]>
Commit | Line | Data |
---|---|---|
4f22f405 RS |
1 | /* |
2 | * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved. | |
aa8f3d76 | 3 | * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved |
4f22f405 RS |
4 | * |
5 | * Licensed under the OpenSSL license (the "License"). You may not use | |
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" |
1dc920c8 BM |
15 | #include "bn_lcl.h" |
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 | ||
25 | static const BN_ULONG SQR_tb[16] = { 0, 1, 4, 5, 16, 17, 20, 21, | |
26 | 64, 65, 68, 69, 80, 81, 84, 85 | |
27 | }; | |
1dc920c8 | 28 | |
1dc920c8 | 29 | /* Platform-specific macros to accelerate squaring. */ |
0f113f3e MC |
30 | # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) |
31 | # define SQR1(w) \ | |
1dc920c8 BM |
32 | SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \ |
33 | SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \ | |
34 | SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \ | |
35 | SQR_tb[(w) >> 36 & 0xF] << 8 | SQR_tb[(w) >> 32 & 0xF] | |
0f113f3e | 36 | # define SQR0(w) \ |
1dc920c8 BM |
37 | SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \ |
38 | SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \ | |
39 | SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \ | |
40 | SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF] | |
0f113f3e MC |
41 | # endif |
42 | # ifdef THIRTY_TWO_BIT | |
43 | # define SQR1(w) \ | |
1dc920c8 BM |
44 | SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \ |
45 | SQR_tb[(w) >> 20 & 0xF] << 8 | SQR_tb[(w) >> 16 & 0xF] | |
0f113f3e | 46 | # define SQR0(w) \ |
1dc920c8 BM |
47 | SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \ |
48 | SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF] | |
0f113f3e | 49 | # endif |
1dc920c8 | 50 | |
0f113f3e MC |
51 | # if !defined(OPENSSL_BN_ASM_GF2m) |
52 | /* | |
53 | * Product of two polynomials a, b each with degree < BN_BITS2 - 1, result is | |
54 | * a polynomial r with degree < 2 * BN_BITS - 1 The caller MUST ensure that | |
55 | * the variables have the right amount of space allocated. | |
1dc920c8 | 56 | */ |
0f113f3e MC |
57 | # ifdef THIRTY_TWO_BIT |
58 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, | |
59 | const BN_ULONG b) | |
60 | { | |
61 | register BN_ULONG h, l, s; | |
62 | BN_ULONG tab[8], top2b = a >> 30; | |
63 | register BN_ULONG a1, a2, a4; | |
64 | ||
65 | a1 = a & (0x3FFFFFFF); | |
66 | a2 = a1 << 1; | |
67 | a4 = a2 << 1; | |
68 | ||
69 | tab[0] = 0; | |
70 | tab[1] = a1; | |
71 | tab[2] = a2; | |
72 | tab[3] = a1 ^ a2; | |
73 | tab[4] = a4; | |
74 | tab[5] = a1 ^ a4; | |
75 | tab[6] = a2 ^ a4; | |
76 | tab[7] = a1 ^ a2 ^ a4; | |
77 | ||
78 | s = tab[b & 0x7]; | |
79 | l = s; | |
80 | s = tab[b >> 3 & 0x7]; | |
81 | l ^= s << 3; | |
82 | h = s >> 29; | |
83 | s = tab[b >> 6 & 0x7]; | |
84 | l ^= s << 6; | |
85 | h ^= s >> 26; | |
86 | s = tab[b >> 9 & 0x7]; | |
87 | l ^= s << 9; | |
88 | h ^= s >> 23; | |
89 | s = tab[b >> 12 & 0x7]; | |
90 | l ^= s << 12; | |
91 | h ^= s >> 20; | |
92 | s = tab[b >> 15 & 0x7]; | |
93 | l ^= s << 15; | |
94 | h ^= s >> 17; | |
95 | s = tab[b >> 18 & 0x7]; | |
96 | l ^= s << 18; | |
97 | h ^= s >> 14; | |
98 | s = tab[b >> 21 & 0x7]; | |
99 | l ^= s << 21; | |
100 | h ^= s >> 11; | |
101 | s = tab[b >> 24 & 0x7]; | |
102 | l ^= s << 24; | |
103 | h ^= s >> 8; | |
104 | s = tab[b >> 27 & 0x7]; | |
105 | l ^= s << 27; | |
106 | h ^= s >> 5; | |
107 | s = tab[b >> 30]; | |
108 | l ^= s << 30; | |
109 | h ^= s >> 2; | |
110 | ||
111 | /* compensate for the top two bits of a */ | |
112 | ||
113 | if (top2b & 01) { | |
114 | l ^= b << 30; | |
115 | h ^= b >> 2; | |
116 | } | |
117 | if (top2b & 02) { | |
118 | l ^= b << 31; | |
119 | h ^= b >> 1; | |
120 | } | |
121 | ||
122 | *r1 = h; | |
123 | *r0 = l; | |
124 | } | |
125 | # endif | |
126 | # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) | |
127 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, | |
128 | const BN_ULONG b) | |
129 | { | |
130 | register BN_ULONG h, l, s; | |
131 | BN_ULONG tab[16], top3b = a >> 61; | |
132 | register BN_ULONG a1, a2, a4, a8; | |
133 | ||
134 | a1 = a & (0x1FFFFFFFFFFFFFFFULL); | |
135 | a2 = a1 << 1; | |
136 | a4 = a2 << 1; | |
137 | a8 = a4 << 1; | |
138 | ||
139 | tab[0] = 0; | |
140 | tab[1] = a1; | |
141 | tab[2] = a2; | |
142 | tab[3] = a1 ^ a2; | |
143 | tab[4] = a4; | |
144 | tab[5] = a1 ^ a4; | |
145 | tab[6] = a2 ^ a4; | |
146 | tab[7] = a1 ^ a2 ^ a4; | |
147 | tab[8] = a8; | |
148 | tab[9] = a1 ^ a8; | |
149 | tab[10] = a2 ^ a8; | |
150 | tab[11] = a1 ^ a2 ^ a8; | |
151 | tab[12] = a4 ^ a8; | |
152 | tab[13] = a1 ^ a4 ^ a8; | |
153 | tab[14] = a2 ^ a4 ^ a8; | |
154 | tab[15] = a1 ^ a2 ^ a4 ^ a8; | |
155 | ||
156 | s = tab[b & 0xF]; | |
157 | l = s; | |
158 | s = tab[b >> 4 & 0xF]; | |
159 | l ^= s << 4; | |
160 | h = s >> 60; | |
161 | s = tab[b >> 8 & 0xF]; | |
162 | l ^= s << 8; | |
163 | h ^= s >> 56; | |
164 | s = tab[b >> 12 & 0xF]; | |
165 | l ^= s << 12; | |
166 | h ^= s >> 52; | |
167 | s = tab[b >> 16 & 0xF]; | |
168 | l ^= s << 16; | |
169 | h ^= s >> 48; | |
170 | s = tab[b >> 20 & 0xF]; | |
171 | l ^= s << 20; | |
172 | h ^= s >> 44; | |
173 | s = tab[b >> 24 & 0xF]; | |
174 | l ^= s << 24; | |
175 | h ^= s >> 40; | |
176 | s = tab[b >> 28 & 0xF]; | |
177 | l ^= s << 28; | |
178 | h ^= s >> 36; | |
179 | s = tab[b >> 32 & 0xF]; | |
180 | l ^= s << 32; | |
181 | h ^= s >> 32; | |
182 | s = tab[b >> 36 & 0xF]; | |
183 | l ^= s << 36; | |
184 | h ^= s >> 28; | |
185 | s = tab[b >> 40 & 0xF]; | |
186 | l ^= s << 40; | |
187 | h ^= s >> 24; | |
188 | s = tab[b >> 44 & 0xF]; | |
189 | l ^= s << 44; | |
190 | h ^= s >> 20; | |
191 | s = tab[b >> 48 & 0xF]; | |
192 | l ^= s << 48; | |
193 | h ^= s >> 16; | |
194 | s = tab[b >> 52 & 0xF]; | |
195 | l ^= s << 52; | |
196 | h ^= s >> 12; | |
197 | s = tab[b >> 56 & 0xF]; | |
198 | l ^= s << 56; | |
199 | h ^= s >> 8; | |
200 | s = tab[b >> 60]; | |
201 | l ^= s << 60; | |
202 | h ^= s >> 4; | |
203 | ||
204 | /* compensate for the top three bits of a */ | |
205 | ||
206 | if (top3b & 01) { | |
207 | l ^= b << 61; | |
208 | h ^= b >> 3; | |
209 | } | |
210 | if (top3b & 02) { | |
211 | l ^= b << 62; | |
212 | h ^= b >> 2; | |
213 | } | |
214 | if (top3b & 04) { | |
215 | l ^= b << 63; | |
216 | h ^= b >> 1; | |
217 | } | |
218 | ||
219 | *r1 = h; | |
220 | *r0 = l; | |
221 | } | |
222 | # endif | |
223 | ||
224 | /* | |
225 | * Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1, | |
226 | * result is a polynomial r with degree < 4 * BN_BITS2 - 1 The caller MUST | |
227 | * ensure that the variables have the right amount of space allocated. | |
1dc920c8 | 228 | */ |
0f113f3e MC |
229 | static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0, |
230 | const BN_ULONG b1, const BN_ULONG b0) | |
231 | { | |
232 | BN_ULONG m1, m0; | |
233 | /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */ | |
234 | bn_GF2m_mul_1x1(r + 3, r + 2, a1, b1); | |
235 | bn_GF2m_mul_1x1(r + 1, r, a0, b0); | |
236 | bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1); | |
237 | /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */ | |
238 | r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */ | |
239 | r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */ | |
240 | } | |
241 | # else | |
242 | void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1, | |
243 | BN_ULONG b0); | |
244 | # endif | |
245 | ||
246 | /* | |
247 | * Add polynomials a and b and store result in r; r could be a or b, a and b | |
1dc920c8 BM |
248 | * could be equal; r is the bitwise XOR of a and b. |
249 | */ | |
0f113f3e MC |
250 | int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) |
251 | { | |
252 | int i; | |
253 | const BIGNUM *at, *bt; | |
254 | ||
255 | bn_check_top(a); | |
256 | bn_check_top(b); | |
257 | ||
258 | if (a->top < b->top) { | |
259 | at = b; | |
260 | bt = a; | |
261 | } else { | |
262 | at = a; | |
263 | bt = b; | |
264 | } | |
265 | ||
266 | if (bn_wexpand(r, at->top) == NULL) | |
267 | return 0; | |
268 | ||
269 | for (i = 0; i < bt->top; i++) { | |
270 | r->d[i] = at->d[i] ^ bt->d[i]; | |
271 | } | |
272 | for (; i < at->top; i++) { | |
273 | r->d[i] = at->d[i]; | |
274 | } | |
275 | ||
276 | r->top = at->top; | |
277 | bn_correct_top(r); | |
278 | ||
279 | return 1; | |
280 | } | |
1dc920c8 | 281 | |
c80fd6b2 MC |
282 | /*- |
283 | * Some functions allow for representation of the irreducible polynomials | |
1dc920c8 BM |
284 | * as an int[], say p. The irreducible f(t) is then of the form: |
285 | * t^p[0] + t^p[1] + ... + t^p[k] | |
286 | * where m = p[0] > p[1] > ... > p[k] = 0. | |
287 | */ | |
288 | ||
1dc920c8 | 289 | /* Performs modular reduction of a and store result in r. r could be a. */ |
c4e7870a | 290 | int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]) |
0f113f3e MC |
291 | { |
292 | int j, k; | |
293 | int n, dN, d0, d1; | |
294 | BN_ULONG zz, *z; | |
295 | ||
296 | bn_check_top(a); | |
297 | ||
298 | if (!p[0]) { | |
299 | /* reduction mod 1 => return 0 */ | |
300 | BN_zero(r); | |
301 | return 1; | |
302 | } | |
303 | ||
304 | /* | |
305 | * Since the algorithm does reduction in the r value, if a != r, copy the | |
306 | * contents of a into r so we can do reduction in r. | |
307 | */ | |
308 | if (a != r) { | |
309 | if (!bn_wexpand(r, a->top)) | |
310 | return 0; | |
311 | for (j = 0; j < a->top; j++) { | |
312 | r->d[j] = a->d[j]; | |
313 | } | |
314 | r->top = a->top; | |
315 | } | |
316 | z = r->d; | |
317 | ||
318 | /* start reduction */ | |
319 | dN = p[0] / BN_BITS2; | |
320 | for (j = r->top - 1; j > dN;) { | |
321 | zz = z[j]; | |
322 | if (z[j] == 0) { | |
323 | j--; | |
324 | continue; | |
325 | } | |
326 | z[j] = 0; | |
327 | ||
328 | for (k = 1; p[k] != 0; k++) { | |
329 | /* reducing component t^p[k] */ | |
330 | n = p[0] - p[k]; | |
331 | d0 = n % BN_BITS2; | |
332 | d1 = BN_BITS2 - d0; | |
333 | n /= BN_BITS2; | |
334 | z[j - n] ^= (zz >> d0); | |
335 | if (d0) | |
336 | z[j - n - 1] ^= (zz << d1); | |
337 | } | |
338 | ||
339 | /* reducing component t^0 */ | |
340 | n = dN; | |
341 | d0 = p[0] % BN_BITS2; | |
342 | d1 = BN_BITS2 - d0; | |
343 | z[j - n] ^= (zz >> d0); | |
344 | if (d0) | |
345 | z[j - n - 1] ^= (zz << d1); | |
346 | } | |
347 | ||
348 | /* final round of reduction */ | |
349 | while (j == dN) { | |
350 | ||
351 | d0 = p[0] % BN_BITS2; | |
352 | zz = z[dN] >> d0; | |
353 | if (zz == 0) | |
354 | break; | |
355 | d1 = BN_BITS2 - d0; | |
356 | ||
357 | /* clear up the top d1 bits */ | |
358 | if (d0) | |
359 | z[dN] = (z[dN] << d1) >> d1; | |
360 | else | |
361 | z[dN] = 0; | |
362 | z[0] ^= zz; /* reduction t^0 component */ | |
363 | ||
364 | for (k = 1; p[k] != 0; k++) { | |
365 | BN_ULONG tmp_ulong; | |
366 | ||
367 | /* reducing component t^p[k] */ | |
368 | n = p[k] / BN_BITS2; | |
369 | d0 = p[k] % BN_BITS2; | |
370 | d1 = BN_BITS2 - d0; | |
371 | z[n] ^= (zz << d0); | |
86e5d1e3 | 372 | if (d0 && (tmp_ulong = zz >> d1)) |
0f113f3e MC |
373 | z[n + 1] ^= tmp_ulong; |
374 | } | |
375 | ||
376 | } | |
377 | ||
378 | bn_correct_top(r); | |
379 | return 1; | |
380 | } | |
381 | ||
382 | /* | |
383 | * Performs modular reduction of a by p and store result in r. r could be a. | |
1dc920c8 | 384 | * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper |
0f113f3e | 385 | * function is only provided for convenience; for best performance, use the |
1dc920c8 BM |
386 | * BN_GF2m_mod_arr function. |
387 | */ | |
0f113f3e MC |
388 | int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p) |
389 | { | |
390 | int ret = 0; | |
391 | int arr[6]; | |
392 | bn_check_top(a); | |
393 | bn_check_top(p); | |
b6eb9827 DSH |
394 | ret = BN_GF2m_poly2arr(p, arr, OSSL_NELEM(arr)); |
395 | if (!ret || ret > (int)OSSL_NELEM(arr)) { | |
0f113f3e MC |
396 | BNerr(BN_F_BN_GF2M_MOD, BN_R_INVALID_LENGTH); |
397 | return 0; | |
398 | } | |
399 | ret = BN_GF2m_mod_arr(r, a, arr); | |
400 | bn_check_top(r); | |
401 | return ret; | |
402 | } | |
403 | ||
404 | /* | |
405 | * Compute the product of two polynomials a and b, reduce modulo p, and store | |
1dc920c8 BM |
406 | * the result in r. r could be a or b; a could be b. |
407 | */ | |
0f113f3e MC |
408 | int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
409 | const int p[], BN_CTX *ctx) | |
410 | { | |
411 | int zlen, i, j, k, ret = 0; | |
412 | BIGNUM *s; | |
413 | BN_ULONG x1, x0, y1, y0, zz[4]; | |
414 | ||
415 | bn_check_top(a); | |
416 | bn_check_top(b); | |
417 | ||
418 | if (a == b) { | |
419 | return BN_GF2m_mod_sqr_arr(r, a, p, ctx); | |
420 | } | |
421 | ||
422 | BN_CTX_start(ctx); | |
423 | if ((s = BN_CTX_get(ctx)) == NULL) | |
424 | goto err; | |
425 | ||
426 | zlen = a->top + b->top + 4; | |
427 | if (!bn_wexpand(s, zlen)) | |
428 | goto err; | |
429 | s->top = zlen; | |
430 | ||
431 | for (i = 0; i < zlen; i++) | |
432 | s->d[i] = 0; | |
433 | ||
434 | for (j = 0; j < b->top; j += 2) { | |
435 | y0 = b->d[j]; | |
436 | y1 = ((j + 1) == b->top) ? 0 : b->d[j + 1]; | |
437 | for (i = 0; i < a->top; i += 2) { | |
438 | x0 = a->d[i]; | |
439 | x1 = ((i + 1) == a->top) ? 0 : a->d[i + 1]; | |
440 | bn_GF2m_mul_2x2(zz, x1, x0, y1, y0); | |
441 | for (k = 0; k < 4; k++) | |
442 | s->d[i + j + k] ^= zz[k]; | |
443 | } | |
444 | } | |
445 | ||
446 | bn_correct_top(s); | |
447 | if (BN_GF2m_mod_arr(r, s, p)) | |
448 | ret = 1; | |
449 | bn_check_top(r); | |
450 | ||
451 | err: | |
452 | BN_CTX_end(ctx); | |
453 | return ret; | |
454 | } | |
455 | ||
456 | /* | |
457 | * Compute the product of two polynomials a and b, reduce modulo p, and store | |
458 | * the result in r. r could be a or b; a could equal b. This function calls | |
459 | * down to the BN_GF2m_mod_mul_arr implementation; this wrapper function is | |
460 | * only provided for convenience; for best performance, use the | |
1dc920c8 BM |
461 | * BN_GF2m_mod_mul_arr function. |
462 | */ | |
0f113f3e MC |
463 | int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
464 | const BIGNUM *p, BN_CTX *ctx) | |
465 | { | |
466 | int ret = 0; | |
467 | const int max = BN_num_bits(p) + 1; | |
468 | int *arr = NULL; | |
469 | bn_check_top(a); | |
470 | bn_check_top(b); | |
471 | bn_check_top(p); | |
b4faea50 | 472 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL) |
0f113f3e MC |
473 | goto err; |
474 | ret = BN_GF2m_poly2arr(p, arr, max); | |
475 | if (!ret || ret > max) { | |
476 | BNerr(BN_F_BN_GF2M_MOD_MUL, BN_R_INVALID_LENGTH); | |
477 | goto err; | |
478 | } | |
479 | ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx); | |
480 | bn_check_top(r); | |
481 | err: | |
b548a1f1 | 482 | OPENSSL_free(arr); |
0f113f3e MC |
483 | return ret; |
484 | } | |
1dc920c8 BM |
485 | |
486 | /* Square a, reduce the result mod p, and store it in a. r could be a. */ | |
0f113f3e MC |
487 | int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[], |
488 | BN_CTX *ctx) | |
489 | { | |
490 | int i, ret = 0; | |
491 | BIGNUM *s; | |
492 | ||
493 | bn_check_top(a); | |
494 | BN_CTX_start(ctx); | |
495 | if ((s = BN_CTX_get(ctx)) == NULL) | |
3f6c7691 | 496 | goto err; |
0f113f3e MC |
497 | if (!bn_wexpand(s, 2 * a->top)) |
498 | goto err; | |
499 | ||
500 | for (i = a->top - 1; i >= 0; i--) { | |
501 | s->d[2 * i + 1] = SQR1(a->d[i]); | |
502 | s->d[2 * i] = SQR0(a->d[i]); | |
503 | } | |
504 | ||
505 | s->top = 2 * a->top; | |
506 | bn_correct_top(s); | |
507 | if (!BN_GF2m_mod_arr(r, s, p)) | |
508 | goto err; | |
509 | bn_check_top(r); | |
510 | ret = 1; | |
511 | err: | |
512 | BN_CTX_end(ctx); | |
513 | return ret; | |
514 | } | |
515 | ||
516 | /* | |
517 | * Square a, reduce the result mod p, and store it in a. r could be a. This | |
518 | * function calls down to the BN_GF2m_mod_sqr_arr implementation; this | |
519 | * wrapper function is only provided for convenience; for best performance, | |
520 | * use the BN_GF2m_mod_sqr_arr function. | |
1dc920c8 | 521 | */ |
0f113f3e MC |
522 | int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) |
523 | { | |
524 | int ret = 0; | |
525 | const int max = BN_num_bits(p) + 1; | |
526 | int *arr = NULL; | |
527 | ||
528 | bn_check_top(a); | |
529 | bn_check_top(p); | |
b4faea50 | 530 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL) |
0f113f3e MC |
531 | goto err; |
532 | ret = BN_GF2m_poly2arr(p, arr, max); | |
533 | if (!ret || ret > max) { | |
534 | BNerr(BN_F_BN_GF2M_MOD_SQR, BN_R_INVALID_LENGTH); | |
535 | goto err; | |
536 | } | |
537 | ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx); | |
538 | bn_check_top(r); | |
539 | err: | |
b548a1f1 | 540 | OPENSSL_free(arr); |
0f113f3e MC |
541 | return ret; |
542 | } | |
543 | ||
544 | /* | |
545 | * Invert a, reduce modulo p, and store the result in r. r could be a. Uses | |
546 | * Modified Almost Inverse Algorithm (Algorithm 10) from Hankerson, D., | |
547 | * Hernandez, J.L., and Menezes, A. "Software Implementation of Elliptic | |
548 | * Curve Cryptography Over Binary Fields". | |
1dc920c8 BM |
549 | */ |
550 | int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) | |
0f113f3e MC |
551 | { |
552 | BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp; | |
553 | int ret = 0; | |
554 | ||
555 | bn_check_top(a); | |
556 | bn_check_top(p); | |
557 | ||
558 | BN_CTX_start(ctx); | |
559 | ||
560 | if ((b = BN_CTX_get(ctx)) == NULL) | |
561 | goto err; | |
562 | if ((c = BN_CTX_get(ctx)) == NULL) | |
563 | goto err; | |
564 | if ((u = BN_CTX_get(ctx)) == NULL) | |
565 | goto err; | |
566 | if ((v = BN_CTX_get(ctx)) == NULL) | |
567 | goto err; | |
568 | ||
569 | if (!BN_GF2m_mod(u, a, p)) | |
570 | goto err; | |
571 | if (BN_is_zero(u)) | |
572 | goto err; | |
573 | ||
574 | if (!BN_copy(v, p)) | |
575 | goto err; | |
576 | # if 0 | |
577 | if (!BN_one(b)) | |
578 | goto err; | |
579 | ||
580 | while (1) { | |
581 | while (!BN_is_odd(u)) { | |
582 | if (BN_is_zero(u)) | |
583 | goto err; | |
584 | if (!BN_rshift1(u, u)) | |
585 | goto err; | |
586 | if (BN_is_odd(b)) { | |
587 | if (!BN_GF2m_add(b, b, p)) | |
588 | goto err; | |
589 | } | |
590 | if (!BN_rshift1(b, b)) | |
591 | goto err; | |
592 | } | |
593 | ||
594 | if (BN_abs_is_word(u, 1)) | |
595 | break; | |
596 | ||
597 | if (BN_num_bits(u) < BN_num_bits(v)) { | |
598 | tmp = u; | |
599 | u = v; | |
600 | v = tmp; | |
601 | tmp = b; | |
602 | b = c; | |
603 | c = tmp; | |
604 | } | |
605 | ||
606 | if (!BN_GF2m_add(u, u, v)) | |
607 | goto err; | |
608 | if (!BN_GF2m_add(b, b, c)) | |
609 | goto err; | |
610 | } | |
611 | # else | |
612 | { | |
4924b37e AP |
613 | int i; |
614 | int ubits = BN_num_bits(u); | |
615 | int vbits = BN_num_bits(v); /* v is copy of p */ | |
616 | int top = p->top; | |
0f113f3e MC |
617 | BN_ULONG *udp, *bdp, *vdp, *cdp; |
618 | ||
94b3664a PC |
619 | if (!bn_wexpand(u, top)) |
620 | goto err; | |
0f113f3e MC |
621 | udp = u->d; |
622 | for (i = u->top; i < top; i++) | |
623 | udp[i] = 0; | |
624 | u->top = top; | |
94b3664a PC |
625 | if (!bn_wexpand(b, top)) |
626 | goto err; | |
0f113f3e MC |
627 | bdp = b->d; |
628 | bdp[0] = 1; | |
629 | for (i = 1; i < top; i++) | |
630 | bdp[i] = 0; | |
631 | b->top = top; | |
94b3664a PC |
632 | if (!bn_wexpand(c, top)) |
633 | goto err; | |
0f113f3e MC |
634 | cdp = c->d; |
635 | for (i = 0; i < top; i++) | |
636 | cdp[i] = 0; | |
637 | c->top = top; | |
638 | vdp = v->d; /* It pays off to "cache" *->d pointers, | |
639 | * because it allows optimizer to be more | |
640 | * aggressive. But we don't have to "cache" | |
641 | * p->d, because *p is declared 'const'... */ | |
642 | while (1) { | |
643 | while (ubits && !(udp[0] & 1)) { | |
644 | BN_ULONG u0, u1, b0, b1, mask; | |
645 | ||
646 | u0 = udp[0]; | |
647 | b0 = bdp[0]; | |
648 | mask = (BN_ULONG)0 - (b0 & 1); | |
649 | b0 ^= p->d[0] & mask; | |
650 | for (i = 0; i < top - 1; i++) { | |
651 | u1 = udp[i + 1]; | |
652 | udp[i] = ((u0 >> 1) | (u1 << (BN_BITS2 - 1))) & BN_MASK2; | |
653 | u0 = u1; | |
654 | b1 = bdp[i + 1] ^ (p->d[i + 1] & mask); | |
655 | bdp[i] = ((b0 >> 1) | (b1 << (BN_BITS2 - 1))) & BN_MASK2; | |
656 | b0 = b1; | |
657 | } | |
658 | udp[i] = u0 >> 1; | |
659 | bdp[i] = b0 >> 1; | |
660 | ubits--; | |
661 | } | |
662 | ||
4924b37e AP |
663 | if (ubits <= BN_BITS2) { |
664 | if (udp[0] == 0) /* poly was reducible */ | |
665 | goto err; | |
666 | if (udp[0] == 1) | |
667 | break; | |
668 | } | |
0f113f3e MC |
669 | |
670 | if (ubits < vbits) { | |
671 | i = ubits; | |
672 | ubits = vbits; | |
673 | vbits = i; | |
674 | tmp = u; | |
675 | u = v; | |
676 | v = tmp; | |
677 | tmp = b; | |
678 | b = c; | |
679 | c = tmp; | |
680 | udp = vdp; | |
681 | vdp = v->d; | |
682 | bdp = cdp; | |
683 | cdp = c->d; | |
684 | } | |
685 | for (i = 0; i < top; i++) { | |
686 | udp[i] ^= vdp[i]; | |
687 | bdp[i] ^= cdp[i]; | |
688 | } | |
689 | if (ubits == vbits) { | |
690 | BN_ULONG ul; | |
691 | int utop = (ubits - 1) / BN_BITS2; | |
692 | ||
693 | while ((ul = udp[utop]) == 0 && utop) | |
694 | utop--; | |
695 | ubits = utop * BN_BITS2 + BN_num_bits_word(ul); | |
696 | } | |
697 | } | |
698 | bn_correct_top(b); | |
699 | } | |
700 | # endif | |
701 | ||
702 | if (!BN_copy(r, b)) | |
703 | goto err; | |
704 | bn_check_top(r); | |
705 | ret = 1; | |
706 | ||
707 | err: | |
708 | # ifdef BN_DEBUG /* BN_CTX_end would complain about the | |
709 | * expanded form */ | |
710 | bn_correct_top(c); | |
711 | bn_correct_top(u); | |
712 | bn_correct_top(v); | |
713 | # endif | |
714 | BN_CTX_end(ctx); | |
715 | return ret; | |
716 | } | |
717 | ||
718 | /* | |
719 | * Invert xx, reduce modulo p, and store the result in r. r could be xx. | |
720 | * This function calls down to the BN_GF2m_mod_inv implementation; this | |
721 | * wrapper function is only provided for convenience; for best performance, | |
722 | * use the BN_GF2m_mod_inv function. | |
1dc920c8 | 723 | */ |
0f113f3e MC |
724 | int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[], |
725 | BN_CTX *ctx) | |
726 | { | |
727 | BIGNUM *field; | |
728 | int ret = 0; | |
729 | ||
730 | bn_check_top(xx); | |
731 | BN_CTX_start(ctx); | |
732 | if ((field = BN_CTX_get(ctx)) == NULL) | |
733 | goto err; | |
734 | if (!BN_GF2m_arr2poly(p, field)) | |
735 | goto err; | |
736 | ||
737 | ret = BN_GF2m_mod_inv(r, xx, field, ctx); | |
738 | bn_check_top(r); | |
739 | ||
740 | err: | |
741 | BN_CTX_end(ctx); | |
742 | return ret; | |
743 | } | |
744 | ||
745 | # ifndef OPENSSL_SUN_GF2M_DIV | |
746 | /* | |
747 | * Divide y by x, reduce modulo p, and store the result in r. r could be x | |
1dc920c8 BM |
748 | * or y, x could equal y. |
749 | */ | |
0f113f3e MC |
750 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, |
751 | const BIGNUM *p, BN_CTX *ctx) | |
752 | { | |
753 | BIGNUM *xinv = NULL; | |
754 | int ret = 0; | |
755 | ||
756 | bn_check_top(y); | |
757 | bn_check_top(x); | |
758 | bn_check_top(p); | |
759 | ||
760 | BN_CTX_start(ctx); | |
761 | xinv = BN_CTX_get(ctx); | |
762 | if (xinv == NULL) | |
763 | goto err; | |
764 | ||
765 | if (!BN_GF2m_mod_inv(xinv, x, p, ctx)) | |
766 | goto err; | |
767 | if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx)) | |
768 | goto err; | |
769 | bn_check_top(r); | |
770 | ret = 1; | |
771 | ||
772 | err: | |
773 | BN_CTX_end(ctx); | |
774 | return ret; | |
775 | } | |
776 | # else | |
777 | /* | |
778 | * Divide y by x, reduce modulo p, and store the result in r. r could be x | |
779 | * or y, x could equal y. Uses algorithm Modular_Division_GF(2^m) from | |
780 | * Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to the | |
781 | * Great Divide". | |
1dc920c8 | 782 | */ |
0f113f3e MC |
783 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, |
784 | const BIGNUM *p, BN_CTX *ctx) | |
785 | { | |
786 | BIGNUM *a, *b, *u, *v; | |
787 | int ret = 0; | |
788 | ||
789 | bn_check_top(y); | |
790 | bn_check_top(x); | |
791 | bn_check_top(p); | |
792 | ||
793 | BN_CTX_start(ctx); | |
794 | ||
795 | a = BN_CTX_get(ctx); | |
796 | b = BN_CTX_get(ctx); | |
797 | u = BN_CTX_get(ctx); | |
798 | v = BN_CTX_get(ctx); | |
799 | if (v == NULL) | |
800 | goto err; | |
801 | ||
802 | /* reduce x and y mod p */ | |
803 | if (!BN_GF2m_mod(u, y, p)) | |
804 | goto err; | |
805 | if (!BN_GF2m_mod(a, x, p)) | |
806 | goto err; | |
807 | if (!BN_copy(b, p)) | |
808 | goto err; | |
809 | ||
810 | while (!BN_is_odd(a)) { | |
811 | if (!BN_rshift1(a, a)) | |
812 | goto err; | |
813 | if (BN_is_odd(u)) | |
814 | if (!BN_GF2m_add(u, u, p)) | |
815 | goto err; | |
816 | if (!BN_rshift1(u, u)) | |
817 | goto err; | |
818 | } | |
819 | ||
820 | do { | |
821 | if (BN_GF2m_cmp(b, a) > 0) { | |
822 | if (!BN_GF2m_add(b, b, a)) | |
823 | goto err; | |
824 | if (!BN_GF2m_add(v, v, u)) | |
825 | goto err; | |
826 | do { | |
827 | if (!BN_rshift1(b, b)) | |
828 | goto err; | |
829 | if (BN_is_odd(v)) | |
830 | if (!BN_GF2m_add(v, v, p)) | |
831 | goto err; | |
832 | if (!BN_rshift1(v, v)) | |
833 | goto err; | |
834 | } while (!BN_is_odd(b)); | |
835 | } else if (BN_abs_is_word(a, 1)) | |
836 | break; | |
837 | else { | |
838 | if (!BN_GF2m_add(a, a, b)) | |
839 | goto err; | |
840 | if (!BN_GF2m_add(u, u, v)) | |
841 | goto err; | |
842 | do { | |
843 | if (!BN_rshift1(a, a)) | |
844 | goto err; | |
845 | if (BN_is_odd(u)) | |
846 | if (!BN_GF2m_add(u, u, p)) | |
847 | goto err; | |
848 | if (!BN_rshift1(u, u)) | |
849 | goto err; | |
850 | } while (!BN_is_odd(a)); | |
851 | } | |
852 | } while (1); | |
853 | ||
854 | if (!BN_copy(r, u)) | |
855 | goto err; | |
856 | bn_check_top(r); | |
857 | ret = 1; | |
858 | ||
859 | err: | |
860 | BN_CTX_end(ctx); | |
861 | return ret; | |
862 | } | |
863 | # endif | |
864 | ||
865 | /* | |
866 | * Divide yy by xx, reduce modulo p, and store the result in r. r could be xx | |
867 | * * or yy, xx could equal yy. This function calls down to the | |
868 | * BN_GF2m_mod_div implementation; this wrapper function is only provided for | |
869 | * convenience; for best performance, use the BN_GF2m_mod_div function. | |
1dc920c8 | 870 | */ |
0f113f3e MC |
871 | int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx, |
872 | const int p[], BN_CTX *ctx) | |
873 | { | |
874 | BIGNUM *field; | |
875 | int ret = 0; | |
876 | ||
877 | bn_check_top(yy); | |
878 | bn_check_top(xx); | |
879 | ||
880 | BN_CTX_start(ctx); | |
881 | if ((field = BN_CTX_get(ctx)) == NULL) | |
882 | goto err; | |
883 | if (!BN_GF2m_arr2poly(p, field)) | |
884 | goto err; | |
885 | ||
886 | ret = BN_GF2m_mod_div(r, yy, xx, field, ctx); | |
887 | bn_check_top(r); | |
888 | ||
889 | err: | |
890 | BN_CTX_end(ctx); | |
891 | return ret; | |
892 | } | |
893 | ||
894 | /* | |
895 | * Compute the bth power of a, reduce modulo p, and store the result in r. r | |
896 | * could be a. Uses simple square-and-multiply algorithm A.5.1 from IEEE | |
897 | * P1363. | |
1dc920c8 | 898 | */ |
0f113f3e MC |
899 | int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
900 | const int p[], BN_CTX *ctx) | |
901 | { | |
902 | int ret = 0, i, n; | |
903 | BIGNUM *u; | |
904 | ||
905 | bn_check_top(a); | |
906 | bn_check_top(b); | |
907 | ||
908 | if (BN_is_zero(b)) | |
909 | return (BN_one(r)); | |
910 | ||
911 | if (BN_abs_is_word(b, 1)) | |
912 | return (BN_copy(r, a) != NULL); | |
913 | ||
914 | BN_CTX_start(ctx); | |
915 | if ((u = BN_CTX_get(ctx)) == NULL) | |
916 | goto err; | |
917 | ||
918 | if (!BN_GF2m_mod_arr(u, a, p)) | |
919 | goto err; | |
920 | ||
921 | n = BN_num_bits(b) - 1; | |
922 | for (i = n - 1; i >= 0; i--) { | |
923 | if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx)) | |
924 | goto err; | |
925 | if (BN_is_bit_set(b, i)) { | |
926 | if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx)) | |
927 | goto err; | |
928 | } | |
929 | } | |
930 | if (!BN_copy(r, u)) | |
931 | goto err; | |
932 | bn_check_top(r); | |
933 | ret = 1; | |
934 | err: | |
935 | BN_CTX_end(ctx); | |
936 | return ret; | |
937 | } | |
938 | ||
939 | /* | |
940 | * Compute the bth power of a, reduce modulo p, and store the result in r. r | |
941 | * could be a. This function calls down to the BN_GF2m_mod_exp_arr | |
942 | * implementation; this wrapper function is only provided for convenience; | |
943 | * for best performance, use the BN_GF2m_mod_exp_arr function. | |
1dc920c8 | 944 | */ |
0f113f3e MC |
945 | int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
946 | const BIGNUM *p, BN_CTX *ctx) | |
947 | { | |
948 | int ret = 0; | |
949 | const int max = BN_num_bits(p) + 1; | |
950 | int *arr = NULL; | |
951 | bn_check_top(a); | |
952 | bn_check_top(b); | |
953 | bn_check_top(p); | |
b4faea50 | 954 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL) |
0f113f3e MC |
955 | goto err; |
956 | ret = BN_GF2m_poly2arr(p, arr, max); | |
957 | if (!ret || ret > max) { | |
958 | BNerr(BN_F_BN_GF2M_MOD_EXP, BN_R_INVALID_LENGTH); | |
959 | goto err; | |
960 | } | |
961 | ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx); | |
962 | bn_check_top(r); | |
963 | err: | |
b548a1f1 | 964 | OPENSSL_free(arr); |
0f113f3e MC |
965 | return ret; |
966 | } | |
967 | ||
968 | /* | |
969 | * Compute the square root of a, reduce modulo p, and store the result in r. | |
970 | * r could be a. Uses exponentiation as in algorithm A.4.1 from IEEE P1363. | |
1dc920c8 | 971 | */ |
0f113f3e MC |
972 | int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[], |
973 | BN_CTX *ctx) | |
974 | { | |
975 | int ret = 0; | |
976 | BIGNUM *u; | |
977 | ||
978 | bn_check_top(a); | |
979 | ||
980 | if (!p[0]) { | |
981 | /* reduction mod 1 => return 0 */ | |
982 | BN_zero(r); | |
983 | return 1; | |
984 | } | |
985 | ||
986 | BN_CTX_start(ctx); | |
987 | if ((u = BN_CTX_get(ctx)) == NULL) | |
988 | goto err; | |
989 | ||
990 | if (!BN_set_bit(u, p[0] - 1)) | |
991 | goto err; | |
992 | ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx); | |
993 | bn_check_top(r); | |
994 | ||
995 | err: | |
996 | BN_CTX_end(ctx); | |
997 | return ret; | |
998 | } | |
999 | ||
1000 | /* | |
1001 | * Compute the square root of a, reduce modulo p, and store the result in r. | |
1002 | * r could be a. This function calls down to the BN_GF2m_mod_sqrt_arr | |
1003 | * implementation; this wrapper function is only provided for convenience; | |
1004 | * for best performance, use the BN_GF2m_mod_sqrt_arr function. | |
1dc920c8 BM |
1005 | */ |
1006 | int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) | |
0f113f3e MC |
1007 | { |
1008 | int ret = 0; | |
1009 | const int max = BN_num_bits(p) + 1; | |
1010 | int *arr = NULL; | |
1011 | bn_check_top(a); | |
1012 | bn_check_top(p); | |
b4faea50 | 1013 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL) |
0f113f3e MC |
1014 | goto err; |
1015 | ret = BN_GF2m_poly2arr(p, arr, max); | |
1016 | if (!ret || ret > max) { | |
1017 | BNerr(BN_F_BN_GF2M_MOD_SQRT, BN_R_INVALID_LENGTH); | |
1018 | goto err; | |
1019 | } | |
1020 | ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx); | |
1021 | bn_check_top(r); | |
1022 | err: | |
b548a1f1 | 1023 | OPENSSL_free(arr); |
0f113f3e MC |
1024 | return ret; |
1025 | } | |
1026 | ||
1027 | /* | |
1028 | * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns | |
1029 | * 0. Uses algorithms A.4.7 and A.4.6 from IEEE P1363. | |
1dc920c8 | 1030 | */ |
0f113f3e MC |
1031 | int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[], |
1032 | BN_CTX *ctx) | |
1033 | { | |
1034 | int ret = 0, count = 0, j; | |
1035 | BIGNUM *a, *z, *rho, *w, *w2, *tmp; | |
1036 | ||
1037 | bn_check_top(a_); | |
1038 | ||
1039 | if (!p[0]) { | |
1040 | /* reduction mod 1 => return 0 */ | |
1041 | BN_zero(r); | |
1042 | return 1; | |
1043 | } | |
1044 | ||
1045 | BN_CTX_start(ctx); | |
1046 | a = BN_CTX_get(ctx); | |
1047 | z = BN_CTX_get(ctx); | |
1048 | w = BN_CTX_get(ctx); | |
1049 | if (w == NULL) | |
1050 | goto err; | |
1051 | ||
1052 | if (!BN_GF2m_mod_arr(a, a_, p)) | |
1053 | goto err; | |
1054 | ||
1055 | if (BN_is_zero(a)) { | |
1056 | BN_zero(r); | |
1057 | ret = 1; | |
1058 | goto err; | |
1059 | } | |
1060 | ||
1061 | if (p[0] & 0x1) { /* m is odd */ | |
1062 | /* compute half-trace of a */ | |
1063 | if (!BN_copy(z, a)) | |
1064 | goto err; | |
1065 | for (j = 1; j <= (p[0] - 1) / 2; j++) { | |
1066 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) | |
1067 | goto err; | |
1068 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) | |
1069 | goto err; | |
1070 | if (!BN_GF2m_add(z, z, a)) | |
1071 | goto err; | |
1072 | } | |
1073 | ||
1074 | } else { /* m is even */ | |
1075 | ||
1076 | rho = BN_CTX_get(ctx); | |
1077 | w2 = BN_CTX_get(ctx); | |
1078 | tmp = BN_CTX_get(ctx); | |
1079 | if (tmp == NULL) | |
1080 | goto err; | |
1081 | do { | |
2301d91d | 1082 | if (!BN_rand(rho, p[0], BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY)) |
0f113f3e MC |
1083 | goto err; |
1084 | if (!BN_GF2m_mod_arr(rho, rho, p)) | |
1085 | goto err; | |
1086 | BN_zero(z); | |
1087 | if (!BN_copy(w, rho)) | |
1088 | goto err; | |
1089 | for (j = 1; j <= p[0] - 1; j++) { | |
1090 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) | |
1091 | goto err; | |
1092 | if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx)) | |
1093 | goto err; | |
1094 | if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx)) | |
1095 | goto err; | |
1096 | if (!BN_GF2m_add(z, z, tmp)) | |
1097 | goto err; | |
1098 | if (!BN_GF2m_add(w, w2, rho)) | |
1099 | goto err; | |
1100 | } | |
1101 | count++; | |
1102 | } while (BN_is_zero(w) && (count < MAX_ITERATIONS)); | |
1103 | if (BN_is_zero(w)) { | |
1104 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_TOO_MANY_ITERATIONS); | |
1105 | goto err; | |
1106 | } | |
1107 | } | |
1108 | ||
1109 | if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx)) | |
1110 | goto err; | |
1111 | if (!BN_GF2m_add(w, z, w)) | |
1112 | goto err; | |
1113 | if (BN_GF2m_cmp(w, a)) { | |
1114 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_NO_SOLUTION); | |
1115 | goto err; | |
1116 | } | |
1117 | ||
1118 | if (!BN_copy(r, z)) | |
1119 | goto err; | |
1120 | bn_check_top(r); | |
1121 | ||
1122 | ret = 1; | |
1123 | ||
1124 | err: | |
1125 | BN_CTX_end(ctx); | |
1126 | return ret; | |
1127 | } | |
1128 | ||
1129 | /* | |
1130 | * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns | |
1131 | * 0. This function calls down to the BN_GF2m_mod_solve_quad_arr | |
1132 | * implementation; this wrapper function is only provided for convenience; | |
1133 | * for best performance, use the BN_GF2m_mod_solve_quad_arr function. | |
1dc920c8 | 1134 | */ |
0f113f3e MC |
1135 | int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
1136 | BN_CTX *ctx) | |
1137 | { | |
1138 | int ret = 0; | |
1139 | const int max = BN_num_bits(p) + 1; | |
1140 | int *arr = NULL; | |
1141 | bn_check_top(a); | |
1142 | bn_check_top(p); | |
b4faea50 | 1143 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL) |
0f113f3e MC |
1144 | goto err; |
1145 | ret = BN_GF2m_poly2arr(p, arr, max); | |
1146 | if (!ret || ret > max) { | |
1147 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD, BN_R_INVALID_LENGTH); | |
1148 | goto err; | |
1149 | } | |
1150 | ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx); | |
1151 | bn_check_top(r); | |
1152 | err: | |
b548a1f1 | 1153 | OPENSSL_free(arr); |
0f113f3e MC |
1154 | return ret; |
1155 | } | |
1156 | ||
1157 | /* | |
1158 | * Convert the bit-string representation of a polynomial ( \sum_{i=0}^n a_i * | |
1159 | * x^i) into an array of integers corresponding to the bits with non-zero | |
1160 | * coefficient. Array is terminated with -1. Up to max elements of the array | |
1161 | * will be filled. Return value is total number of array elements that would | |
1162 | * be filled if array was large enough. | |
1dc920c8 | 1163 | */ |
c4e7870a | 1164 | int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max) |
0f113f3e MC |
1165 | { |
1166 | int i, j, k = 0; | |
1167 | BN_ULONG mask; | |
1168 | ||
1169 | if (BN_is_zero(a)) | |
1170 | return 0; | |
1171 | ||
1172 | for (i = a->top - 1; i >= 0; i--) { | |
1173 | if (!a->d[i]) | |
1174 | /* skip word if a->d[i] == 0 */ | |
1175 | continue; | |
1176 | mask = BN_TBIT; | |
1177 | for (j = BN_BITS2 - 1; j >= 0; j--) { | |
1178 | if (a->d[i] & mask) { | |
1179 | if (k < max) | |
1180 | p[k] = BN_BITS2 * i + j; | |
1181 | k++; | |
1182 | } | |
1183 | mask >>= 1; | |
1184 | } | |
1185 | } | |
1186 | ||
1187 | if (k < max) { | |
1188 | p[k] = -1; | |
1189 | k++; | |
1190 | } | |
1191 | ||
1192 | return k; | |
1193 | } | |
1194 | ||
1195 | /* | |
1196 | * Convert the coefficient array representation of a polynomial to a | |
c4e7870a | 1197 | * bit-string. The array must be terminated by -1. |
1dc920c8 | 1198 | */ |
c4e7870a | 1199 | int BN_GF2m_arr2poly(const int p[], BIGNUM *a) |
0f113f3e MC |
1200 | { |
1201 | int i; | |
1202 | ||
1203 | bn_check_top(a); | |
1204 | BN_zero(a); | |
1205 | for (i = 0; p[i] != -1; i++) { | |
1206 | if (BN_set_bit(a, p[i]) == 0) | |
1207 | return 0; | |
1208 | } | |
1209 | bn_check_top(a); | |
1210 | ||
1211 | return 1; | |
1212 | } | |
1dc920c8 | 1213 | |
b3310161 | 1214 | #endif |