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4f22f405 | 1 | /* |
f5afac4b | 2 | * Copyright 2002-2021 The OpenSSL Project Authors. All Rights Reserved. |
aa8f3d76 | 3 | * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved |
4f22f405 | 4 | * |
367ace68 | 5 | * Licensed under the Apache License 2.0 (the "License"). You may not use |
4f22f405 RS |
6 | * this file except in compliance with the License. You can obtain a copy |
7 | * in the file LICENSE in the source distribution or at | |
8 | * https://www.openssl.org/source/license.html | |
9 | */ | |
10 | ||
1dc920c8 BM |
11 | #include <assert.h> |
12 | #include <limits.h> | |
13 | #include <stdio.h> | |
b39fc560 | 14 | #include "internal/cryptlib.h" |
706457b7 | 15 | #include "bn_local.h" |
1dc920c8 | 16 | |
b3310161 DSH |
17 | #ifndef OPENSSL_NO_EC2M |
18 | ||
0f113f3e MC |
19 | /* |
20 | * Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should | |
21 | * fail. | |
22 | */ | |
23 | # define MAX_ITERATIONS 50 | |
24 | ||
b336ce57 MC |
25 | # define SQR_nibble(w) ((((w) & 8) << 3) \ |
26 | | (((w) & 4) << 2) \ | |
27 | | (((w) & 2) << 1) \ | |
28 | | ((w) & 1)) | |
29 | ||
1dc920c8 | 30 | |
1dc920c8 | 31 | /* Platform-specific macros to accelerate squaring. */ |
0f113f3e MC |
32 | # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) |
33 | # define SQR1(w) \ | |
b336ce57 MC |
34 | SQR_nibble((w) >> 60) << 56 | SQR_nibble((w) >> 56) << 48 | \ |
35 | SQR_nibble((w) >> 52) << 40 | SQR_nibble((w) >> 48) << 32 | \ | |
36 | SQR_nibble((w) >> 44) << 24 | SQR_nibble((w) >> 40) << 16 | \ | |
37 | SQR_nibble((w) >> 36) << 8 | SQR_nibble((w) >> 32) | |
0f113f3e | 38 | # define SQR0(w) \ |
b336ce57 MC |
39 | SQR_nibble((w) >> 28) << 56 | SQR_nibble((w) >> 24) << 48 | \ |
40 | SQR_nibble((w) >> 20) << 40 | SQR_nibble((w) >> 16) << 32 | \ | |
41 | SQR_nibble((w) >> 12) << 24 | SQR_nibble((w) >> 8) << 16 | \ | |
42 | SQR_nibble((w) >> 4) << 8 | SQR_nibble((w) ) | |
0f113f3e MC |
43 | # endif |
44 | # ifdef THIRTY_TWO_BIT | |
45 | # define SQR1(w) \ | |
b336ce57 MC |
46 | SQR_nibble((w) >> 28) << 24 | SQR_nibble((w) >> 24) << 16 | \ |
47 | SQR_nibble((w) >> 20) << 8 | SQR_nibble((w) >> 16) | |
0f113f3e | 48 | # define SQR0(w) \ |
b336ce57 MC |
49 | SQR_nibble((w) >> 12) << 24 | SQR_nibble((w) >> 8) << 16 | \ |
50 | SQR_nibble((w) >> 4) << 8 | SQR_nibble((w) ) | |
0f113f3e | 51 | # endif |
1dc920c8 | 52 | |
0f113f3e MC |
53 | # if !defined(OPENSSL_BN_ASM_GF2m) |
54 | /* | |
55 | * Product of two polynomials a, b each with degree < BN_BITS2 - 1, result is | |
56 | * a polynomial r with degree < 2 * BN_BITS - 1 The caller MUST ensure that | |
57 | * the variables have the right amount of space allocated. | |
1dc920c8 | 58 | */ |
0f113f3e MC |
59 | # ifdef THIRTY_TWO_BIT |
60 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, | |
61 | const BN_ULONG b) | |
62 | { | |
63 | register BN_ULONG h, l, s; | |
64 | BN_ULONG tab[8], top2b = a >> 30; | |
65 | register BN_ULONG a1, a2, a4; | |
66 | ||
67 | a1 = a & (0x3FFFFFFF); | |
68 | a2 = a1 << 1; | |
69 | a4 = a2 << 1; | |
70 | ||
71 | tab[0] = 0; | |
72 | tab[1] = a1; | |
73 | tab[2] = a2; | |
74 | tab[3] = a1 ^ a2; | |
75 | tab[4] = a4; | |
76 | tab[5] = a1 ^ a4; | |
77 | tab[6] = a2 ^ a4; | |
78 | tab[7] = a1 ^ a2 ^ a4; | |
79 | ||
80 | s = tab[b & 0x7]; | |
81 | l = s; | |
82 | s = tab[b >> 3 & 0x7]; | |
83 | l ^= s << 3; | |
84 | h = s >> 29; | |
85 | s = tab[b >> 6 & 0x7]; | |
86 | l ^= s << 6; | |
87 | h ^= s >> 26; | |
88 | s = tab[b >> 9 & 0x7]; | |
89 | l ^= s << 9; | |
90 | h ^= s >> 23; | |
91 | s = tab[b >> 12 & 0x7]; | |
92 | l ^= s << 12; | |
93 | h ^= s >> 20; | |
94 | s = tab[b >> 15 & 0x7]; | |
95 | l ^= s << 15; | |
96 | h ^= s >> 17; | |
97 | s = tab[b >> 18 & 0x7]; | |
98 | l ^= s << 18; | |
99 | h ^= s >> 14; | |
100 | s = tab[b >> 21 & 0x7]; | |
101 | l ^= s << 21; | |
102 | h ^= s >> 11; | |
103 | s = tab[b >> 24 & 0x7]; | |
104 | l ^= s << 24; | |
105 | h ^= s >> 8; | |
106 | s = tab[b >> 27 & 0x7]; | |
107 | l ^= s << 27; | |
108 | h ^= s >> 5; | |
109 | s = tab[b >> 30]; | |
110 | l ^= s << 30; | |
111 | h ^= s >> 2; | |
112 | ||
113 | /* compensate for the top two bits of a */ | |
114 | ||
115 | if (top2b & 01) { | |
116 | l ^= b << 30; | |
117 | h ^= b >> 2; | |
118 | } | |
119 | if (top2b & 02) { | |
120 | l ^= b << 31; | |
121 | h ^= b >> 1; | |
122 | } | |
123 | ||
124 | *r1 = h; | |
125 | *r0 = l; | |
126 | } | |
127 | # endif | |
128 | # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) | |
129 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, | |
130 | const BN_ULONG b) | |
131 | { | |
132 | register BN_ULONG h, l, s; | |
133 | BN_ULONG tab[16], top3b = a >> 61; | |
134 | register BN_ULONG a1, a2, a4, a8; | |
135 | ||
136 | a1 = a & (0x1FFFFFFFFFFFFFFFULL); | |
137 | a2 = a1 << 1; | |
138 | a4 = a2 << 1; | |
139 | a8 = a4 << 1; | |
140 | ||
141 | tab[0] = 0; | |
142 | tab[1] = a1; | |
143 | tab[2] = a2; | |
144 | tab[3] = a1 ^ a2; | |
145 | tab[4] = a4; | |
146 | tab[5] = a1 ^ a4; | |
147 | tab[6] = a2 ^ a4; | |
148 | tab[7] = a1 ^ a2 ^ a4; | |
149 | tab[8] = a8; | |
150 | tab[9] = a1 ^ a8; | |
151 | tab[10] = a2 ^ a8; | |
152 | tab[11] = a1 ^ a2 ^ a8; | |
153 | tab[12] = a4 ^ a8; | |
154 | tab[13] = a1 ^ a4 ^ a8; | |
155 | tab[14] = a2 ^ a4 ^ a8; | |
156 | tab[15] = a1 ^ a2 ^ a4 ^ a8; | |
157 | ||
158 | s = tab[b & 0xF]; | |
159 | l = s; | |
160 | s = tab[b >> 4 & 0xF]; | |
161 | l ^= s << 4; | |
162 | h = s >> 60; | |
163 | s = tab[b >> 8 & 0xF]; | |
164 | l ^= s << 8; | |
165 | h ^= s >> 56; | |
166 | s = tab[b >> 12 & 0xF]; | |
167 | l ^= s << 12; | |
168 | h ^= s >> 52; | |
169 | s = tab[b >> 16 & 0xF]; | |
170 | l ^= s << 16; | |
171 | h ^= s >> 48; | |
172 | s = tab[b >> 20 & 0xF]; | |
173 | l ^= s << 20; | |
174 | h ^= s >> 44; | |
175 | s = tab[b >> 24 & 0xF]; | |
176 | l ^= s << 24; | |
177 | h ^= s >> 40; | |
178 | s = tab[b >> 28 & 0xF]; | |
179 | l ^= s << 28; | |
180 | h ^= s >> 36; | |
181 | s = tab[b >> 32 & 0xF]; | |
182 | l ^= s << 32; | |
183 | h ^= s >> 32; | |
184 | s = tab[b >> 36 & 0xF]; | |
185 | l ^= s << 36; | |
186 | h ^= s >> 28; | |
187 | s = tab[b >> 40 & 0xF]; | |
188 | l ^= s << 40; | |
189 | h ^= s >> 24; | |
190 | s = tab[b >> 44 & 0xF]; | |
191 | l ^= s << 44; | |
192 | h ^= s >> 20; | |
193 | s = tab[b >> 48 & 0xF]; | |
194 | l ^= s << 48; | |
195 | h ^= s >> 16; | |
196 | s = tab[b >> 52 & 0xF]; | |
197 | l ^= s << 52; | |
198 | h ^= s >> 12; | |
199 | s = tab[b >> 56 & 0xF]; | |
200 | l ^= s << 56; | |
201 | h ^= s >> 8; | |
202 | s = tab[b >> 60]; | |
203 | l ^= s << 60; | |
204 | h ^= s >> 4; | |
205 | ||
206 | /* compensate for the top three bits of a */ | |
207 | ||
208 | if (top3b & 01) { | |
209 | l ^= b << 61; | |
210 | h ^= b >> 3; | |
211 | } | |
212 | if (top3b & 02) { | |
213 | l ^= b << 62; | |
214 | h ^= b >> 2; | |
215 | } | |
216 | if (top3b & 04) { | |
217 | l ^= b << 63; | |
218 | h ^= b >> 1; | |
219 | } | |
220 | ||
221 | *r1 = h; | |
222 | *r0 = l; | |
223 | } | |
224 | # endif | |
225 | ||
226 | /* | |
227 | * Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1, | |
228 | * result is a polynomial r with degree < 4 * BN_BITS2 - 1 The caller MUST | |
229 | * ensure that the variables have the right amount of space allocated. | |
1dc920c8 | 230 | */ |
0f113f3e MC |
231 | static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0, |
232 | const BN_ULONG b1, const BN_ULONG b0) | |
233 | { | |
234 | BN_ULONG m1, m0; | |
235 | /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */ | |
236 | bn_GF2m_mul_1x1(r + 3, r + 2, a1, b1); | |
237 | bn_GF2m_mul_1x1(r + 1, r, a0, b0); | |
238 | bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1); | |
239 | /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */ | |
240 | r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */ | |
241 | r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */ | |
242 | } | |
243 | # else | |
244 | void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1, | |
245 | BN_ULONG b0); | |
246 | # endif | |
247 | ||
248 | /* | |
249 | * Add polynomials a and b and store result in r; r could be a or b, a and b | |
1dc920c8 BM |
250 | * could be equal; r is the bitwise XOR of a and b. |
251 | */ | |
0f113f3e MC |
252 | int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) |
253 | { | |
254 | int i; | |
255 | const BIGNUM *at, *bt; | |
256 | ||
257 | bn_check_top(a); | |
258 | bn_check_top(b); | |
259 | ||
260 | if (a->top < b->top) { | |
261 | at = b; | |
262 | bt = a; | |
263 | } else { | |
264 | at = a; | |
265 | bt = b; | |
266 | } | |
267 | ||
268 | if (bn_wexpand(r, at->top) == NULL) | |
269 | return 0; | |
270 | ||
271 | for (i = 0; i < bt->top; i++) { | |
272 | r->d[i] = at->d[i] ^ bt->d[i]; | |
273 | } | |
274 | for (; i < at->top; i++) { | |
275 | r->d[i] = at->d[i]; | |
276 | } | |
277 | ||
278 | r->top = at->top; | |
279 | bn_correct_top(r); | |
280 | ||
281 | return 1; | |
282 | } | |
1dc920c8 | 283 | |
c80fd6b2 MC |
284 | /*- |
285 | * Some functions allow for representation of the irreducible polynomials | |
1dc920c8 BM |
286 | * as an int[], say p. The irreducible f(t) is then of the form: |
287 | * t^p[0] + t^p[1] + ... + t^p[k] | |
288 | * where m = p[0] > p[1] > ... > p[k] = 0. | |
289 | */ | |
290 | ||
1dc920c8 | 291 | /* Performs modular reduction of a and store result in r. r could be a. */ |
c4e7870a | 292 | int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]) |
0f113f3e MC |
293 | { |
294 | int j, k; | |
295 | int n, dN, d0, d1; | |
296 | BN_ULONG zz, *z; | |
297 | ||
298 | bn_check_top(a); | |
299 | ||
12a765a5 | 300 | if (p[0] == 0) { |
0f113f3e MC |
301 | /* reduction mod 1 => return 0 */ |
302 | BN_zero(r); | |
303 | return 1; | |
304 | } | |
305 | ||
306 | /* | |
307 | * Since the algorithm does reduction in the r value, if a != r, copy the | |
308 | * contents of a into r so we can do reduction in r. | |
309 | */ | |
310 | if (a != r) { | |
311 | if (!bn_wexpand(r, a->top)) | |
312 | return 0; | |
313 | for (j = 0; j < a->top; j++) { | |
314 | r->d[j] = a->d[j]; | |
315 | } | |
316 | r->top = a->top; | |
317 | } | |
318 | z = r->d; | |
319 | ||
320 | /* start reduction */ | |
321 | dN = p[0] / BN_BITS2; | |
322 | for (j = r->top - 1; j > dN;) { | |
323 | zz = z[j]; | |
324 | if (z[j] == 0) { | |
325 | j--; | |
326 | continue; | |
327 | } | |
328 | z[j] = 0; | |
329 | ||
330 | for (k = 1; p[k] != 0; k++) { | |
331 | /* reducing component t^p[k] */ | |
332 | n = p[0] - p[k]; | |
333 | d0 = n % BN_BITS2; | |
334 | d1 = BN_BITS2 - d0; | |
335 | n /= BN_BITS2; | |
336 | z[j - n] ^= (zz >> d0); | |
337 | if (d0) | |
338 | z[j - n - 1] ^= (zz << d1); | |
339 | } | |
340 | ||
341 | /* reducing component t^0 */ | |
342 | n = dN; | |
343 | d0 = p[0] % BN_BITS2; | |
344 | d1 = BN_BITS2 - d0; | |
345 | z[j - n] ^= (zz >> d0); | |
346 | if (d0) | |
347 | z[j - n - 1] ^= (zz << d1); | |
348 | } | |
349 | ||
350 | /* final round of reduction */ | |
351 | while (j == dN) { | |
352 | ||
353 | d0 = p[0] % BN_BITS2; | |
354 | zz = z[dN] >> d0; | |
355 | if (zz == 0) | |
356 | break; | |
357 | d1 = BN_BITS2 - d0; | |
358 | ||
359 | /* clear up the top d1 bits */ | |
360 | if (d0) | |
361 | z[dN] = (z[dN] << d1) >> d1; | |
362 | else | |
363 | z[dN] = 0; | |
364 | z[0] ^= zz; /* reduction t^0 component */ | |
365 | ||
366 | for (k = 1; p[k] != 0; k++) { | |
367 | BN_ULONG tmp_ulong; | |
368 | ||
369 | /* reducing component t^p[k] */ | |
370 | n = p[k] / BN_BITS2; | |
371 | d0 = p[k] % BN_BITS2; | |
372 | d1 = BN_BITS2 - d0; | |
373 | z[n] ^= (zz << d0); | |
86e5d1e3 | 374 | if (d0 && (tmp_ulong = zz >> d1)) |
0f113f3e MC |
375 | z[n + 1] ^= tmp_ulong; |
376 | } | |
377 | ||
378 | } | |
379 | ||
380 | bn_correct_top(r); | |
381 | return 1; | |
382 | } | |
383 | ||
384 | /* | |
385 | * Performs modular reduction of a by p and store result in r. r could be a. | |
1dc920c8 | 386 | * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper |
0f113f3e | 387 | * function is only provided for convenience; for best performance, use the |
1dc920c8 BM |
388 | * BN_GF2m_mod_arr function. |
389 | */ | |
0f113f3e MC |
390 | int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p) |
391 | { | |
392 | int ret = 0; | |
393 | int arr[6]; | |
394 | bn_check_top(a); | |
395 | bn_check_top(p); | |
b6eb9827 DSH |
396 | ret = BN_GF2m_poly2arr(p, arr, OSSL_NELEM(arr)); |
397 | if (!ret || ret > (int)OSSL_NELEM(arr)) { | |
9311d0c4 | 398 | ERR_raise(ERR_LIB_BN, BN_R_INVALID_LENGTH); |
0f113f3e MC |
399 | return 0; |
400 | } | |
401 | ret = BN_GF2m_mod_arr(r, a, arr); | |
402 | bn_check_top(r); | |
403 | return ret; | |
404 | } | |
405 | ||
406 | /* | |
407 | * Compute the product of two polynomials a and b, reduce modulo p, and store | |
1dc920c8 BM |
408 | * the result in r. r could be a or b; a could be b. |
409 | */ | |
0f113f3e MC |
410 | int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
411 | const int p[], BN_CTX *ctx) | |
412 | { | |
413 | int zlen, i, j, k, ret = 0; | |
414 | BIGNUM *s; | |
415 | BN_ULONG x1, x0, y1, y0, zz[4]; | |
416 | ||
417 | bn_check_top(a); | |
418 | bn_check_top(b); | |
419 | ||
420 | if (a == b) { | |
421 | return BN_GF2m_mod_sqr_arr(r, a, p, ctx); | |
422 | } | |
423 | ||
424 | BN_CTX_start(ctx); | |
425 | if ((s = BN_CTX_get(ctx)) == NULL) | |
426 | goto err; | |
427 | ||
428 | zlen = a->top + b->top + 4; | |
429 | if (!bn_wexpand(s, zlen)) | |
430 | goto err; | |
431 | s->top = zlen; | |
432 | ||
433 | for (i = 0; i < zlen; i++) | |
434 | s->d[i] = 0; | |
435 | ||
436 | for (j = 0; j < b->top; j += 2) { | |
437 | y0 = b->d[j]; | |
438 | y1 = ((j + 1) == b->top) ? 0 : b->d[j + 1]; | |
439 | for (i = 0; i < a->top; i += 2) { | |
440 | x0 = a->d[i]; | |
441 | x1 = ((i + 1) == a->top) ? 0 : a->d[i + 1]; | |
442 | bn_GF2m_mul_2x2(zz, x1, x0, y1, y0); | |
443 | for (k = 0; k < 4; k++) | |
444 | s->d[i + j + k] ^= zz[k]; | |
445 | } | |
446 | } | |
447 | ||
448 | bn_correct_top(s); | |
449 | if (BN_GF2m_mod_arr(r, s, p)) | |
450 | ret = 1; | |
451 | bn_check_top(r); | |
452 | ||
453 | err: | |
454 | BN_CTX_end(ctx); | |
455 | return ret; | |
456 | } | |
457 | ||
458 | /* | |
459 | * Compute the product of two polynomials a and b, reduce modulo p, and store | |
460 | * the result in r. r could be a or b; a could equal b. This function calls | |
461 | * down to the BN_GF2m_mod_mul_arr implementation; this wrapper function is | |
462 | * only provided for convenience; for best performance, use the | |
1dc920c8 BM |
463 | * BN_GF2m_mod_mul_arr function. |
464 | */ | |
0f113f3e MC |
465 | int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
466 | const BIGNUM *p, BN_CTX *ctx) | |
467 | { | |
468 | int ret = 0; | |
469 | const int max = BN_num_bits(p) + 1; | |
89947af2 F |
470 | int *arr; |
471 | ||
0f113f3e MC |
472 | bn_check_top(a); |
473 | bn_check_top(b); | |
474 | bn_check_top(p); | |
89947af2 F |
475 | |
476 | arr = OPENSSL_malloc(sizeof(*arr) * max); | |
477 | if (arr == NULL) { | |
478 | ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE); | |
479 | return 0; | |
480 | } | |
0f113f3e MC |
481 | ret = BN_GF2m_poly2arr(p, arr, max); |
482 | if (!ret || ret > max) { | |
9311d0c4 | 483 | ERR_raise(ERR_LIB_BN, BN_R_INVALID_LENGTH); |
0f113f3e MC |
484 | goto err; |
485 | } | |
486 | ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx); | |
487 | bn_check_top(r); | |
488 | err: | |
b548a1f1 | 489 | OPENSSL_free(arr); |
0f113f3e MC |
490 | return ret; |
491 | } | |
1dc920c8 BM |
492 | |
493 | /* Square a, reduce the result mod p, and store it in a. r could be a. */ | |
0f113f3e MC |
494 | int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[], |
495 | BN_CTX *ctx) | |
496 | { | |
497 | int i, ret = 0; | |
498 | BIGNUM *s; | |
499 | ||
500 | bn_check_top(a); | |
501 | BN_CTX_start(ctx); | |
502 | if ((s = BN_CTX_get(ctx)) == NULL) | |
3f6c7691 | 503 | goto err; |
0f113f3e MC |
504 | if (!bn_wexpand(s, 2 * a->top)) |
505 | goto err; | |
506 | ||
507 | for (i = a->top - 1; i >= 0; i--) { | |
508 | s->d[2 * i + 1] = SQR1(a->d[i]); | |
509 | s->d[2 * i] = SQR0(a->d[i]); | |
510 | } | |
511 | ||
512 | s->top = 2 * a->top; | |
513 | bn_correct_top(s); | |
514 | if (!BN_GF2m_mod_arr(r, s, p)) | |
515 | goto err; | |
516 | bn_check_top(r); | |
517 | ret = 1; | |
518 | err: | |
519 | BN_CTX_end(ctx); | |
520 | return ret; | |
521 | } | |
522 | ||
523 | /* | |
524 | * Square a, reduce the result mod p, and store it in a. r could be a. This | |
525 | * function calls down to the BN_GF2m_mod_sqr_arr implementation; this | |
526 | * wrapper function is only provided for convenience; for best performance, | |
527 | * use the BN_GF2m_mod_sqr_arr function. | |
1dc920c8 | 528 | */ |
0f113f3e MC |
529 | int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) |
530 | { | |
531 | int ret = 0; | |
532 | const int max = BN_num_bits(p) + 1; | |
89947af2 | 533 | int *arr; |
0f113f3e MC |
534 | |
535 | bn_check_top(a); | |
536 | bn_check_top(p); | |
89947af2 F |
537 | |
538 | arr = OPENSSL_malloc(sizeof(*arr) * max); | |
539 | if (arr == NULL) { | |
540 | ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE); | |
541 | return 0; | |
542 | } | |
0f113f3e MC |
543 | ret = BN_GF2m_poly2arr(p, arr, max); |
544 | if (!ret || ret > max) { | |
9311d0c4 | 545 | ERR_raise(ERR_LIB_BN, BN_R_INVALID_LENGTH); |
0f113f3e MC |
546 | goto err; |
547 | } | |
548 | ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx); | |
549 | bn_check_top(r); | |
550 | err: | |
b548a1f1 | 551 | OPENSSL_free(arr); |
0f113f3e MC |
552 | return ret; |
553 | } | |
554 | ||
555 | /* | |
556 | * Invert a, reduce modulo p, and store the result in r. r could be a. Uses | |
557 | * Modified Almost Inverse Algorithm (Algorithm 10) from Hankerson, D., | |
558 | * Hernandez, J.L., and Menezes, A. "Software Implementation of Elliptic | |
559 | * Curve Cryptography Over Binary Fields". | |
1dc920c8 | 560 | */ |
0dae8baf BB |
561 | static int BN_GF2m_mod_inv_vartime(BIGNUM *r, const BIGNUM *a, |
562 | const BIGNUM *p, BN_CTX *ctx) | |
0f113f3e MC |
563 | { |
564 | BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp; | |
565 | int ret = 0; | |
566 | ||
567 | bn_check_top(a); | |
568 | bn_check_top(p); | |
569 | ||
570 | BN_CTX_start(ctx); | |
571 | ||
edea42c6 PY |
572 | b = BN_CTX_get(ctx); |
573 | c = BN_CTX_get(ctx); | |
574 | u = BN_CTX_get(ctx); | |
575 | v = BN_CTX_get(ctx); | |
576 | if (v == NULL) | |
0f113f3e MC |
577 | goto err; |
578 | ||
579 | if (!BN_GF2m_mod(u, a, p)) | |
580 | goto err; | |
581 | if (BN_is_zero(u)) | |
582 | goto err; | |
583 | ||
584 | if (!BN_copy(v, p)) | |
585 | goto err; | |
586 | # if 0 | |
587 | if (!BN_one(b)) | |
588 | goto err; | |
589 | ||
590 | while (1) { | |
591 | while (!BN_is_odd(u)) { | |
592 | if (BN_is_zero(u)) | |
593 | goto err; | |
594 | if (!BN_rshift1(u, u)) | |
595 | goto err; | |
596 | if (BN_is_odd(b)) { | |
597 | if (!BN_GF2m_add(b, b, p)) | |
598 | goto err; | |
599 | } | |
600 | if (!BN_rshift1(b, b)) | |
601 | goto err; | |
602 | } | |
603 | ||
604 | if (BN_abs_is_word(u, 1)) | |
605 | break; | |
606 | ||
607 | if (BN_num_bits(u) < BN_num_bits(v)) { | |
608 | tmp = u; | |
609 | u = v; | |
610 | v = tmp; | |
611 | tmp = b; | |
612 | b = c; | |
613 | c = tmp; | |
614 | } | |
615 | ||
616 | if (!BN_GF2m_add(u, u, v)) | |
617 | goto err; | |
618 | if (!BN_GF2m_add(b, b, c)) | |
619 | goto err; | |
620 | } | |
621 | # else | |
622 | { | |
4924b37e AP |
623 | int i; |
624 | int ubits = BN_num_bits(u); | |
625 | int vbits = BN_num_bits(v); /* v is copy of p */ | |
626 | int top = p->top; | |
0f113f3e MC |
627 | BN_ULONG *udp, *bdp, *vdp, *cdp; |
628 | ||
94b3664a PC |
629 | if (!bn_wexpand(u, top)) |
630 | goto err; | |
0f113f3e MC |
631 | udp = u->d; |
632 | for (i = u->top; i < top; i++) | |
633 | udp[i] = 0; | |
634 | u->top = top; | |
94b3664a PC |
635 | if (!bn_wexpand(b, top)) |
636 | goto err; | |
0f113f3e MC |
637 | bdp = b->d; |
638 | bdp[0] = 1; | |
639 | for (i = 1; i < top; i++) | |
640 | bdp[i] = 0; | |
641 | b->top = top; | |
94b3664a PC |
642 | if (!bn_wexpand(c, top)) |
643 | goto err; | |
0f113f3e MC |
644 | cdp = c->d; |
645 | for (i = 0; i < top; i++) | |
646 | cdp[i] = 0; | |
647 | c->top = top; | |
648 | vdp = v->d; /* It pays off to "cache" *->d pointers, | |
649 | * because it allows optimizer to be more | |
650 | * aggressive. But we don't have to "cache" | |
651 | * p->d, because *p is declared 'const'... */ | |
652 | while (1) { | |
653 | while (ubits && !(udp[0] & 1)) { | |
654 | BN_ULONG u0, u1, b0, b1, mask; | |
655 | ||
656 | u0 = udp[0]; | |
657 | b0 = bdp[0]; | |
658 | mask = (BN_ULONG)0 - (b0 & 1); | |
659 | b0 ^= p->d[0] & mask; | |
660 | for (i = 0; i < top - 1; i++) { | |
661 | u1 = udp[i + 1]; | |
662 | udp[i] = ((u0 >> 1) | (u1 << (BN_BITS2 - 1))) & BN_MASK2; | |
663 | u0 = u1; | |
664 | b1 = bdp[i + 1] ^ (p->d[i + 1] & mask); | |
665 | bdp[i] = ((b0 >> 1) | (b1 << (BN_BITS2 - 1))) & BN_MASK2; | |
666 | b0 = b1; | |
667 | } | |
668 | udp[i] = u0 >> 1; | |
669 | bdp[i] = b0 >> 1; | |
670 | ubits--; | |
671 | } | |
672 | ||
4924b37e AP |
673 | if (ubits <= BN_BITS2) { |
674 | if (udp[0] == 0) /* poly was reducible */ | |
675 | goto err; | |
676 | if (udp[0] == 1) | |
677 | break; | |
678 | } | |
0f113f3e MC |
679 | |
680 | if (ubits < vbits) { | |
681 | i = ubits; | |
682 | ubits = vbits; | |
683 | vbits = i; | |
684 | tmp = u; | |
685 | u = v; | |
686 | v = tmp; | |
687 | tmp = b; | |
688 | b = c; | |
689 | c = tmp; | |
690 | udp = vdp; | |
691 | vdp = v->d; | |
692 | bdp = cdp; | |
693 | cdp = c->d; | |
694 | } | |
695 | for (i = 0; i < top; i++) { | |
696 | udp[i] ^= vdp[i]; | |
697 | bdp[i] ^= cdp[i]; | |
698 | } | |
699 | if (ubits == vbits) { | |
700 | BN_ULONG ul; | |
701 | int utop = (ubits - 1) / BN_BITS2; | |
702 | ||
703 | while ((ul = udp[utop]) == 0 && utop) | |
704 | utop--; | |
705 | ubits = utop * BN_BITS2 + BN_num_bits_word(ul); | |
706 | } | |
707 | } | |
708 | bn_correct_top(b); | |
709 | } | |
710 | # endif | |
711 | ||
712 | if (!BN_copy(r, b)) | |
713 | goto err; | |
714 | bn_check_top(r); | |
715 | ret = 1; | |
716 | ||
717 | err: | |
718 | # ifdef BN_DEBUG /* BN_CTX_end would complain about the | |
719 | * expanded form */ | |
720 | bn_correct_top(c); | |
721 | bn_correct_top(u); | |
722 | bn_correct_top(v); | |
723 | # endif | |
724 | BN_CTX_end(ctx); | |
725 | return ret; | |
726 | } | |
727 | ||
0dae8baf BB |
728 | /*- |
729 | * Wrapper for BN_GF2m_mod_inv_vartime that blinds the input before calling. | |
730 | * This is not constant time. | |
731 | * But it does eliminate first order deduction on the input. | |
732 | */ | |
733 | int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) | |
734 | { | |
735 | BIGNUM *b = NULL; | |
736 | int ret = 0; | |
737 | ||
738 | BN_CTX_start(ctx); | |
739 | if ((b = BN_CTX_get(ctx)) == NULL) | |
740 | goto err; | |
741 | ||
742 | /* generate blinding value */ | |
743 | do { | |
2934be91 MC |
744 | if (!BN_priv_rand_ex(b, BN_num_bits(p) - 1, |
745 | BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY, ctx)) | |
0dae8baf BB |
746 | goto err; |
747 | } while (BN_is_zero(b)); | |
748 | ||
749 | /* r := a * b */ | |
750 | if (!BN_GF2m_mod_mul(r, a, b, p, ctx)) | |
751 | goto err; | |
752 | ||
753 | /* r := 1/(a * b) */ | |
754 | if (!BN_GF2m_mod_inv_vartime(r, r, p, ctx)) | |
755 | goto err; | |
756 | ||
757 | /* r := b/(a * b) = 1/a */ | |
758 | if (!BN_GF2m_mod_mul(r, r, b, p, ctx)) | |
759 | goto err; | |
760 | ||
761 | ret = 1; | |
762 | ||
763 | err: | |
764 | BN_CTX_end(ctx); | |
765 | return ret; | |
766 | } | |
767 | ||
0f113f3e MC |
768 | /* |
769 | * Invert xx, reduce modulo p, and store the result in r. r could be xx. | |
770 | * This function calls down to the BN_GF2m_mod_inv implementation; this | |
771 | * wrapper function is only provided for convenience; for best performance, | |
772 | * use the BN_GF2m_mod_inv function. | |
1dc920c8 | 773 | */ |
0f113f3e MC |
774 | int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[], |
775 | BN_CTX *ctx) | |
776 | { | |
777 | BIGNUM *field; | |
778 | int ret = 0; | |
779 | ||
780 | bn_check_top(xx); | |
781 | BN_CTX_start(ctx); | |
782 | if ((field = BN_CTX_get(ctx)) == NULL) | |
783 | goto err; | |
784 | if (!BN_GF2m_arr2poly(p, field)) | |
785 | goto err; | |
786 | ||
787 | ret = BN_GF2m_mod_inv(r, xx, field, ctx); | |
788 | bn_check_top(r); | |
789 | ||
790 | err: | |
791 | BN_CTX_end(ctx); | |
792 | return ret; | |
793 | } | |
794 | ||
0f113f3e MC |
795 | /* |
796 | * Divide y by x, reduce modulo p, and store the result in r. r could be x | |
1dc920c8 BM |
797 | * or y, x could equal y. |
798 | */ | |
0f113f3e MC |
799 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, |
800 | const BIGNUM *p, BN_CTX *ctx) | |
801 | { | |
802 | BIGNUM *xinv = NULL; | |
803 | int ret = 0; | |
804 | ||
805 | bn_check_top(y); | |
806 | bn_check_top(x); | |
807 | bn_check_top(p); | |
808 | ||
809 | BN_CTX_start(ctx); | |
810 | xinv = BN_CTX_get(ctx); | |
811 | if (xinv == NULL) | |
812 | goto err; | |
813 | ||
814 | if (!BN_GF2m_mod_inv(xinv, x, p, ctx)) | |
815 | goto err; | |
816 | if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx)) | |
817 | goto err; | |
818 | bn_check_top(r); | |
819 | ret = 1; | |
820 | ||
821 | err: | |
822 | BN_CTX_end(ctx); | |
823 | return ret; | |
824 | } | |
0f113f3e MC |
825 | |
826 | /* | |
827 | * Divide yy by xx, reduce modulo p, and store the result in r. r could be xx | |
828 | * * or yy, xx could equal yy. This function calls down to the | |
829 | * BN_GF2m_mod_div implementation; this wrapper function is only provided for | |
830 | * convenience; for best performance, use the BN_GF2m_mod_div function. | |
1dc920c8 | 831 | */ |
0f113f3e MC |
832 | int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx, |
833 | const int p[], BN_CTX *ctx) | |
834 | { | |
835 | BIGNUM *field; | |
836 | int ret = 0; | |
837 | ||
838 | bn_check_top(yy); | |
839 | bn_check_top(xx); | |
840 | ||
841 | BN_CTX_start(ctx); | |
842 | if ((field = BN_CTX_get(ctx)) == NULL) | |
843 | goto err; | |
844 | if (!BN_GF2m_arr2poly(p, field)) | |
845 | goto err; | |
846 | ||
847 | ret = BN_GF2m_mod_div(r, yy, xx, field, ctx); | |
848 | bn_check_top(r); | |
849 | ||
850 | err: | |
851 | BN_CTX_end(ctx); | |
852 | return ret; | |
853 | } | |
854 | ||
855 | /* | |
856 | * Compute the bth power of a, reduce modulo p, and store the result in r. r | |
857 | * could be a. Uses simple square-and-multiply algorithm A.5.1 from IEEE | |
858 | * P1363. | |
1dc920c8 | 859 | */ |
0f113f3e MC |
860 | int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
861 | const int p[], BN_CTX *ctx) | |
862 | { | |
863 | int ret = 0, i, n; | |
864 | BIGNUM *u; | |
865 | ||
866 | bn_check_top(a); | |
867 | bn_check_top(b); | |
868 | ||
869 | if (BN_is_zero(b)) | |
26a7d938 | 870 | return BN_one(r); |
0f113f3e MC |
871 | |
872 | if (BN_abs_is_word(b, 1)) | |
873 | return (BN_copy(r, a) != NULL); | |
874 | ||
875 | BN_CTX_start(ctx); | |
876 | if ((u = BN_CTX_get(ctx)) == NULL) | |
877 | goto err; | |
878 | ||
879 | if (!BN_GF2m_mod_arr(u, a, p)) | |
880 | goto err; | |
881 | ||
882 | n = BN_num_bits(b) - 1; | |
883 | for (i = n - 1; i >= 0; i--) { | |
884 | if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx)) | |
885 | goto err; | |
886 | if (BN_is_bit_set(b, i)) { | |
887 | if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx)) | |
888 | goto err; | |
889 | } | |
890 | } | |
891 | if (!BN_copy(r, u)) | |
892 | goto err; | |
893 | bn_check_top(r); | |
894 | ret = 1; | |
895 | err: | |
896 | BN_CTX_end(ctx); | |
897 | return ret; | |
898 | } | |
899 | ||
900 | /* | |
901 | * Compute the bth power of a, reduce modulo p, and store the result in r. r | |
902 | * could be a. This function calls down to the BN_GF2m_mod_exp_arr | |
903 | * implementation; this wrapper function is only provided for convenience; | |
904 | * for best performance, use the BN_GF2m_mod_exp_arr function. | |
1dc920c8 | 905 | */ |
0f113f3e MC |
906 | int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
907 | const BIGNUM *p, BN_CTX *ctx) | |
908 | { | |
909 | int ret = 0; | |
910 | const int max = BN_num_bits(p) + 1; | |
89947af2 F |
911 | int *arr; |
912 | ||
0f113f3e MC |
913 | bn_check_top(a); |
914 | bn_check_top(b); | |
915 | bn_check_top(p); | |
89947af2 F |
916 | |
917 | arr = OPENSSL_malloc(sizeof(*arr) * max); | |
918 | if (arr == NULL) { | |
919 | ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE); | |
920 | return 0; | |
921 | } | |
0f113f3e MC |
922 | ret = BN_GF2m_poly2arr(p, arr, max); |
923 | if (!ret || ret > max) { | |
9311d0c4 | 924 | ERR_raise(ERR_LIB_BN, BN_R_INVALID_LENGTH); |
0f113f3e MC |
925 | goto err; |
926 | } | |
927 | ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx); | |
928 | bn_check_top(r); | |
929 | err: | |
b548a1f1 | 930 | OPENSSL_free(arr); |
0f113f3e MC |
931 | return ret; |
932 | } | |
933 | ||
934 | /* | |
935 | * Compute the square root of a, reduce modulo p, and store the result in r. | |
936 | * r could be a. Uses exponentiation as in algorithm A.4.1 from IEEE P1363. | |
1dc920c8 | 937 | */ |
0f113f3e MC |
938 | int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[], |
939 | BN_CTX *ctx) | |
940 | { | |
941 | int ret = 0; | |
942 | BIGNUM *u; | |
943 | ||
944 | bn_check_top(a); | |
945 | ||
12a765a5 | 946 | if (p[0] == 0) { |
0f113f3e MC |
947 | /* reduction mod 1 => return 0 */ |
948 | BN_zero(r); | |
949 | return 1; | |
950 | } | |
951 | ||
952 | BN_CTX_start(ctx); | |
953 | if ((u = BN_CTX_get(ctx)) == NULL) | |
954 | goto err; | |
955 | ||
956 | if (!BN_set_bit(u, p[0] - 1)) | |
957 | goto err; | |
958 | ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx); | |
959 | bn_check_top(r); | |
960 | ||
961 | err: | |
962 | BN_CTX_end(ctx); | |
963 | return ret; | |
964 | } | |
965 | ||
966 | /* | |
967 | * Compute the square root of a, reduce modulo p, and store the result in r. | |
968 | * r could be a. This function calls down to the BN_GF2m_mod_sqrt_arr | |
969 | * implementation; this wrapper function is only provided for convenience; | |
970 | * for best performance, use the BN_GF2m_mod_sqrt_arr function. | |
1dc920c8 BM |
971 | */ |
972 | int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) | |
0f113f3e MC |
973 | { |
974 | int ret = 0; | |
975 | const int max = BN_num_bits(p) + 1; | |
89947af2 F |
976 | int *arr; |
977 | ||
0f113f3e MC |
978 | bn_check_top(a); |
979 | bn_check_top(p); | |
89947af2 F |
980 | |
981 | arr = OPENSSL_malloc(sizeof(*arr) * max); | |
982 | if (arr == NULL) { | |
983 | ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE); | |
984 | return 0; | |
985 | } | |
0f113f3e MC |
986 | ret = BN_GF2m_poly2arr(p, arr, max); |
987 | if (!ret || ret > max) { | |
9311d0c4 | 988 | ERR_raise(ERR_LIB_BN, BN_R_INVALID_LENGTH); |
0f113f3e MC |
989 | goto err; |
990 | } | |
991 | ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx); | |
992 | bn_check_top(r); | |
993 | err: | |
b548a1f1 | 994 | OPENSSL_free(arr); |
0f113f3e MC |
995 | return ret; |
996 | } | |
997 | ||
998 | /* | |
999 | * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns | |
1000 | * 0. Uses algorithms A.4.7 and A.4.6 from IEEE P1363. | |
1dc920c8 | 1001 | */ |
0f113f3e MC |
1002 | int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[], |
1003 | BN_CTX *ctx) | |
1004 | { | |
1005 | int ret = 0, count = 0, j; | |
1006 | BIGNUM *a, *z, *rho, *w, *w2, *tmp; | |
1007 | ||
1008 | bn_check_top(a_); | |
1009 | ||
12a765a5 | 1010 | if (p[0] == 0) { |
0f113f3e MC |
1011 | /* reduction mod 1 => return 0 */ |
1012 | BN_zero(r); | |
1013 | return 1; | |
1014 | } | |
1015 | ||
1016 | BN_CTX_start(ctx); | |
1017 | a = BN_CTX_get(ctx); | |
1018 | z = BN_CTX_get(ctx); | |
1019 | w = BN_CTX_get(ctx); | |
1020 | if (w == NULL) | |
1021 | goto err; | |
1022 | ||
1023 | if (!BN_GF2m_mod_arr(a, a_, p)) | |
1024 | goto err; | |
1025 | ||
1026 | if (BN_is_zero(a)) { | |
1027 | BN_zero(r); | |
1028 | ret = 1; | |
1029 | goto err; | |
1030 | } | |
1031 | ||
1032 | if (p[0] & 0x1) { /* m is odd */ | |
1033 | /* compute half-trace of a */ | |
1034 | if (!BN_copy(z, a)) | |
1035 | goto err; | |
1036 | for (j = 1; j <= (p[0] - 1) / 2; j++) { | |
1037 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) | |
1038 | goto err; | |
1039 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) | |
1040 | goto err; | |
1041 | if (!BN_GF2m_add(z, z, a)) | |
1042 | goto err; | |
1043 | } | |
1044 | ||
1045 | } else { /* m is even */ | |
1046 | ||
1047 | rho = BN_CTX_get(ctx); | |
1048 | w2 = BN_CTX_get(ctx); | |
1049 | tmp = BN_CTX_get(ctx); | |
1050 | if (tmp == NULL) | |
1051 | goto err; | |
1052 | do { | |
2934be91 MC |
1053 | if (!BN_priv_rand_ex(rho, p[0], BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY, |
1054 | ctx)) | |
0f113f3e MC |
1055 | goto err; |
1056 | if (!BN_GF2m_mod_arr(rho, rho, p)) | |
1057 | goto err; | |
1058 | BN_zero(z); | |
1059 | if (!BN_copy(w, rho)) | |
1060 | goto err; | |
1061 | for (j = 1; j <= p[0] - 1; j++) { | |
1062 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) | |
1063 | goto err; | |
1064 | if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx)) | |
1065 | goto err; | |
1066 | if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx)) | |
1067 | goto err; | |
1068 | if (!BN_GF2m_add(z, z, tmp)) | |
1069 | goto err; | |
1070 | if (!BN_GF2m_add(w, w2, rho)) | |
1071 | goto err; | |
1072 | } | |
1073 | count++; | |
1074 | } while (BN_is_zero(w) && (count < MAX_ITERATIONS)); | |
1075 | if (BN_is_zero(w)) { | |
9311d0c4 | 1076 | ERR_raise(ERR_LIB_BN, BN_R_TOO_MANY_ITERATIONS); |
0f113f3e MC |
1077 | goto err; |
1078 | } | |
1079 | } | |
1080 | ||
1081 | if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx)) | |
1082 | goto err; | |
1083 | if (!BN_GF2m_add(w, z, w)) | |
1084 | goto err; | |
1085 | if (BN_GF2m_cmp(w, a)) { | |
9311d0c4 | 1086 | ERR_raise(ERR_LIB_BN, BN_R_NO_SOLUTION); |
0f113f3e MC |
1087 | goto err; |
1088 | } | |
1089 | ||
1090 | if (!BN_copy(r, z)) | |
1091 | goto err; | |
1092 | bn_check_top(r); | |
1093 | ||
1094 | ret = 1; | |
1095 | ||
1096 | err: | |
1097 | BN_CTX_end(ctx); | |
1098 | return ret; | |
1099 | } | |
1100 | ||
1101 | /* | |
1102 | * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns | |
1103 | * 0. This function calls down to the BN_GF2m_mod_solve_quad_arr | |
1104 | * implementation; this wrapper function is only provided for convenience; | |
1105 | * for best performance, use the BN_GF2m_mod_solve_quad_arr function. | |
1dc920c8 | 1106 | */ |
0f113f3e MC |
1107 | int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
1108 | BN_CTX *ctx) | |
1109 | { | |
1110 | int ret = 0; | |
1111 | const int max = BN_num_bits(p) + 1; | |
89947af2 F |
1112 | int *arr; |
1113 | ||
0f113f3e MC |
1114 | bn_check_top(a); |
1115 | bn_check_top(p); | |
89947af2 F |
1116 | |
1117 | arr = OPENSSL_malloc(sizeof(*arr) * max); | |
1118 | if (arr == NULL) { | |
1119 | ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE); | |
0f113f3e | 1120 | goto err; |
89947af2 | 1121 | } |
0f113f3e MC |
1122 | ret = BN_GF2m_poly2arr(p, arr, max); |
1123 | if (!ret || ret > max) { | |
9311d0c4 | 1124 | ERR_raise(ERR_LIB_BN, BN_R_INVALID_LENGTH); |
0f113f3e MC |
1125 | goto err; |
1126 | } | |
1127 | ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx); | |
1128 | bn_check_top(r); | |
1129 | err: | |
b548a1f1 | 1130 | OPENSSL_free(arr); |
0f113f3e MC |
1131 | return ret; |
1132 | } | |
1133 | ||
1134 | /* | |
1135 | * Convert the bit-string representation of a polynomial ( \sum_{i=0}^n a_i * | |
1136 | * x^i) into an array of integers corresponding to the bits with non-zero | |
1137 | * coefficient. Array is terminated with -1. Up to max elements of the array | |
1138 | * will be filled. Return value is total number of array elements that would | |
1139 | * be filled if array was large enough. | |
1dc920c8 | 1140 | */ |
c4e7870a | 1141 | int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max) |
0f113f3e MC |
1142 | { |
1143 | int i, j, k = 0; | |
1144 | BN_ULONG mask; | |
1145 | ||
1146 | if (BN_is_zero(a)) | |
1147 | return 0; | |
1148 | ||
1149 | for (i = a->top - 1; i >= 0; i--) { | |
1150 | if (!a->d[i]) | |
1151 | /* skip word if a->d[i] == 0 */ | |
1152 | continue; | |
1153 | mask = BN_TBIT; | |
1154 | for (j = BN_BITS2 - 1; j >= 0; j--) { | |
1155 | if (a->d[i] & mask) { | |
1156 | if (k < max) | |
1157 | p[k] = BN_BITS2 * i + j; | |
1158 | k++; | |
1159 | } | |
1160 | mask >>= 1; | |
1161 | } | |
1162 | } | |
1163 | ||
1164 | if (k < max) { | |
1165 | p[k] = -1; | |
1166 | k++; | |
1167 | } | |
1168 | ||
1169 | return k; | |
1170 | } | |
1171 | ||
1172 | /* | |
1173 | * Convert the coefficient array representation of a polynomial to a | |
c4e7870a | 1174 | * bit-string. The array must be terminated by -1. |
1dc920c8 | 1175 | */ |
c4e7870a | 1176 | int BN_GF2m_arr2poly(const int p[], BIGNUM *a) |
0f113f3e MC |
1177 | { |
1178 | int i; | |
1179 | ||
1180 | bn_check_top(a); | |
1181 | BN_zero(a); | |
1182 | for (i = 0; p[i] != -1; i++) { | |
1183 | if (BN_set_bit(a, p[i]) == 0) | |
1184 | return 0; | |
1185 | } | |
1186 | bn_check_top(a); | |
1187 | ||
1188 | return 1; | |
1189 | } | |
1dc920c8 | 1190 | |
b3310161 | 1191 | #endif |