1); *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); u = (r >> ((mp_word) DIGIT_BIT)); } } mp_clamp (&t); mp_exch (&t, b); mp_clear (&t); return MP_OKAY; } /* End: bn_s_mp_sqr.c */ /* Start: bn_s_mp_sub.c */ /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is 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, tomstdenis@iahu.ca, http://math.libtomcrypt.org */ #include <tommath.h> /* 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; /* sub digits from lower part */ { register mp_digit u, *tmpa, *tmpb, *tmpc; register 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 required to get the carry */ u = *tmpc >> (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 >> (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; } /* End: bn_s_mp_sub.c */ /* EOF */