Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1 | /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
| 2 | * All rights reserved. |
| 3 | * |
| 4 | * This package is an SSL implementation written |
| 5 | * by Eric Young (eay@cryptsoft.com). |
| 6 | * The implementation was written so as to conform with Netscapes SSL. |
| 7 | * |
| 8 | * This library is free for commercial and non-commercial use as long as |
| 9 | * the following conditions are aheared to. The following conditions |
| 10 | * apply to all code found in this distribution, be it the RC4, RSA, |
| 11 | * lhash, DES, etc., code; not just the SSL code. The SSL documentation |
| 12 | * included with this distribution is covered by the same copyright terms |
| 13 | * except that the holder is Tim Hudson (tjh@cryptsoft.com). |
| 14 | * |
| 15 | * Copyright remains Eric Young's, and as such any Copyright notices in |
| 16 | * the code are not to be removed. |
| 17 | * If this package is used in a product, Eric Young should be given attribution |
| 18 | * as the author of the parts of the library used. |
| 19 | * This can be in the form of a textual message at program startup or |
| 20 | * in documentation (online or textual) provided with the package. |
| 21 | * |
| 22 | * Redistribution and use in source and binary forms, with or without |
| 23 | * modification, are permitted provided that the following conditions |
| 24 | * are met: |
| 25 | * 1. Redistributions of source code must retain the copyright |
| 26 | * notice, this list of conditions and the following disclaimer. |
| 27 | * 2. Redistributions in binary form must reproduce the above copyright |
| 28 | * notice, this list of conditions and the following disclaimer in the |
| 29 | * documentation and/or other materials provided with the distribution. |
| 30 | * 3. All advertising materials mentioning features or use of this software |
| 31 | * must display the following acknowledgement: |
| 32 | * "This product includes cryptographic software written by |
| 33 | * Eric Young (eay@cryptsoft.com)" |
| 34 | * The word 'cryptographic' can be left out if the rouines from the library |
| 35 | * being used are not cryptographic related :-). |
| 36 | * 4. If you include any Windows specific code (or a derivative thereof) from |
| 37 | * the apps directory (application code) you must include an acknowledgement: |
| 38 | * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" |
| 39 | * |
| 40 | * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND |
| 41 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 42 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| 43 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| 44 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| 45 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| 46 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 47 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| 48 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| 49 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| 50 | * SUCH DAMAGE. |
| 51 | * |
| 52 | * The licence and distribution terms for any publically available version or |
| 53 | * derivative of this code cannot be changed. i.e. this code cannot simply be |
| 54 | * copied and put under another distribution licence |
| 55 | * [including the GNU Public Licence.] */ |
| 56 | |
| 57 | #include <openssl/bn.h> |
| 58 | |
| 59 | #include <assert.h> |
| 60 | #include <string.h> |
| 61 | |
| 62 | #include "internal.h" |
| 63 | |
| 64 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 65 | #define BN_MUL_RECURSIVE_SIZE_NORMAL 16 |
| 66 | #define BN_SQR_RECURSIVE_SIZE_NORMAL BN_MUL_RECURSIVE_SIZE_NORMAL |
| 67 | |
| 68 | |
| 69 | static void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, |
| 70 | int nb) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 71 | BN_ULONG *rr; |
| 72 | |
| 73 | if (na < nb) { |
| 74 | int itmp; |
| 75 | BN_ULONG *ltmp; |
| 76 | |
| 77 | itmp = na; |
| 78 | na = nb; |
| 79 | nb = itmp; |
| 80 | ltmp = a; |
| 81 | a = b; |
| 82 | b = ltmp; |
| 83 | } |
| 84 | rr = &(r[na]); |
| 85 | if (nb <= 0) { |
| 86 | (void)bn_mul_words(r, a, na, 0); |
| 87 | return; |
| 88 | } else { |
| 89 | rr[0] = bn_mul_words(r, a, na, b[0]); |
| 90 | } |
| 91 | |
| 92 | for (;;) { |
| 93 | if (--nb <= 0) { |
| 94 | return; |
| 95 | } |
| 96 | rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]); |
| 97 | if (--nb <= 0) { |
| 98 | return; |
| 99 | } |
| 100 | rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]); |
| 101 | if (--nb <= 0) { |
| 102 | return; |
| 103 | } |
| 104 | rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]); |
| 105 | if (--nb <= 0) { |
| 106 | return; |
| 107 | } |
| 108 | rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]); |
| 109 | rr += 4; |
| 110 | r += 4; |
| 111 | b += 4; |
| 112 | } |
| 113 | } |
| 114 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 115 | #if !defined(OPENSSL_X86) || defined(OPENSSL_NO_ASM) |
| 116 | /* Here follows specialised variants of bn_add_words() and bn_sub_words(). They |
| 117 | * have the property performing operations on arrays of different sizes. The |
| 118 | * sizes of those arrays is expressed through cl, which is the common length ( |
| 119 | * basicall, min(len(a),len(b)) ), and dl, which is the delta between the two |
| 120 | * lengths, calculated as len(a)-len(b). All lengths are the number of |
| 121 | * BN_ULONGs... For the operations that require a result array as parameter, |
| 122 | * it must have the length cl+abs(dl). These functions should probably end up |
| 123 | * in bn_asm.c as soon as there are assembler counterparts for the systems that |
| 124 | * use assembler files. */ |
| 125 | |
| 126 | static BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, |
| 127 | const BN_ULONG *b, int cl, int dl) { |
| 128 | BN_ULONG c, t; |
| 129 | |
| 130 | assert(cl >= 0); |
| 131 | c = bn_sub_words(r, a, b, cl); |
| 132 | |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 133 | if (dl == 0) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 134 | return c; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 135 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 136 | |
| 137 | r += cl; |
| 138 | a += cl; |
| 139 | b += cl; |
| 140 | |
| 141 | if (dl < 0) { |
| 142 | for (;;) { |
| 143 | t = b[0]; |
| 144 | r[0] = (0 - t - c) & BN_MASK2; |
| 145 | if (t != 0) { |
| 146 | c = 1; |
| 147 | } |
| 148 | if (++dl >= 0) { |
| 149 | break; |
| 150 | } |
| 151 | |
| 152 | t = b[1]; |
| 153 | r[1] = (0 - t - c) & BN_MASK2; |
| 154 | if (t != 0) { |
| 155 | c = 1; |
| 156 | } |
| 157 | if (++dl >= 0) { |
| 158 | break; |
| 159 | } |
| 160 | |
| 161 | t = b[2]; |
| 162 | r[2] = (0 - t - c) & BN_MASK2; |
| 163 | if (t != 0) { |
| 164 | c = 1; |
| 165 | } |
| 166 | if (++dl >= 0) { |
| 167 | break; |
| 168 | } |
| 169 | |
| 170 | t = b[3]; |
| 171 | r[3] = (0 - t - c) & BN_MASK2; |
| 172 | if (t != 0) { |
| 173 | c = 1; |
| 174 | } |
| 175 | if (++dl >= 0) { |
| 176 | break; |
| 177 | } |
| 178 | |
| 179 | b += 4; |
| 180 | r += 4; |
| 181 | } |
| 182 | } else { |
| 183 | int save_dl = dl; |
| 184 | while (c) { |
| 185 | t = a[0]; |
| 186 | r[0] = (t - c) & BN_MASK2; |
| 187 | if (t != 0) { |
| 188 | c = 0; |
| 189 | } |
| 190 | if (--dl <= 0) { |
| 191 | break; |
| 192 | } |
| 193 | |
| 194 | t = a[1]; |
| 195 | r[1] = (t - c) & BN_MASK2; |
| 196 | if (t != 0) { |
| 197 | c = 0; |
| 198 | } |
| 199 | if (--dl <= 0) { |
| 200 | break; |
| 201 | } |
| 202 | |
| 203 | t = a[2]; |
| 204 | r[2] = (t - c) & BN_MASK2; |
| 205 | if (t != 0) { |
| 206 | c = 0; |
| 207 | } |
| 208 | if (--dl <= 0) { |
| 209 | break; |
| 210 | } |
| 211 | |
| 212 | t = a[3]; |
| 213 | r[3] = (t - c) & BN_MASK2; |
| 214 | if (t != 0) { |
| 215 | c = 0; |
| 216 | } |
| 217 | if (--dl <= 0) { |
| 218 | break; |
| 219 | } |
| 220 | |
| 221 | save_dl = dl; |
| 222 | a += 4; |
| 223 | r += 4; |
| 224 | } |
| 225 | if (dl > 0) { |
| 226 | if (save_dl > dl) { |
| 227 | switch (save_dl - dl) { |
| 228 | case 1: |
| 229 | r[1] = a[1]; |
| 230 | if (--dl <= 0) { |
| 231 | break; |
| 232 | } |
| 233 | case 2: |
| 234 | r[2] = a[2]; |
| 235 | if (--dl <= 0) { |
| 236 | break; |
| 237 | } |
| 238 | case 3: |
| 239 | r[3] = a[3]; |
| 240 | if (--dl <= 0) { |
| 241 | break; |
| 242 | } |
| 243 | } |
| 244 | a += 4; |
| 245 | r += 4; |
| 246 | } |
| 247 | } |
| 248 | |
| 249 | if (dl > 0) { |
| 250 | for (;;) { |
| 251 | r[0] = a[0]; |
| 252 | if (--dl <= 0) { |
| 253 | break; |
| 254 | } |
| 255 | r[1] = a[1]; |
| 256 | if (--dl <= 0) { |
| 257 | break; |
| 258 | } |
| 259 | r[2] = a[2]; |
| 260 | if (--dl <= 0) { |
| 261 | break; |
| 262 | } |
| 263 | r[3] = a[3]; |
| 264 | if (--dl <= 0) { |
| 265 | break; |
| 266 | } |
| 267 | |
| 268 | a += 4; |
| 269 | r += 4; |
| 270 | } |
| 271 | } |
| 272 | } |
| 273 | |
| 274 | return c; |
| 275 | } |
| 276 | #else |
| 277 | /* On other platforms the function is defined in asm. */ |
| 278 | BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
| 279 | int cl, int dl); |
| 280 | #endif |
| 281 | |
| 282 | /* Karatsuba recursive multiplication algorithm |
| 283 | * (cf. Knuth, The Art of Computer Programming, Vol. 2) */ |
| 284 | |
| 285 | /* r is 2*n2 words in size, |
| 286 | * a and b are both n2 words in size. |
| 287 | * n2 must be a power of 2. |
| 288 | * We multiply and return the result. |
| 289 | * t must be 2*n2 words in size |
| 290 | * We calculate |
| 291 | * a[0]*b[0] |
| 292 | * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0]) |
| 293 | * a[1]*b[1] |
| 294 | */ |
| 295 | /* dnX may not be positive, but n2/2+dnX has to be */ |
| 296 | static void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, |
| 297 | int dna, int dnb, BN_ULONG *t) { |
| 298 | int n = n2 / 2, c1, c2; |
| 299 | int tna = n + dna, tnb = n + dnb; |
| 300 | unsigned int neg, zero; |
| 301 | BN_ULONG ln, lo, *p; |
| 302 | |
| 303 | /* Only call bn_mul_comba 8 if n2 == 8 and the |
| 304 | * two arrays are complete [steve] |
| 305 | */ |
| 306 | if (n2 == 8 && dna == 0 && dnb == 0) { |
| 307 | bn_mul_comba8(r, a, b); |
| 308 | return; |
| 309 | } |
| 310 | |
| 311 | /* Else do normal multiply */ |
| 312 | if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) { |
| 313 | bn_mul_normal(r, a, n2 + dna, b, n2 + dnb); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 314 | if ((dna + dnb) < 0) { |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 315 | OPENSSL_memset(&r[2 * n2 + dna + dnb], 0, |
| 316 | sizeof(BN_ULONG) * -(dna + dnb)); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 317 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 318 | return; |
| 319 | } |
| 320 | |
| 321 | /* r=(a[0]-a[1])*(b[1]-b[0]) */ |
| 322 | c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna); |
| 323 | c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n); |
| 324 | zero = neg = 0; |
| 325 | switch (c1 * 3 + c2) { |
| 326 | case -4: |
| 327 | bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */ |
| 328 | bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */ |
| 329 | break; |
| 330 | case -3: |
| 331 | zero = 1; |
| 332 | break; |
| 333 | case -2: |
| 334 | bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */ |
| 335 | bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */ |
| 336 | neg = 1; |
| 337 | break; |
| 338 | case -1: |
| 339 | case 0: |
| 340 | case 1: |
| 341 | zero = 1; |
| 342 | break; |
| 343 | case 2: |
| 344 | bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */ |
| 345 | bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */ |
| 346 | neg = 1; |
| 347 | break; |
| 348 | case 3: |
| 349 | zero = 1; |
| 350 | break; |
| 351 | case 4: |
| 352 | bn_sub_part_words(t, a, &(a[n]), tna, n - tna); |
| 353 | bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); |
| 354 | break; |
| 355 | } |
| 356 | |
| 357 | if (n == 4 && dna == 0 && dnb == 0) { |
| 358 | /* XXX: bn_mul_comba4 could take extra args to do this well */ |
| 359 | if (!zero) { |
| 360 | bn_mul_comba4(&(t[n2]), t, &(t[n])); |
| 361 | } else { |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 362 | OPENSSL_memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG)); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 363 | } |
| 364 | |
| 365 | bn_mul_comba4(r, a, b); |
| 366 | bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n])); |
| 367 | } else if (n == 8 && dna == 0 && dnb == 0) { |
| 368 | /* XXX: bn_mul_comba8 could take extra args to do this well */ |
| 369 | if (!zero) { |
| 370 | bn_mul_comba8(&(t[n2]), t, &(t[n])); |
| 371 | } else { |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 372 | OPENSSL_memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG)); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 373 | } |
| 374 | |
| 375 | bn_mul_comba8(r, a, b); |
| 376 | bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n])); |
| 377 | } else { |
| 378 | p = &(t[n2 * 2]); |
| 379 | if (!zero) { |
| 380 | bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p); |
| 381 | } else { |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 382 | OPENSSL_memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG)); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 383 | } |
| 384 | bn_mul_recursive(r, a, b, n, 0, 0, p); |
| 385 | bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p); |
| 386 | } |
| 387 | |
| 388 | /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign |
| 389 | * r[10] holds (a[0]*b[0]) |
| 390 | * r[32] holds (b[1]*b[1]) */ |
| 391 | |
| 392 | c1 = (int)(bn_add_words(t, r, &(r[n2]), n2)); |
| 393 | |
| 394 | if (neg) { |
| 395 | /* if t[32] is negative */ |
| 396 | c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2)); |
| 397 | } else { |
| 398 | /* Might have a carry */ |
| 399 | c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2)); |
| 400 | } |
| 401 | |
| 402 | /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) |
| 403 | * r[10] holds (a[0]*b[0]) |
| 404 | * r[32] holds (b[1]*b[1]) |
| 405 | * c1 holds the carry bits */ |
| 406 | c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2)); |
| 407 | if (c1) { |
| 408 | p = &(r[n + n2]); |
| 409 | lo = *p; |
| 410 | ln = (lo + c1) & BN_MASK2; |
| 411 | *p = ln; |
| 412 | |
| 413 | /* The overflow will stop before we over write |
| 414 | * words we should not overwrite */ |
| 415 | if (ln < (BN_ULONG)c1) { |
| 416 | do { |
| 417 | p++; |
| 418 | lo = *p; |
| 419 | ln = (lo + 1) & BN_MASK2; |
| 420 | *p = ln; |
| 421 | } while (ln == 0); |
| 422 | } |
| 423 | } |
| 424 | } |
| 425 | |
| 426 | /* n+tn is the word length |
| 427 | * t needs to be n*4 is size, as does r */ |
| 428 | /* tnX may not be negative but less than n */ |
| 429 | static void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n, |
| 430 | int tna, int tnb, BN_ULONG *t) { |
| 431 | int i, j, n2 = n * 2; |
| 432 | int c1, c2, neg; |
| 433 | BN_ULONG ln, lo, *p; |
| 434 | |
| 435 | if (n < 8) { |
| 436 | bn_mul_normal(r, a, n + tna, b, n + tnb); |
| 437 | return; |
| 438 | } |
| 439 | |
| 440 | /* r=(a[0]-a[1])*(b[1]-b[0]) */ |
| 441 | c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna); |
| 442 | c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n); |
| 443 | neg = 0; |
| 444 | switch (c1 * 3 + c2) { |
| 445 | case -4: |
| 446 | bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */ |
| 447 | bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */ |
| 448 | break; |
| 449 | case -3: |
| 450 | /* break; */ |
| 451 | case -2: |
| 452 | bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */ |
| 453 | bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */ |
| 454 | neg = 1; |
| 455 | break; |
| 456 | case -1: |
| 457 | case 0: |
| 458 | case 1: |
| 459 | /* break; */ |
| 460 | case 2: |
| 461 | bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */ |
| 462 | bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */ |
| 463 | neg = 1; |
| 464 | break; |
| 465 | case 3: |
| 466 | /* break; */ |
| 467 | case 4: |
| 468 | bn_sub_part_words(t, a, &(a[n]), tna, n - tna); |
| 469 | bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); |
| 470 | break; |
| 471 | } |
| 472 | |
| 473 | if (n == 8) { |
| 474 | bn_mul_comba8(&(t[n2]), t, &(t[n])); |
| 475 | bn_mul_comba8(r, a, b); |
| 476 | bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb); |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 477 | OPENSSL_memset(&(r[n2 + tna + tnb]), 0, sizeof(BN_ULONG) * (n2 - tna - tnb)); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 478 | } else { |
| 479 | p = &(t[n2 * 2]); |
| 480 | bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p); |
| 481 | bn_mul_recursive(r, a, b, n, 0, 0, p); |
| 482 | i = n / 2; |
| 483 | /* If there is only a bottom half to the number, |
| 484 | * just do it */ |
| 485 | if (tna > tnb) { |
| 486 | j = tna - i; |
| 487 | } else { |
| 488 | j = tnb - i; |
| 489 | } |
| 490 | |
| 491 | if (j == 0) { |
| 492 | bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i, p); |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 493 | OPENSSL_memset(&(r[n2 + i * 2]), 0, sizeof(BN_ULONG) * (n2 - i * 2)); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 494 | } else if (j > 0) { |
| 495 | /* eg, n == 16, i == 8 and tn == 11 */ |
| 496 | bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i, p); |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 497 | OPENSSL_memset(&(r[n2 + tna + tnb]), 0, |
| 498 | sizeof(BN_ULONG) * (n2 - tna - tnb)); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 499 | } else { |
| 500 | /* (j < 0) eg, n == 16, i == 8 and tn == 5 */ |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 501 | OPENSSL_memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 502 | if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL && |
| 503 | tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) { |
| 504 | bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb); |
| 505 | } else { |
| 506 | for (;;) { |
| 507 | i /= 2; |
| 508 | /* these simplified conditions work |
| 509 | * exclusively because difference |
| 510 | * between tna and tnb is 1 or 0 */ |
| 511 | if (i < tna || i < tnb) { |
| 512 | bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, |
| 513 | tnb - i, p); |
| 514 | break; |
| 515 | } else if (i == tna || i == tnb) { |
| 516 | bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i, |
| 517 | p); |
| 518 | break; |
| 519 | } |
| 520 | } |
| 521 | } |
| 522 | } |
| 523 | } |
| 524 | |
| 525 | /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign |
| 526 | * r[10] holds (a[0]*b[0]) |
| 527 | * r[32] holds (b[1]*b[1]) |
| 528 | */ |
| 529 | |
| 530 | c1 = (int)(bn_add_words(t, r, &(r[n2]), n2)); |
| 531 | |
| 532 | if (neg) { |
| 533 | /* if t[32] is negative */ |
| 534 | c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2)); |
| 535 | } else { |
| 536 | /* Might have a carry */ |
| 537 | c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2)); |
| 538 | } |
| 539 | |
| 540 | /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) |
| 541 | * r[10] holds (a[0]*b[0]) |
| 542 | * r[32] holds (b[1]*b[1]) |
| 543 | * c1 holds the carry bits */ |
| 544 | c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2)); |
| 545 | if (c1) { |
| 546 | p = &(r[n + n2]); |
| 547 | lo = *p; |
| 548 | ln = (lo + c1) & BN_MASK2; |
| 549 | *p = ln; |
| 550 | |
| 551 | /* The overflow will stop before we over write |
| 552 | * words we should not overwrite */ |
| 553 | if (ln < (BN_ULONG)c1) { |
| 554 | do { |
| 555 | p++; |
| 556 | lo = *p; |
| 557 | ln = (lo + 1) & BN_MASK2; |
| 558 | *p = ln; |
| 559 | } while (ln == 0); |
| 560 | } |
| 561 | } |
| 562 | } |
| 563 | |
| 564 | int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { |
| 565 | int ret = 0; |
| 566 | int top, al, bl; |
| 567 | BIGNUM *rr; |
| 568 | int i; |
| 569 | BIGNUM *t = NULL; |
| 570 | int j = 0, k; |
| 571 | |
| 572 | al = a->top; |
| 573 | bl = b->top; |
| 574 | |
| 575 | if ((al == 0) || (bl == 0)) { |
| 576 | BN_zero(r); |
| 577 | return 1; |
| 578 | } |
| 579 | top = al + bl; |
| 580 | |
| 581 | BN_CTX_start(ctx); |
| 582 | if ((r == a) || (r == b)) { |
| 583 | if ((rr = BN_CTX_get(ctx)) == NULL) { |
| 584 | goto err; |
| 585 | } |
| 586 | } else { |
| 587 | rr = r; |
| 588 | } |
| 589 | rr->neg = a->neg ^ b->neg; |
| 590 | |
| 591 | i = al - bl; |
| 592 | if (i == 0) { |
| 593 | if (al == 8) { |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 594 | if (!bn_wexpand(rr, 16)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 595 | goto err; |
| 596 | } |
| 597 | rr->top = 16; |
| 598 | bn_mul_comba8(rr->d, a->d, b->d); |
| 599 | goto end; |
| 600 | } |
| 601 | } |
| 602 | |
David Benjamin | 4969cc9 | 2016-04-22 15:02:23 -0400 | [diff] [blame] | 603 | static const int kMulNormalSize = 16; |
| 604 | if (al >= kMulNormalSize && bl >= kMulNormalSize) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 605 | if (i >= -1 && i <= 1) { |
| 606 | /* Find out the power of two lower or equal |
| 607 | to the longest of the two numbers */ |
| 608 | if (i >= 0) { |
| 609 | j = BN_num_bits_word((BN_ULONG)al); |
| 610 | } |
| 611 | if (i == -1) { |
| 612 | j = BN_num_bits_word((BN_ULONG)bl); |
| 613 | } |
| 614 | j = 1 << (j - 1); |
| 615 | assert(j <= al || j <= bl); |
| 616 | k = j + j; |
| 617 | t = BN_CTX_get(ctx); |
| 618 | if (t == NULL) { |
| 619 | goto err; |
| 620 | } |
| 621 | if (al > j || bl > j) { |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 622 | if (!bn_wexpand(t, k * 4)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 623 | goto err; |
| 624 | } |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 625 | if (!bn_wexpand(rr, k * 4)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 626 | goto err; |
| 627 | } |
| 628 | bn_mul_part_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d); |
| 629 | } else { |
| 630 | /* al <= j || bl <= j */ |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 631 | if (!bn_wexpand(t, k * 2)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 632 | goto err; |
| 633 | } |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 634 | if (!bn_wexpand(rr, k * 2)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 635 | goto err; |
| 636 | } |
| 637 | bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d); |
| 638 | } |
| 639 | rr->top = top; |
| 640 | goto end; |
| 641 | } |
| 642 | } |
| 643 | |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 644 | if (!bn_wexpand(rr, top)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 645 | goto err; |
| 646 | } |
| 647 | rr->top = top; |
| 648 | bn_mul_normal(rr->d, a->d, al, b->d, bl); |
| 649 | |
| 650 | end: |
| 651 | bn_correct_top(rr); |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 652 | if (r != rr && !BN_copy(r, rr)) { |
| 653 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 654 | } |
| 655 | ret = 1; |
| 656 | |
| 657 | err: |
| 658 | BN_CTX_end(ctx); |
| 659 | return ret; |
| 660 | } |
| 661 | |
| 662 | /* tmp must have 2*n words */ |
| 663 | static void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp) { |
| 664 | int i, j, max; |
| 665 | const BN_ULONG *ap; |
| 666 | BN_ULONG *rp; |
| 667 | |
| 668 | max = n * 2; |
| 669 | ap = a; |
| 670 | rp = r; |
| 671 | rp[0] = rp[max - 1] = 0; |
| 672 | rp++; |
| 673 | j = n; |
| 674 | |
| 675 | if (--j > 0) { |
| 676 | ap++; |
| 677 | rp[j] = bn_mul_words(rp, ap, j, ap[-1]); |
| 678 | rp += 2; |
| 679 | } |
| 680 | |
| 681 | for (i = n - 2; i > 0; i--) { |
| 682 | j--; |
| 683 | ap++; |
| 684 | rp[j] = bn_mul_add_words(rp, ap, j, ap[-1]); |
| 685 | rp += 2; |
| 686 | } |
| 687 | |
| 688 | bn_add_words(r, r, r, max); |
| 689 | |
| 690 | /* There will not be a carry */ |
| 691 | |
| 692 | bn_sqr_words(tmp, a, n); |
| 693 | |
| 694 | bn_add_words(r, r, tmp, max); |
| 695 | } |
| 696 | |
| 697 | /* r is 2*n words in size, |
| 698 | * a and b are both n words in size. (There's not actually a 'b' here ...) |
| 699 | * n must be a power of 2. |
| 700 | * We multiply and return the result. |
| 701 | * t must be 2*n words in size |
| 702 | * We calculate |
| 703 | * a[0]*b[0] |
| 704 | * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0]) |
| 705 | * a[1]*b[1] |
| 706 | */ |
| 707 | static void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t) { |
| 708 | int n = n2 / 2; |
| 709 | int zero, c1; |
| 710 | BN_ULONG ln, lo, *p; |
| 711 | |
| 712 | if (n2 == 4) { |
| 713 | bn_sqr_comba4(r, a); |
| 714 | return; |
| 715 | } else if (n2 == 8) { |
| 716 | bn_sqr_comba8(r, a); |
| 717 | return; |
| 718 | } |
| 719 | if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) { |
| 720 | bn_sqr_normal(r, a, n2, t); |
| 721 | return; |
| 722 | } |
| 723 | /* r=(a[0]-a[1])*(a[1]-a[0]) */ |
| 724 | c1 = bn_cmp_words(a, &(a[n]), n); |
| 725 | zero = 0; |
| 726 | if (c1 > 0) { |
| 727 | bn_sub_words(t, a, &(a[n]), n); |
| 728 | } else if (c1 < 0) { |
| 729 | bn_sub_words(t, &(a[n]), a, n); |
| 730 | } else { |
| 731 | zero = 1; |
| 732 | } |
| 733 | |
| 734 | /* The result will always be negative unless it is zero */ |
| 735 | p = &(t[n2 * 2]); |
| 736 | |
| 737 | if (!zero) { |
| 738 | bn_sqr_recursive(&(t[n2]), t, n, p); |
| 739 | } else { |
Robert Sloan | 69939df | 2017-01-09 10:53:07 -0800 | [diff] [blame] | 740 | OPENSSL_memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG)); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 741 | } |
| 742 | bn_sqr_recursive(r, a, n, p); |
| 743 | bn_sqr_recursive(&(r[n2]), &(a[n]), n, p); |
| 744 | |
| 745 | /* t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero |
| 746 | * r[10] holds (a[0]*b[0]) |
| 747 | * r[32] holds (b[1]*b[1]) */ |
| 748 | |
| 749 | c1 = (int)(bn_add_words(t, r, &(r[n2]), n2)); |
| 750 | |
| 751 | /* t[32] is negative */ |
| 752 | c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2)); |
| 753 | |
| 754 | /* t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1]) |
| 755 | * r[10] holds (a[0]*a[0]) |
| 756 | * r[32] holds (a[1]*a[1]) |
| 757 | * c1 holds the carry bits */ |
| 758 | c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2)); |
| 759 | if (c1) { |
| 760 | p = &(r[n + n2]); |
| 761 | lo = *p; |
| 762 | ln = (lo + c1) & BN_MASK2; |
| 763 | *p = ln; |
| 764 | |
| 765 | /* The overflow will stop before we over write |
| 766 | * words we should not overwrite */ |
| 767 | if (ln < (BN_ULONG)c1) { |
| 768 | do { |
| 769 | p++; |
| 770 | lo = *p; |
| 771 | ln = (lo + 1) & BN_MASK2; |
| 772 | *p = ln; |
| 773 | } while (ln == 0); |
| 774 | } |
| 775 | } |
| 776 | } |
| 777 | |
| 778 | int BN_mul_word(BIGNUM *bn, BN_ULONG w) { |
| 779 | BN_ULONG ll; |
| 780 | |
| 781 | w &= BN_MASK2; |
| 782 | if (!bn->top) { |
| 783 | return 1; |
| 784 | } |
| 785 | |
| 786 | if (w == 0) { |
| 787 | BN_zero(bn); |
| 788 | return 1; |
| 789 | } |
| 790 | |
| 791 | ll = bn_mul_words(bn->d, bn->d, bn->top, w); |
| 792 | if (ll) { |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 793 | if (!bn_wexpand(bn, bn->top + 1)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 794 | return 0; |
| 795 | } |
| 796 | bn->d[bn->top++] = ll; |
| 797 | } |
| 798 | |
| 799 | return 1; |
| 800 | } |
| 801 | |
| 802 | int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) { |
| 803 | int max, al; |
| 804 | int ret = 0; |
| 805 | BIGNUM *tmp, *rr; |
| 806 | |
| 807 | al = a->top; |
| 808 | if (al <= 0) { |
| 809 | r->top = 0; |
| 810 | r->neg = 0; |
| 811 | return 1; |
| 812 | } |
| 813 | |
| 814 | BN_CTX_start(ctx); |
| 815 | rr = (a != r) ? r : BN_CTX_get(ctx); |
| 816 | tmp = BN_CTX_get(ctx); |
| 817 | if (!rr || !tmp) { |
| 818 | goto err; |
| 819 | } |
| 820 | |
| 821 | max = 2 * al; /* Non-zero (from above) */ |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 822 | if (!bn_wexpand(rr, max)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 823 | goto err; |
| 824 | } |
| 825 | |
| 826 | if (al == 4) { |
| 827 | bn_sqr_comba4(rr->d, a->d); |
| 828 | } else if (al == 8) { |
| 829 | bn_sqr_comba8(rr->d, a->d); |
| 830 | } else { |
| 831 | if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) { |
| 832 | BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2]; |
| 833 | bn_sqr_normal(rr->d, a->d, al, t); |
| 834 | } else { |
| 835 | int j, k; |
| 836 | |
| 837 | j = BN_num_bits_word((BN_ULONG)al); |
| 838 | j = 1 << (j - 1); |
| 839 | k = j + j; |
| 840 | if (al == j) { |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 841 | if (!bn_wexpand(tmp, k * 2)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 842 | goto err; |
| 843 | } |
| 844 | bn_sqr_recursive(rr->d, a->d, al, tmp->d); |
| 845 | } else { |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 846 | if (!bn_wexpand(tmp, max)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 847 | goto err; |
| 848 | } |
| 849 | bn_sqr_normal(rr->d, a->d, al, tmp->d); |
| 850 | } |
| 851 | } |
| 852 | } |
| 853 | |
| 854 | rr->neg = 0; |
| 855 | /* If the most-significant half of the top word of 'a' is zero, then |
| 856 | * the square of 'a' will max-1 words. */ |
| 857 | if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l)) { |
| 858 | rr->top = max - 1; |
| 859 | } else { |
| 860 | rr->top = max; |
| 861 | } |
| 862 | |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 863 | if (rr != r && !BN_copy(r, rr)) { |
| 864 | goto err; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 865 | } |
| 866 | ret = 1; |
| 867 | |
| 868 | err: |
| 869 | BN_CTX_end(ctx); |
| 870 | return ret; |
| 871 | } |