Commit 448f35e2e179460f29713b23179ebb27d1df9fdd
2019-10-29T20:07:29
simplifications: prime functions
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478
diff --git a/mp_prime_fermat.c b/mp_prime_fermat.c
index 50d2e5e..ac8116f 100644
--- a/mp_prime_fermat.c
+++ b/mp_prime_fermat.c
@@ -16,9 +16,6 @@ mp_err mp_prime_fermat(const mp_int *a, const mp_int *b, bool *result)
mp_int t;
mp_err err;
- /* default to composite */
- *result = false;
-
/* ensure b > 1 */
if (mp_cmp_d(b, 1uL) != MP_GT) {
return MP_VAL;
@@ -31,16 +28,13 @@ mp_err mp_prime_fermat(const mp_int *a, const mp_int *b, bool *result)
/* compute t = b**a mod a */
if ((err = mp_exptmod(b, a, a, &t)) != MP_OKAY) {
- goto LBL_T;
+ goto LBL_ERR;
}
/* is it equal to b? */
- if (mp_cmp(&t, b) == MP_EQ) {
- *result = true;
- }
+ *result = mp_cmp(&t, b) == MP_EQ;
- err = MP_OKAY;
-LBL_T:
+LBL_ERR:
mp_clear(&t);
return err;
}
diff --git a/mp_prime_frobenius_underwood.c b/mp_prime_frobenius_underwood.c
index 543b8b4..62d3476 100644
--- a/mp_prime_frobenius_underwood.c
+++ b/mp_prime_frobenius_underwood.c
@@ -23,17 +23,16 @@
mp_err mp_prime_frobenius_underwood(const mp_int *N, bool *result)
{
mp_int T1z, T2z, Np1z, sz, tz;
-
- int a, ap2, length, i, j;
+ int a, ap2, i;
mp_err err;
- *result = false;
-
if ((err = mp_init_multi(&T1z, &T2z, &Np1z, &sz, &tz, NULL)) != MP_OKAY) {
return err;
}
for (a = 0; a < LTM_FROBENIUS_UNDERWOOD_A; a++) {
+ int j;
+
/* TODO: That's ugly! No, really, it is! */
if ((a==2) || (a==4) || (a==7) || (a==8) || (a==10) ||
(a==14) || (a==18) || (a==23) || (a==26) || (a==28)) {
@@ -42,7 +41,7 @@ mp_err mp_prime_frobenius_underwood(const mp_int *N, bool *result)
mp_set_i32(&T1z, (int32_t)((a * a) - 4));
- if ((err = mp_kronecker(&T1z, N, &j)) != MP_OKAY) goto LBL_FU_ERR;
+ if ((err = mp_kronecker(&T1z, N, &j)) != MP_OKAY) goto LBL_END;
if (j == -1) {
break;
@@ -50,73 +49,76 @@ mp_err mp_prime_frobenius_underwood(const mp_int *N, bool *result)
if (j == 0) {
/* composite */
- goto LBL_FU_ERR;
+ *result = false;
+ goto LBL_END;
}
}
/* Tell it a composite and set return value accordingly */
if (a >= LTM_FROBENIUS_UNDERWOOD_A) {
err = MP_ITER;
- goto LBL_FU_ERR;
+ goto LBL_END;
}
/* Composite if N and (a+4)*(2*a+5) are not coprime */
mp_set_u32(&T1z, (uint32_t)((a+4)*((2*a)+5)));
- if ((err = mp_gcd(N, &T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
+ if ((err = mp_gcd(N, &T1z, &T1z)) != MP_OKAY) goto LBL_END;
- if (!((T1z.used == 1) && (T1z.dp[0] == 1u))) goto LBL_FU_ERR;
+ if (!((T1z.used == 1) && (T1z.dp[0] == 1u))) {
+ /* composite */
+ *result = false;
+ goto LBL_END;
+ }
ap2 = a + 2;
- if ((err = mp_add_d(N, 1uL, &Np1z)) != MP_OKAY) goto LBL_FU_ERR;
+ if ((err = mp_add_d(N, 1uL, &Np1z)) != MP_OKAY) goto LBL_END;
mp_set(&sz, 1uL);
mp_set(&tz, 2uL);
- length = mp_count_bits(&Np1z);
- for (i = length - 2; i >= 0; i--) {
+ for (i = mp_count_bits(&Np1z) - 2; i >= 0; i--) {
/*
* temp = (sz*(a*sz+2*tz))%N;
* tz = ((tz-sz)*(tz+sz))%N;
* sz = temp;
*/
- if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
+ if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_END;
/* a = 0 at about 50% of the cases (non-square and odd input) */
if (a != 0) {
- if ((err = mp_mul_d(&sz, (mp_digit)a, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
- if ((err = mp_add(&T1z, &T2z, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
+ if ((err = mp_mul_d(&sz, (mp_digit)a, &T1z)) != MP_OKAY) goto LBL_END;
+ if ((err = mp_add(&T1z, &T2z, &T2z)) != MP_OKAY) goto LBL_END;
}
- if ((err = mp_mul(&T2z, &sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
- if ((err = mp_sub(&tz, &sz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
- if ((err = mp_add(&sz, &tz, &sz)) != MP_OKAY) goto LBL_FU_ERR;
- if ((err = mp_mul(&sz, &T2z, &tz)) != MP_OKAY) goto LBL_FU_ERR;
- if ((err = mp_mod(&tz, N, &tz)) != MP_OKAY) goto LBL_FU_ERR;
- if ((err = mp_mod(&T1z, N, &sz)) != MP_OKAY) goto LBL_FU_ERR;
- if (s_mp_get_bit(&Np1z, (unsigned int)i)) {
+ if ((err = mp_mul(&T2z, &sz, &T1z)) != MP_OKAY) goto LBL_END;
+ if ((err = mp_sub(&tz, &sz, &T2z)) != MP_OKAY) goto LBL_END;
+ if ((err = mp_add(&sz, &tz, &sz)) != MP_OKAY) goto LBL_END;
+ if ((err = mp_mul(&sz, &T2z, &tz)) != MP_OKAY) goto LBL_END;
+ if ((err = mp_mod(&tz, N, &tz)) != MP_OKAY) goto LBL_END;
+ if ((err = mp_mod(&T1z, N, &sz)) != MP_OKAY) goto LBL_END;
+ if (s_mp_get_bit(&Np1z, i)) {
/*
* temp = (a+2) * sz + tz
* tz = 2 * tz - sz
* sz = temp
*/
if (a == 0) {
- if ((err = mp_mul_2(&sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
+ if ((err = mp_mul_2(&sz, &T1z)) != MP_OKAY) goto LBL_END;
} else {
- if ((err = mp_mul_d(&sz, (mp_digit)ap2, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
+ if ((err = mp_mul_d(&sz, (mp_digit)ap2, &T1z)) != MP_OKAY) goto LBL_END;
}
- if ((err = mp_add(&T1z, &tz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
- if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
- if ((err = mp_sub(&T2z, &sz, &tz)) != MP_OKAY) goto LBL_FU_ERR;
+ if ((err = mp_add(&T1z, &tz, &T1z)) != MP_OKAY) goto LBL_END;
+ if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_END;
+ if ((err = mp_sub(&T2z, &sz, &tz)) != MP_OKAY) goto LBL_END;
mp_exch(&sz, &T1z);
}
}
mp_set_u32(&T1z, (uint32_t)((2 * a) + 5));
- if ((err = mp_mod(&T1z, N, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
- if (mp_iszero(&sz) && (mp_cmp(&tz, &T1z) == MP_EQ)) {
- *result = true;
- }
+ if ((err = mp_mod(&T1z, N, &T1z)) != MP_OKAY) goto LBL_END;
+
+ *result = mp_iszero(&sz) && (mp_cmp(&tz, &T1z) == MP_EQ);
-LBL_FU_ERR:
+LBL_END:
mp_clear_multi(&tz, &sz, &Np1z, &T2z, &T1z, NULL);
return err;
}
diff --git a/mp_prime_is_prime.c b/mp_prime_is_prime.c
index d0eca2c..7d73864 100644
--- a/mp_prime_is_prime.c
+++ b/mp_prime_is_prime.c
@@ -13,14 +13,12 @@ static unsigned int s_floor_ilog2(int value)
return r;
}
-
mp_err mp_prime_is_prime(const mp_int *a, int t, bool *result)
{
mp_int b;
- int ix, p_max = 0, size_a, len;
- bool res;
+ int ix;
+ bool res;
mp_err err;
- unsigned int fips_rand, mask;
/* default to no */
*result = false;
@@ -133,6 +131,8 @@ mp_err mp_prime_is_prime(const mp_int *a, int t, bool *result)
TODO: can be made a bit finer grained but comparing is not free.
*/
if (t < 0) {
+ int p_max = 0;
+
/*
Sorenson, Jonathan; Webster, Jonathan (2015).
"Strong Pseudoprimes to Twelve Prime Bases".
@@ -174,6 +174,9 @@ mp_err mp_prime_is_prime(const mp_int *a, int t, bool *result)
See Fips 186.4 p. 126ff
*/
else if (t > 0) {
+ unsigned int mask;
+ int size_a;
+
/*
* The mp_digit's have a defined bit-size but the size of the
* array a.dp is a simple 'int' and this library can not assume full
@@ -219,6 +222,9 @@ mp_err mp_prime_is_prime(const mp_int *a, int t, bool *result)
need to be prime.
*/
for (ix = 0; ix < t; ix++) {
+ unsigned int fips_rand;
+ int len;
+
/* mp_rand() guarantees the first digit to be non-zero */
if ((err = mp_rand(&b, 1)) != MP_OKAY) {
goto LBL_B;
diff --git a/mp_prime_miller_rabin.c b/mp_prime_miller_rabin.c
index a3af8bc..4c23a9f 100644
--- a/mp_prime_miller_rabin.c
+++ b/mp_prime_miller_rabin.c
@@ -16,9 +16,6 @@ mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, bool *result)
mp_err err;
int s, j;
- /* default */
- *result = false;
-
/* ensure b > 1 */
if (mp_cmp_d(b, 1uL) != MP_GT) {
return MP_VAL;
@@ -29,12 +26,12 @@ mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, bool *result)
return err;
}
if ((err = mp_sub_d(&n1, 1uL, &n1)) != MP_OKAY) {
- goto LBL_N1;
+ goto LBL_ERR1;
}
/* set 2**s * r = n1 */
if ((err = mp_init_copy(&r, &n1)) != MP_OKAY) {
- goto LBL_N1;
+ goto LBL_ERR1;
}
/* count the number of least significant bits
@@ -44,15 +41,15 @@ mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, bool *result)
/* now divide n - 1 by 2**s */
if ((err = mp_div_2d(&r, s, &r, NULL)) != MP_OKAY) {
- goto LBL_R;
+ goto LBL_ERR2;
}
/* compute y = b**r mod a */
if ((err = mp_init(&y)) != MP_OKAY) {
- goto LBL_R;
+ goto LBL_ERR2;
}
if ((err = mp_exptmod(b, &r, a, &y)) != MP_OKAY) {
- goto LBL_Y;
+ goto LBL_END;
}
/* if y != 1 and y != n1 do */
@@ -61,12 +58,13 @@ mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, bool *result)
/* while j <= s-1 and y != n1 */
while ((j <= (s - 1)) && (mp_cmp(&y, &n1) != MP_EQ)) {
if ((err = mp_sqrmod(&y, a, &y)) != MP_OKAY) {
- goto LBL_Y;
+ goto LBL_END;
}
/* if y == 1 then composite */
if (mp_cmp_d(&y, 1uL) == MP_EQ) {
- goto LBL_Y;
+ *result = false;
+ goto LBL_END;
}
++j;
@@ -74,17 +72,19 @@ mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, bool *result)
/* if y != n1 then composite */
if (mp_cmp(&y, &n1) != MP_EQ) {
- goto LBL_Y;
+ *result = false;
+ goto LBL_END;
}
}
/* probably prime now */
*result = true;
-LBL_Y:
+
+LBL_END:
mp_clear(&y);
-LBL_R:
+LBL_ERR2:
mp_clear(&r);
-LBL_N1:
+LBL_ERR1:
mp_clear(&n1);
return err;
}
diff --git a/mp_prime_next_prime.c b/mp_prime_next_prime.c
index 40c94a4..6faa08d 100644
--- a/mp_prime_next_prime.c
+++ b/mp_prime_next_prime.c
@@ -10,11 +10,10 @@
*/
mp_err mp_prime_next_prime(mp_int *a, int t, bool bbs_style)
{
- int x, y;
- mp_ord cmp;
+ int x;
mp_err err;
bool res = false;
- mp_digit res_tab[MP_PRIME_TAB_SIZE], step, kstep;
+ mp_digit res_tab[MP_PRIME_TAB_SIZE], kstep;
mp_int b;
/* force positive */
@@ -24,7 +23,7 @@ mp_err mp_prime_next_prime(mp_int *a, int t, bool bbs_style)
if (mp_cmp_d(a, s_mp_prime_tab[MP_PRIME_TAB_SIZE-1]) == MP_LT) {
/* find which prime it is bigger than "a" */
for (x = 0; x < MP_PRIME_TAB_SIZE; x++) {
- cmp = mp_cmp_d(a, s_mp_prime_tab[x]);
+ mp_ord cmp = mp_cmp_d(a, s_mp_prime_tab[x]);
if (cmp == MP_EQ) {
continue;
}
@@ -42,11 +41,7 @@ mp_err mp_prime_next_prime(mp_int *a, int t, bool bbs_style)
}
/* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
- if (bbs_style) {
- kstep = 4;
- } else {
- kstep = 2;
- }
+ kstep = bbs_style ? 4 : 2;
/* at this point we will use a combination of a sieve and Miller-Rabin */
@@ -79,11 +74,12 @@ mp_err mp_prime_next_prime(mp_int *a, int t, bool bbs_style)
}
for (;;) {
+ mp_digit step = 0;
+ bool y;
/* skip to the next non-trivially divisible candidate */
- step = 0;
do {
- /* y == 1 if any residue was zero [e.g. cannot be prime] */
- y = 0;
+ /* y == true if any residue was zero [e.g. cannot be prime] */
+ y = false;
/* increase step to next candidate */
step += kstep;
@@ -100,10 +96,10 @@ mp_err mp_prime_next_prime(mp_int *a, int t, bool bbs_style)
/* set flag if zero */
if (res_tab[x] == 0u) {
- y = 1;
+ y = true;
}
}
- } while ((y == 1) && (step < (((mp_digit)1 << MP_DIGIT_BIT) - kstep)));
+ } while (y && (step < (((mp_digit)1 << MP_DIGIT_BIT) - kstep)));
/* add the step */
if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
@@ -111,7 +107,7 @@ mp_err mp_prime_next_prime(mp_int *a, int t, bool bbs_style)
}
/* if didn't pass sieve and step == MP_MAX then skip test */
- if ((y == 1) && (step >= (((mp_digit)1 << MP_DIGIT_BIT) - kstep))) {
+ if (y && (step >= (((mp_digit)1 << MP_DIGIT_BIT) - kstep))) {
continue;
}
@@ -123,7 +119,6 @@ mp_err mp_prime_next_prime(mp_int *a, int t, bool bbs_style)
}
}
- err = MP_OKAY;
LBL_ERR:
mp_clear(&b);
return err;
diff --git a/mp_prime_strong_lucas_selfridge.c b/mp_prime_strong_lucas_selfridge.c
index df5de96..6262e07 100644
--- a/mp_prime_strong_lucas_selfridge.c
+++ b/mp_prime_strong_lucas_selfridge.c
@@ -192,7 +192,7 @@ mp_err mp_prime_strong_lucas_selfridge(const mp_int *a, bool *result)
if ((err = mp_mod(&Qmz, a, &Qmz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR;
- if (s_mp_get_bit(&Dz, (unsigned int)u)) {
+ if (s_mp_get_bit(&Dz, u)) {
/* Formulas for addition of indices (carried out mod N);
*
* U_(m+n) = (U_m*V_n + U_n*V_m)/2
diff --git a/s_mp_get_bit.c b/s_mp_get_bit.c
index f077f61..a509bce 100644
--- a/s_mp_get_bit.c
+++ b/s_mp_get_bit.c
@@ -5,12 +5,12 @@
/* SPDX-License-Identifier: Unlicense */
/* Get bit at position b and return true if the bit is 1, false if it is 0 */
-bool s_mp_get_bit(const mp_int *a, unsigned int b)
+bool s_mp_get_bit(const mp_int *a, int b)
{
mp_digit bit;
- int limb = (int)(b / MP_DIGIT_BIT);
+ int limb = b / MP_DIGIT_BIT;
- if (limb >= a->used) {
+ if (limb < 0 || limb >= a->used) {
return false;
}
diff --git a/s_mp_prime_is_divisible.c b/s_mp_prime_is_divisible.c
index 0cca5a6..63b2405 100644
--- a/s_mp_prime_is_divisible.c
+++ b/s_mp_prime_is_divisible.c
@@ -10,16 +10,12 @@
*/
mp_err s_mp_prime_is_divisible(const mp_int *a, bool *result)
{
- int ix;
- mp_err err;
- mp_digit res;
-
- /* default to not */
- *result = false;
-
- for (ix = 0; ix < MP_PRIME_TAB_SIZE; ix++) {
- /* what is a mod LBL_prime_tab[ix] */
- if ((err = mp_mod_d(a, s_mp_prime_tab[ix], &res)) != MP_OKAY) {
+ int i;
+ for (i = 0; i < MP_PRIME_TAB_SIZE; i++) {
+ /* what is a mod LBL_prime_tab[i] */
+ mp_err err;
+ mp_digit res;
+ if ((err = mp_mod_d(a, s_mp_prime_tab[i], &res)) != MP_OKAY) {
return err;
}
@@ -30,6 +26,8 @@ mp_err s_mp_prime_is_divisible(const mp_int *a, bool *result)
}
}
+ /* default to not */
+ *result = false;
return MP_OKAY;
}
#endif
diff --git a/tommath_private.h b/tommath_private.h
index f2989d4..aaa3d23 100644
--- a/tommath_private.h
+++ b/tommath_private.h
@@ -188,7 +188,7 @@ MP_STATIC_ASSERT(prec_geq_min_prec, MP_PREC >= MP_MIN_PREC)
extern MP_PRIVATE mp_err(*s_mp_rand_source)(void *out, size_t size);
/* lowlevel functions, do not call! */
-MP_PRIVATE bool s_mp_get_bit(const mp_int *a, unsigned int b);
+MP_PRIVATE bool s_mp_get_bit(const mp_int *a, int b);
MP_PRIVATE mp_err s_mp_add(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
MP_PRIVATE mp_err s_mp_sub(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR;
MP_PRIVATE mp_err s_mp_mul_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs) MP_WUR;