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1dc920c8 BM |
1 | /* crypto/bn/bn_gf2m.c */ |
2 | /* ==================================================================== | |
3 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. | |
4 | * | |
5 | * The Elliptic Curve Public-Key Crypto Library (ECC Code) included | |
6 | * herein is developed by SUN MICROSYSTEMS, INC., and is contributed | |
7 | * to the OpenSSL project. | |
8 | * | |
9 | * The ECC Code is licensed pursuant to the OpenSSL open source | |
10 | * license provided below. | |
11 | * | |
12 | * In addition, Sun covenants to all licensees who provide a reciprocal | |
13 | * covenant with respect to their own patents if any, not to sue under | |
14 | * current and future patent claims necessarily infringed by the making, | |
15 | * using, practicing, selling, offering for sale and/or otherwise | |
16 | * disposing of the ECC Code as delivered hereunder (or portions thereof), | |
17 | * provided that such covenant shall not apply: | |
18 | * 1) for code that a licensee deletes from the ECC Code; | |
19 | * 2) separates from the ECC Code; or | |
20 | * 3) for infringements caused by: | |
21 | * i) the modification of the ECC Code or | |
22 | * ii) the combination of the ECC Code with other software or | |
23 | * devices where such combination causes the infringement. | |
24 | * | |
25 | * The software is originally written by Sheueling Chang Shantz and | |
26 | * Douglas Stebila of Sun Microsystems Laboratories. | |
27 | * | |
28 | */ | |
29 | ||
0f113f3e MC |
30 | /* |
31 | * NOTE: This file is licensed pursuant to the OpenSSL license below and may | |
32 | * be modified; but after modifications, the above covenant may no longer | |
33 | * apply! In such cases, the corresponding paragraph ["In addition, Sun | |
34 | * covenants ... causes the infringement."] and this note can be edited out; | |
35 | * but please keep the Sun copyright notice and attribution. | |
36 | */ | |
6c950e0d | 37 | |
1dc920c8 BM |
38 | /* ==================================================================== |
39 | * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. | |
40 | * | |
41 | * Redistribution and use in source and binary forms, with or without | |
42 | * modification, are permitted provided that the following conditions | |
43 | * are met: | |
44 | * | |
45 | * 1. Redistributions of source code must retain the above copyright | |
0f113f3e | 46 | * notice, this list of conditions and the following disclaimer. |
1dc920c8 BM |
47 | * |
48 | * 2. Redistributions in binary form must reproduce the above copyright | |
49 | * notice, this list of conditions and the following disclaimer in | |
50 | * the documentation and/or other materials provided with the | |
51 | * distribution. | |
52 | * | |
53 | * 3. All advertising materials mentioning features or use of this | |
54 | * software must display the following acknowledgment: | |
55 | * "This product includes software developed by the OpenSSL Project | |
56 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
57 | * | |
58 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
59 | * endorse or promote products derived from this software without | |
60 | * prior written permission. For written permission, please contact | |
61 | * openssl-core@openssl.org. | |
62 | * | |
63 | * 5. Products derived from this software may not be called "OpenSSL" | |
64 | * nor may "OpenSSL" appear in their names without prior written | |
65 | * permission of the OpenSSL Project. | |
66 | * | |
67 | * 6. Redistributions of any form whatsoever must retain the following | |
68 | * acknowledgment: | |
69 | * "This product includes software developed by the OpenSSL Project | |
70 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
71 | * | |
72 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
73 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
74 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
75 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
76 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
77 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
78 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
79 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
80 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
81 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
82 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
83 | * OF THE POSSIBILITY OF SUCH DAMAGE. | |
84 | * ==================================================================== | |
85 | * | |
86 | * This product includes cryptographic software written by Eric Young | |
87 | * (eay@cryptsoft.com). This product includes software written by Tim | |
88 | * Hudson (tjh@cryptsoft.com). | |
89 | * | |
90 | */ | |
91 | ||
92 | #include <assert.h> | |
93 | #include <limits.h> | |
94 | #include <stdio.h> | |
b39fc560 | 95 | #include "internal/cryptlib.h" |
1dc920c8 BM |
96 | #include "bn_lcl.h" |
97 | ||
b3310161 DSH |
98 | #ifndef OPENSSL_NO_EC2M |
99 | ||
0f113f3e MC |
100 | /* |
101 | * Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should | |
102 | * fail. | |
103 | */ | |
104 | # define MAX_ITERATIONS 50 | |
105 | ||
106 | static const BN_ULONG SQR_tb[16] = { 0, 1, 4, 5, 16, 17, 20, 21, | |
107 | 64, 65, 68, 69, 80, 81, 84, 85 | |
108 | }; | |
1dc920c8 | 109 | |
1dc920c8 | 110 | /* Platform-specific macros to accelerate squaring. */ |
0f113f3e MC |
111 | # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) |
112 | # define SQR1(w) \ | |
1dc920c8 BM |
113 | SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \ |
114 | SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \ | |
115 | SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \ | |
116 | SQR_tb[(w) >> 36 & 0xF] << 8 | SQR_tb[(w) >> 32 & 0xF] | |
0f113f3e | 117 | # define SQR0(w) \ |
1dc920c8 BM |
118 | SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \ |
119 | SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \ | |
120 | SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \ | |
121 | SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF] | |
0f113f3e MC |
122 | # endif |
123 | # ifdef THIRTY_TWO_BIT | |
124 | # define SQR1(w) \ | |
1dc920c8 BM |
125 | SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \ |
126 | SQR_tb[(w) >> 20 & 0xF] << 8 | SQR_tb[(w) >> 16 & 0xF] | |
0f113f3e | 127 | # define SQR0(w) \ |
1dc920c8 BM |
128 | SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \ |
129 | SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF] | |
0f113f3e | 130 | # endif |
1dc920c8 | 131 | |
0f113f3e MC |
132 | # if !defined(OPENSSL_BN_ASM_GF2m) |
133 | /* | |
134 | * Product of two polynomials a, b each with degree < BN_BITS2 - 1, result is | |
135 | * a polynomial r with degree < 2 * BN_BITS - 1 The caller MUST ensure that | |
136 | * the variables have the right amount of space allocated. | |
1dc920c8 | 137 | */ |
0f113f3e MC |
138 | # ifdef THIRTY_TWO_BIT |
139 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, | |
140 | const BN_ULONG b) | |
141 | { | |
142 | register BN_ULONG h, l, s; | |
143 | BN_ULONG tab[8], top2b = a >> 30; | |
144 | register BN_ULONG a1, a2, a4; | |
145 | ||
146 | a1 = a & (0x3FFFFFFF); | |
147 | a2 = a1 << 1; | |
148 | a4 = a2 << 1; | |
149 | ||
150 | tab[0] = 0; | |
151 | tab[1] = a1; | |
152 | tab[2] = a2; | |
153 | tab[3] = a1 ^ a2; | |
154 | tab[4] = a4; | |
155 | tab[5] = a1 ^ a4; | |
156 | tab[6] = a2 ^ a4; | |
157 | tab[7] = a1 ^ a2 ^ a4; | |
158 | ||
159 | s = tab[b & 0x7]; | |
160 | l = s; | |
161 | s = tab[b >> 3 & 0x7]; | |
162 | l ^= s << 3; | |
163 | h = s >> 29; | |
164 | s = tab[b >> 6 & 0x7]; | |
165 | l ^= s << 6; | |
166 | h ^= s >> 26; | |
167 | s = tab[b >> 9 & 0x7]; | |
168 | l ^= s << 9; | |
169 | h ^= s >> 23; | |
170 | s = tab[b >> 12 & 0x7]; | |
171 | l ^= s << 12; | |
172 | h ^= s >> 20; | |
173 | s = tab[b >> 15 & 0x7]; | |
174 | l ^= s << 15; | |
175 | h ^= s >> 17; | |
176 | s = tab[b >> 18 & 0x7]; | |
177 | l ^= s << 18; | |
178 | h ^= s >> 14; | |
179 | s = tab[b >> 21 & 0x7]; | |
180 | l ^= s << 21; | |
181 | h ^= s >> 11; | |
182 | s = tab[b >> 24 & 0x7]; | |
183 | l ^= s << 24; | |
184 | h ^= s >> 8; | |
185 | s = tab[b >> 27 & 0x7]; | |
186 | l ^= s << 27; | |
187 | h ^= s >> 5; | |
188 | s = tab[b >> 30]; | |
189 | l ^= s << 30; | |
190 | h ^= s >> 2; | |
191 | ||
192 | /* compensate for the top two bits of a */ | |
193 | ||
194 | if (top2b & 01) { | |
195 | l ^= b << 30; | |
196 | h ^= b >> 2; | |
197 | } | |
198 | if (top2b & 02) { | |
199 | l ^= b << 31; | |
200 | h ^= b >> 1; | |
201 | } | |
202 | ||
203 | *r1 = h; | |
204 | *r0 = l; | |
205 | } | |
206 | # endif | |
207 | # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) | |
208 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, | |
209 | const BN_ULONG b) | |
210 | { | |
211 | register BN_ULONG h, l, s; | |
212 | BN_ULONG tab[16], top3b = a >> 61; | |
213 | register BN_ULONG a1, a2, a4, a8; | |
214 | ||
215 | a1 = a & (0x1FFFFFFFFFFFFFFFULL); | |
216 | a2 = a1 << 1; | |
217 | a4 = a2 << 1; | |
218 | a8 = a4 << 1; | |
219 | ||
220 | tab[0] = 0; | |
221 | tab[1] = a1; | |
222 | tab[2] = a2; | |
223 | tab[3] = a1 ^ a2; | |
224 | tab[4] = a4; | |
225 | tab[5] = a1 ^ a4; | |
226 | tab[6] = a2 ^ a4; | |
227 | tab[7] = a1 ^ a2 ^ a4; | |
228 | tab[8] = a8; | |
229 | tab[9] = a1 ^ a8; | |
230 | tab[10] = a2 ^ a8; | |
231 | tab[11] = a1 ^ a2 ^ a8; | |
232 | tab[12] = a4 ^ a8; | |
233 | tab[13] = a1 ^ a4 ^ a8; | |
234 | tab[14] = a2 ^ a4 ^ a8; | |
235 | tab[15] = a1 ^ a2 ^ a4 ^ a8; | |
236 | ||
237 | s = tab[b & 0xF]; | |
238 | l = s; | |
239 | s = tab[b >> 4 & 0xF]; | |
240 | l ^= s << 4; | |
241 | h = s >> 60; | |
242 | s = tab[b >> 8 & 0xF]; | |
243 | l ^= s << 8; | |
244 | h ^= s >> 56; | |
245 | s = tab[b >> 12 & 0xF]; | |
246 | l ^= s << 12; | |
247 | h ^= s >> 52; | |
248 | s = tab[b >> 16 & 0xF]; | |
249 | l ^= s << 16; | |
250 | h ^= s >> 48; | |
251 | s = tab[b >> 20 & 0xF]; | |
252 | l ^= s << 20; | |
253 | h ^= s >> 44; | |
254 | s = tab[b >> 24 & 0xF]; | |
255 | l ^= s << 24; | |
256 | h ^= s >> 40; | |
257 | s = tab[b >> 28 & 0xF]; | |
258 | l ^= s << 28; | |
259 | h ^= s >> 36; | |
260 | s = tab[b >> 32 & 0xF]; | |
261 | l ^= s << 32; | |
262 | h ^= s >> 32; | |
263 | s = tab[b >> 36 & 0xF]; | |
264 | l ^= s << 36; | |
265 | h ^= s >> 28; | |
266 | s = tab[b >> 40 & 0xF]; | |
267 | l ^= s << 40; | |
268 | h ^= s >> 24; | |
269 | s = tab[b >> 44 & 0xF]; | |
270 | l ^= s << 44; | |
271 | h ^= s >> 20; | |
272 | s = tab[b >> 48 & 0xF]; | |
273 | l ^= s << 48; | |
274 | h ^= s >> 16; | |
275 | s = tab[b >> 52 & 0xF]; | |
276 | l ^= s << 52; | |
277 | h ^= s >> 12; | |
278 | s = tab[b >> 56 & 0xF]; | |
279 | l ^= s << 56; | |
280 | h ^= s >> 8; | |
281 | s = tab[b >> 60]; | |
282 | l ^= s << 60; | |
283 | h ^= s >> 4; | |
284 | ||
285 | /* compensate for the top three bits of a */ | |
286 | ||
287 | if (top3b & 01) { | |
288 | l ^= b << 61; | |
289 | h ^= b >> 3; | |
290 | } | |
291 | if (top3b & 02) { | |
292 | l ^= b << 62; | |
293 | h ^= b >> 2; | |
294 | } | |
295 | if (top3b & 04) { | |
296 | l ^= b << 63; | |
297 | h ^= b >> 1; | |
298 | } | |
299 | ||
300 | *r1 = h; | |
301 | *r0 = l; | |
302 | } | |
303 | # endif | |
304 | ||
305 | /* | |
306 | * Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1, | |
307 | * result is a polynomial r with degree < 4 * BN_BITS2 - 1 The caller MUST | |
308 | * ensure that the variables have the right amount of space allocated. | |
1dc920c8 | 309 | */ |
0f113f3e MC |
310 | static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0, |
311 | const BN_ULONG b1, const BN_ULONG b0) | |
312 | { | |
313 | BN_ULONG m1, m0; | |
314 | /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */ | |
315 | bn_GF2m_mul_1x1(r + 3, r + 2, a1, b1); | |
316 | bn_GF2m_mul_1x1(r + 1, r, a0, b0); | |
317 | bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1); | |
318 | /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */ | |
319 | r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */ | |
320 | r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */ | |
321 | } | |
322 | # else | |
323 | void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1, | |
324 | BN_ULONG b0); | |
325 | # endif | |
326 | ||
327 | /* | |
328 | * Add polynomials a and b and store result in r; r could be a or b, a and b | |
1dc920c8 BM |
329 | * could be equal; r is the bitwise XOR of a and b. |
330 | */ | |
0f113f3e MC |
331 | int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) |
332 | { | |
333 | int i; | |
334 | const BIGNUM *at, *bt; | |
335 | ||
336 | bn_check_top(a); | |
337 | bn_check_top(b); | |
338 | ||
339 | if (a->top < b->top) { | |
340 | at = b; | |
341 | bt = a; | |
342 | } else { | |
343 | at = a; | |
344 | bt = b; | |
345 | } | |
346 | ||
347 | if (bn_wexpand(r, at->top) == NULL) | |
348 | return 0; | |
349 | ||
350 | for (i = 0; i < bt->top; i++) { | |
351 | r->d[i] = at->d[i] ^ bt->d[i]; | |
352 | } | |
353 | for (; i < at->top; i++) { | |
354 | r->d[i] = at->d[i]; | |
355 | } | |
356 | ||
357 | r->top = at->top; | |
358 | bn_correct_top(r); | |
359 | ||
360 | return 1; | |
361 | } | |
1dc920c8 | 362 | |
c80fd6b2 MC |
363 | /*- |
364 | * Some functions allow for representation of the irreducible polynomials | |
1dc920c8 BM |
365 | * as an int[], say p. The irreducible f(t) is then of the form: |
366 | * t^p[0] + t^p[1] + ... + t^p[k] | |
367 | * where m = p[0] > p[1] > ... > p[k] = 0. | |
368 | */ | |
369 | ||
1dc920c8 | 370 | /* Performs modular reduction of a and store result in r. r could be a. */ |
c4e7870a | 371 | int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]) |
0f113f3e MC |
372 | { |
373 | int j, k; | |
374 | int n, dN, d0, d1; | |
375 | BN_ULONG zz, *z; | |
376 | ||
377 | bn_check_top(a); | |
378 | ||
379 | if (!p[0]) { | |
380 | /* reduction mod 1 => return 0 */ | |
381 | BN_zero(r); | |
382 | return 1; | |
383 | } | |
384 | ||
385 | /* | |
386 | * Since the algorithm does reduction in the r value, if a != r, copy the | |
387 | * contents of a into r so we can do reduction in r. | |
388 | */ | |
389 | if (a != r) { | |
390 | if (!bn_wexpand(r, a->top)) | |
391 | return 0; | |
392 | for (j = 0; j < a->top; j++) { | |
393 | r->d[j] = a->d[j]; | |
394 | } | |
395 | r->top = a->top; | |
396 | } | |
397 | z = r->d; | |
398 | ||
399 | /* start reduction */ | |
400 | dN = p[0] / BN_BITS2; | |
401 | for (j = r->top - 1; j > dN;) { | |
402 | zz = z[j]; | |
403 | if (z[j] == 0) { | |
404 | j--; | |
405 | continue; | |
406 | } | |
407 | z[j] = 0; | |
408 | ||
409 | for (k = 1; p[k] != 0; k++) { | |
410 | /* reducing component t^p[k] */ | |
411 | n = p[0] - p[k]; | |
412 | d0 = n % BN_BITS2; | |
413 | d1 = BN_BITS2 - d0; | |
414 | n /= BN_BITS2; | |
415 | z[j - n] ^= (zz >> d0); | |
416 | if (d0) | |
417 | z[j - n - 1] ^= (zz << d1); | |
418 | } | |
419 | ||
420 | /* reducing component t^0 */ | |
421 | n = dN; | |
422 | d0 = p[0] % BN_BITS2; | |
423 | d1 = BN_BITS2 - d0; | |
424 | z[j - n] ^= (zz >> d0); | |
425 | if (d0) | |
426 | z[j - n - 1] ^= (zz << d1); | |
427 | } | |
428 | ||
429 | /* final round of reduction */ | |
430 | while (j == dN) { | |
431 | ||
432 | d0 = p[0] % BN_BITS2; | |
433 | zz = z[dN] >> d0; | |
434 | if (zz == 0) | |
435 | break; | |
436 | d1 = BN_BITS2 - d0; | |
437 | ||
438 | /* clear up the top d1 bits */ | |
439 | if (d0) | |
440 | z[dN] = (z[dN] << d1) >> d1; | |
441 | else | |
442 | z[dN] = 0; | |
443 | z[0] ^= zz; /* reduction t^0 component */ | |
444 | ||
445 | for (k = 1; p[k] != 0; k++) { | |
446 | BN_ULONG tmp_ulong; | |
447 | ||
448 | /* reducing component t^p[k] */ | |
449 | n = p[k] / BN_BITS2; | |
450 | d0 = p[k] % BN_BITS2; | |
451 | d1 = BN_BITS2 - d0; | |
452 | z[n] ^= (zz << d0); | |
86e5d1e3 | 453 | if (d0 && (tmp_ulong = zz >> d1)) |
0f113f3e MC |
454 | z[n + 1] ^= tmp_ulong; |
455 | } | |
456 | ||
457 | } | |
458 | ||
459 | bn_correct_top(r); | |
460 | return 1; | |
461 | } | |
462 | ||
463 | /* | |
464 | * Performs modular reduction of a by p and store result in r. r could be a. | |
1dc920c8 | 465 | * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper |
0f113f3e | 466 | * function is only provided for convenience; for best performance, use the |
1dc920c8 BM |
467 | * BN_GF2m_mod_arr function. |
468 | */ | |
0f113f3e MC |
469 | int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p) |
470 | { | |
471 | int ret = 0; | |
472 | int arr[6]; | |
473 | bn_check_top(a); | |
474 | bn_check_top(p); | |
b6eb9827 DSH |
475 | ret = BN_GF2m_poly2arr(p, arr, OSSL_NELEM(arr)); |
476 | if (!ret || ret > (int)OSSL_NELEM(arr)) { | |
0f113f3e MC |
477 | BNerr(BN_F_BN_GF2M_MOD, BN_R_INVALID_LENGTH); |
478 | return 0; | |
479 | } | |
480 | ret = BN_GF2m_mod_arr(r, a, arr); | |
481 | bn_check_top(r); | |
482 | return ret; | |
483 | } | |
484 | ||
485 | /* | |
486 | * Compute the product of two polynomials a and b, reduce modulo p, and store | |
1dc920c8 BM |
487 | * the result in r. r could be a or b; a could be b. |
488 | */ | |
0f113f3e MC |
489 | int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
490 | const int p[], BN_CTX *ctx) | |
491 | { | |
492 | int zlen, i, j, k, ret = 0; | |
493 | BIGNUM *s; | |
494 | BN_ULONG x1, x0, y1, y0, zz[4]; | |
495 | ||
496 | bn_check_top(a); | |
497 | bn_check_top(b); | |
498 | ||
499 | if (a == b) { | |
500 | return BN_GF2m_mod_sqr_arr(r, a, p, ctx); | |
501 | } | |
502 | ||
503 | BN_CTX_start(ctx); | |
504 | if ((s = BN_CTX_get(ctx)) == NULL) | |
505 | goto err; | |
506 | ||
507 | zlen = a->top + b->top + 4; | |
508 | if (!bn_wexpand(s, zlen)) | |
509 | goto err; | |
510 | s->top = zlen; | |
511 | ||
512 | for (i = 0; i < zlen; i++) | |
513 | s->d[i] = 0; | |
514 | ||
515 | for (j = 0; j < b->top; j += 2) { | |
516 | y0 = b->d[j]; | |
517 | y1 = ((j + 1) == b->top) ? 0 : b->d[j + 1]; | |
518 | for (i = 0; i < a->top; i += 2) { | |
519 | x0 = a->d[i]; | |
520 | x1 = ((i + 1) == a->top) ? 0 : a->d[i + 1]; | |
521 | bn_GF2m_mul_2x2(zz, x1, x0, y1, y0); | |
522 | for (k = 0; k < 4; k++) | |
523 | s->d[i + j + k] ^= zz[k]; | |
524 | } | |
525 | } | |
526 | ||
527 | bn_correct_top(s); | |
528 | if (BN_GF2m_mod_arr(r, s, p)) | |
529 | ret = 1; | |
530 | bn_check_top(r); | |
531 | ||
532 | err: | |
533 | BN_CTX_end(ctx); | |
534 | return ret; | |
535 | } | |
536 | ||
537 | /* | |
538 | * Compute the product of two polynomials a and b, reduce modulo p, and store | |
539 | * the result in r. r could be a or b; a could equal b. This function calls | |
540 | * down to the BN_GF2m_mod_mul_arr implementation; this wrapper function is | |
541 | * only provided for convenience; for best performance, use the | |
1dc920c8 BM |
542 | * BN_GF2m_mod_mul_arr function. |
543 | */ | |
0f113f3e MC |
544 | int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
545 | const BIGNUM *p, BN_CTX *ctx) | |
546 | { | |
547 | int ret = 0; | |
548 | const int max = BN_num_bits(p) + 1; | |
549 | int *arr = NULL; | |
550 | bn_check_top(a); | |
551 | bn_check_top(b); | |
552 | bn_check_top(p); | |
b4faea50 | 553 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL) |
0f113f3e MC |
554 | goto err; |
555 | ret = BN_GF2m_poly2arr(p, arr, max); | |
556 | if (!ret || ret > max) { | |
557 | BNerr(BN_F_BN_GF2M_MOD_MUL, BN_R_INVALID_LENGTH); | |
558 | goto err; | |
559 | } | |
560 | ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx); | |
561 | bn_check_top(r); | |
562 | err: | |
b548a1f1 | 563 | OPENSSL_free(arr); |
0f113f3e MC |
564 | return ret; |
565 | } | |
1dc920c8 BM |
566 | |
567 | /* Square a, reduce the result mod p, and store it in a. r could be a. */ | |
0f113f3e MC |
568 | int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[], |
569 | BN_CTX *ctx) | |
570 | { | |
571 | int i, ret = 0; | |
572 | BIGNUM *s; | |
573 | ||
574 | bn_check_top(a); | |
575 | BN_CTX_start(ctx); | |
576 | if ((s = BN_CTX_get(ctx)) == NULL) | |
3f6c7691 | 577 | goto err; |
0f113f3e MC |
578 | if (!bn_wexpand(s, 2 * a->top)) |
579 | goto err; | |
580 | ||
581 | for (i = a->top - 1; i >= 0; i--) { | |
582 | s->d[2 * i + 1] = SQR1(a->d[i]); | |
583 | s->d[2 * i] = SQR0(a->d[i]); | |
584 | } | |
585 | ||
586 | s->top = 2 * a->top; | |
587 | bn_correct_top(s); | |
588 | if (!BN_GF2m_mod_arr(r, s, p)) | |
589 | goto err; | |
590 | bn_check_top(r); | |
591 | ret = 1; | |
592 | err: | |
593 | BN_CTX_end(ctx); | |
594 | return ret; | |
595 | } | |
596 | ||
597 | /* | |
598 | * Square a, reduce the result mod p, and store it in a. r could be a. This | |
599 | * function calls down to the BN_GF2m_mod_sqr_arr implementation; this | |
600 | * wrapper function is only provided for convenience; for best performance, | |
601 | * use the BN_GF2m_mod_sqr_arr function. | |
1dc920c8 | 602 | */ |
0f113f3e MC |
603 | int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) |
604 | { | |
605 | int ret = 0; | |
606 | const int max = BN_num_bits(p) + 1; | |
607 | int *arr = NULL; | |
608 | ||
609 | bn_check_top(a); | |
610 | bn_check_top(p); | |
b4faea50 | 611 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL) |
0f113f3e MC |
612 | goto err; |
613 | ret = BN_GF2m_poly2arr(p, arr, max); | |
614 | if (!ret || ret > max) { | |
615 | BNerr(BN_F_BN_GF2M_MOD_SQR, BN_R_INVALID_LENGTH); | |
616 | goto err; | |
617 | } | |
618 | ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx); | |
619 | bn_check_top(r); | |
620 | err: | |
b548a1f1 | 621 | OPENSSL_free(arr); |
0f113f3e MC |
622 | return ret; |
623 | } | |
624 | ||
625 | /* | |
626 | * Invert a, reduce modulo p, and store the result in r. r could be a. Uses | |
627 | * Modified Almost Inverse Algorithm (Algorithm 10) from Hankerson, D., | |
628 | * Hernandez, J.L., and Menezes, A. "Software Implementation of Elliptic | |
629 | * Curve Cryptography Over Binary Fields". | |
1dc920c8 BM |
630 | */ |
631 | int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) | |
0f113f3e MC |
632 | { |
633 | BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp; | |
634 | int ret = 0; | |
635 | ||
636 | bn_check_top(a); | |
637 | bn_check_top(p); | |
638 | ||
639 | BN_CTX_start(ctx); | |
640 | ||
641 | if ((b = BN_CTX_get(ctx)) == NULL) | |
642 | goto err; | |
643 | if ((c = BN_CTX_get(ctx)) == NULL) | |
644 | goto err; | |
645 | if ((u = BN_CTX_get(ctx)) == NULL) | |
646 | goto err; | |
647 | if ((v = BN_CTX_get(ctx)) == NULL) | |
648 | goto err; | |
649 | ||
650 | if (!BN_GF2m_mod(u, a, p)) | |
651 | goto err; | |
652 | if (BN_is_zero(u)) | |
653 | goto err; | |
654 | ||
655 | if (!BN_copy(v, p)) | |
656 | goto err; | |
657 | # if 0 | |
658 | if (!BN_one(b)) | |
659 | goto err; | |
660 | ||
661 | while (1) { | |
662 | while (!BN_is_odd(u)) { | |
663 | if (BN_is_zero(u)) | |
664 | goto err; | |
665 | if (!BN_rshift1(u, u)) | |
666 | goto err; | |
667 | if (BN_is_odd(b)) { | |
668 | if (!BN_GF2m_add(b, b, p)) | |
669 | goto err; | |
670 | } | |
671 | if (!BN_rshift1(b, b)) | |
672 | goto err; | |
673 | } | |
674 | ||
675 | if (BN_abs_is_word(u, 1)) | |
676 | break; | |
677 | ||
678 | if (BN_num_bits(u) < BN_num_bits(v)) { | |
679 | tmp = u; | |
680 | u = v; | |
681 | v = tmp; | |
682 | tmp = b; | |
683 | b = c; | |
684 | c = tmp; | |
685 | } | |
686 | ||
687 | if (!BN_GF2m_add(u, u, v)) | |
688 | goto err; | |
689 | if (!BN_GF2m_add(b, b, c)) | |
690 | goto err; | |
691 | } | |
692 | # else | |
693 | { | |
4924b37e AP |
694 | int i; |
695 | int ubits = BN_num_bits(u); | |
696 | int vbits = BN_num_bits(v); /* v is copy of p */ | |
697 | int top = p->top; | |
0f113f3e MC |
698 | BN_ULONG *udp, *bdp, *vdp, *cdp; |
699 | ||
700 | bn_wexpand(u, top); | |
701 | udp = u->d; | |
702 | for (i = u->top; i < top; i++) | |
703 | udp[i] = 0; | |
704 | u->top = top; | |
705 | bn_wexpand(b, top); | |
706 | bdp = b->d; | |
707 | bdp[0] = 1; | |
708 | for (i = 1; i < top; i++) | |
709 | bdp[i] = 0; | |
710 | b->top = top; | |
711 | bn_wexpand(c, top); | |
712 | cdp = c->d; | |
713 | for (i = 0; i < top; i++) | |
714 | cdp[i] = 0; | |
715 | c->top = top; | |
716 | vdp = v->d; /* It pays off to "cache" *->d pointers, | |
717 | * because it allows optimizer to be more | |
718 | * aggressive. But we don't have to "cache" | |
719 | * p->d, because *p is declared 'const'... */ | |
720 | while (1) { | |
721 | while (ubits && !(udp[0] & 1)) { | |
722 | BN_ULONG u0, u1, b0, b1, mask; | |
723 | ||
724 | u0 = udp[0]; | |
725 | b0 = bdp[0]; | |
726 | mask = (BN_ULONG)0 - (b0 & 1); | |
727 | b0 ^= p->d[0] & mask; | |
728 | for (i = 0; i < top - 1; i++) { | |
729 | u1 = udp[i + 1]; | |
730 | udp[i] = ((u0 >> 1) | (u1 << (BN_BITS2 - 1))) & BN_MASK2; | |
731 | u0 = u1; | |
732 | b1 = bdp[i + 1] ^ (p->d[i + 1] & mask); | |
733 | bdp[i] = ((b0 >> 1) | (b1 << (BN_BITS2 - 1))) & BN_MASK2; | |
734 | b0 = b1; | |
735 | } | |
736 | udp[i] = u0 >> 1; | |
737 | bdp[i] = b0 >> 1; | |
738 | ubits--; | |
739 | } | |
740 | ||
4924b37e AP |
741 | if (ubits <= BN_BITS2) { |
742 | if (udp[0] == 0) /* poly was reducible */ | |
743 | goto err; | |
744 | if (udp[0] == 1) | |
745 | break; | |
746 | } | |
0f113f3e MC |
747 | |
748 | if (ubits < vbits) { | |
749 | i = ubits; | |
750 | ubits = vbits; | |
751 | vbits = i; | |
752 | tmp = u; | |
753 | u = v; | |
754 | v = tmp; | |
755 | tmp = b; | |
756 | b = c; | |
757 | c = tmp; | |
758 | udp = vdp; | |
759 | vdp = v->d; | |
760 | bdp = cdp; | |
761 | cdp = c->d; | |
762 | } | |
763 | for (i = 0; i < top; i++) { | |
764 | udp[i] ^= vdp[i]; | |
765 | bdp[i] ^= cdp[i]; | |
766 | } | |
767 | if (ubits == vbits) { | |
768 | BN_ULONG ul; | |
769 | int utop = (ubits - 1) / BN_BITS2; | |
770 | ||
771 | while ((ul = udp[utop]) == 0 && utop) | |
772 | utop--; | |
773 | ubits = utop * BN_BITS2 + BN_num_bits_word(ul); | |
774 | } | |
775 | } | |
776 | bn_correct_top(b); | |
777 | } | |
778 | # endif | |
779 | ||
780 | if (!BN_copy(r, b)) | |
781 | goto err; | |
782 | bn_check_top(r); | |
783 | ret = 1; | |
784 | ||
785 | err: | |
786 | # ifdef BN_DEBUG /* BN_CTX_end would complain about the | |
787 | * expanded form */ | |
788 | bn_correct_top(c); | |
789 | bn_correct_top(u); | |
790 | bn_correct_top(v); | |
791 | # endif | |
792 | BN_CTX_end(ctx); | |
793 | return ret; | |
794 | } | |
795 | ||
796 | /* | |
797 | * Invert xx, reduce modulo p, and store the result in r. r could be xx. | |
798 | * This function calls down to the BN_GF2m_mod_inv implementation; this | |
799 | * wrapper function is only provided for convenience; for best performance, | |
800 | * use the BN_GF2m_mod_inv function. | |
1dc920c8 | 801 | */ |
0f113f3e MC |
802 | int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[], |
803 | BN_CTX *ctx) | |
804 | { | |
805 | BIGNUM *field; | |
806 | int ret = 0; | |
807 | ||
808 | bn_check_top(xx); | |
809 | BN_CTX_start(ctx); | |
810 | if ((field = BN_CTX_get(ctx)) == NULL) | |
811 | goto err; | |
812 | if (!BN_GF2m_arr2poly(p, field)) | |
813 | goto err; | |
814 | ||
815 | ret = BN_GF2m_mod_inv(r, xx, field, ctx); | |
816 | bn_check_top(r); | |
817 | ||
818 | err: | |
819 | BN_CTX_end(ctx); | |
820 | return ret; | |
821 | } | |
822 | ||
823 | # ifndef OPENSSL_SUN_GF2M_DIV | |
824 | /* | |
825 | * Divide y by x, reduce modulo p, and store the result in r. r could be x | |
1dc920c8 BM |
826 | * or y, x could equal y. |
827 | */ | |
0f113f3e MC |
828 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, |
829 | const BIGNUM *p, BN_CTX *ctx) | |
830 | { | |
831 | BIGNUM *xinv = NULL; | |
832 | int ret = 0; | |
833 | ||
834 | bn_check_top(y); | |
835 | bn_check_top(x); | |
836 | bn_check_top(p); | |
837 | ||
838 | BN_CTX_start(ctx); | |
839 | xinv = BN_CTX_get(ctx); | |
840 | if (xinv == NULL) | |
841 | goto err; | |
842 | ||
843 | if (!BN_GF2m_mod_inv(xinv, x, p, ctx)) | |
844 | goto err; | |
845 | if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx)) | |
846 | goto err; | |
847 | bn_check_top(r); | |
848 | ret = 1; | |
849 | ||
850 | err: | |
851 | BN_CTX_end(ctx); | |
852 | return ret; | |
853 | } | |
854 | # else | |
855 | /* | |
856 | * Divide y by x, reduce modulo p, and store the result in r. r could be x | |
857 | * or y, x could equal y. Uses algorithm Modular_Division_GF(2^m) from | |
858 | * Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to the | |
859 | * Great Divide". | |
1dc920c8 | 860 | */ |
0f113f3e MC |
861 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, |
862 | const BIGNUM *p, BN_CTX *ctx) | |
863 | { | |
864 | BIGNUM *a, *b, *u, *v; | |
865 | int ret = 0; | |
866 | ||
867 | bn_check_top(y); | |
868 | bn_check_top(x); | |
869 | bn_check_top(p); | |
870 | ||
871 | BN_CTX_start(ctx); | |
872 | ||
873 | a = BN_CTX_get(ctx); | |
874 | b = BN_CTX_get(ctx); | |
875 | u = BN_CTX_get(ctx); | |
876 | v = BN_CTX_get(ctx); | |
877 | if (v == NULL) | |
878 | goto err; | |
879 | ||
880 | /* reduce x and y mod p */ | |
881 | if (!BN_GF2m_mod(u, y, p)) | |
882 | goto err; | |
883 | if (!BN_GF2m_mod(a, x, p)) | |
884 | goto err; | |
885 | if (!BN_copy(b, p)) | |
886 | goto err; | |
887 | ||
888 | while (!BN_is_odd(a)) { | |
889 | if (!BN_rshift1(a, a)) | |
890 | goto err; | |
891 | if (BN_is_odd(u)) | |
892 | if (!BN_GF2m_add(u, u, p)) | |
893 | goto err; | |
894 | if (!BN_rshift1(u, u)) | |
895 | goto err; | |
896 | } | |
897 | ||
898 | do { | |
899 | if (BN_GF2m_cmp(b, a) > 0) { | |
900 | if (!BN_GF2m_add(b, b, a)) | |
901 | goto err; | |
902 | if (!BN_GF2m_add(v, v, u)) | |
903 | goto err; | |
904 | do { | |
905 | if (!BN_rshift1(b, b)) | |
906 | goto err; | |
907 | if (BN_is_odd(v)) | |
908 | if (!BN_GF2m_add(v, v, p)) | |
909 | goto err; | |
910 | if (!BN_rshift1(v, v)) | |
911 | goto err; | |
912 | } while (!BN_is_odd(b)); | |
913 | } else if (BN_abs_is_word(a, 1)) | |
914 | break; | |
915 | else { | |
916 | if (!BN_GF2m_add(a, a, b)) | |
917 | goto err; | |
918 | if (!BN_GF2m_add(u, u, v)) | |
919 | goto err; | |
920 | do { | |
921 | if (!BN_rshift1(a, a)) | |
922 | goto err; | |
923 | if (BN_is_odd(u)) | |
924 | if (!BN_GF2m_add(u, u, p)) | |
925 | goto err; | |
926 | if (!BN_rshift1(u, u)) | |
927 | goto err; | |
928 | } while (!BN_is_odd(a)); | |
929 | } | |
930 | } while (1); | |
931 | ||
932 | if (!BN_copy(r, u)) | |
933 | goto err; | |
934 | bn_check_top(r); | |
935 | ret = 1; | |
936 | ||
937 | err: | |
938 | BN_CTX_end(ctx); | |
939 | return ret; | |
940 | } | |
941 | # endif | |
942 | ||
943 | /* | |
944 | * Divide yy by xx, reduce modulo p, and store the result in r. r could be xx | |
945 | * * or yy, xx could equal yy. This function calls down to the | |
946 | * BN_GF2m_mod_div implementation; this wrapper function is only provided for | |
947 | * convenience; for best performance, use the BN_GF2m_mod_div function. | |
1dc920c8 | 948 | */ |
0f113f3e MC |
949 | int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx, |
950 | const int p[], BN_CTX *ctx) | |
951 | { | |
952 | BIGNUM *field; | |
953 | int ret = 0; | |
954 | ||
955 | bn_check_top(yy); | |
956 | bn_check_top(xx); | |
957 | ||
958 | BN_CTX_start(ctx); | |
959 | if ((field = BN_CTX_get(ctx)) == NULL) | |
960 | goto err; | |
961 | if (!BN_GF2m_arr2poly(p, field)) | |
962 | goto err; | |
963 | ||
964 | ret = BN_GF2m_mod_div(r, yy, xx, field, ctx); | |
965 | bn_check_top(r); | |
966 | ||
967 | err: | |
968 | BN_CTX_end(ctx); | |
969 | return ret; | |
970 | } | |
971 | ||
972 | /* | |
973 | * Compute the bth power of a, reduce modulo p, and store the result in r. r | |
974 | * could be a. Uses simple square-and-multiply algorithm A.5.1 from IEEE | |
975 | * P1363. | |
1dc920c8 | 976 | */ |
0f113f3e MC |
977 | int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
978 | const int p[], BN_CTX *ctx) | |
979 | { | |
980 | int ret = 0, i, n; | |
981 | BIGNUM *u; | |
982 | ||
983 | bn_check_top(a); | |
984 | bn_check_top(b); | |
985 | ||
986 | if (BN_is_zero(b)) | |
987 | return (BN_one(r)); | |
988 | ||
989 | if (BN_abs_is_word(b, 1)) | |
990 | return (BN_copy(r, a) != NULL); | |
991 | ||
992 | BN_CTX_start(ctx); | |
993 | if ((u = BN_CTX_get(ctx)) == NULL) | |
994 | goto err; | |
995 | ||
996 | if (!BN_GF2m_mod_arr(u, a, p)) | |
997 | goto err; | |
998 | ||
999 | n = BN_num_bits(b) - 1; | |
1000 | for (i = n - 1; i >= 0; i--) { | |
1001 | if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx)) | |
1002 | goto err; | |
1003 | if (BN_is_bit_set(b, i)) { | |
1004 | if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx)) | |
1005 | goto err; | |
1006 | } | |
1007 | } | |
1008 | if (!BN_copy(r, u)) | |
1009 | goto err; | |
1010 | bn_check_top(r); | |
1011 | ret = 1; | |
1012 | err: | |
1013 | BN_CTX_end(ctx); | |
1014 | return ret; | |
1015 | } | |
1016 | ||
1017 | /* | |
1018 | * Compute the bth power of a, reduce modulo p, and store the result in r. r | |
1019 | * could be a. This function calls down to the BN_GF2m_mod_exp_arr | |
1020 | * implementation; this wrapper function is only provided for convenience; | |
1021 | * for best performance, use the BN_GF2m_mod_exp_arr function. | |
1dc920c8 | 1022 | */ |
0f113f3e MC |
1023 | int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
1024 | const BIGNUM *p, BN_CTX *ctx) | |
1025 | { | |
1026 | int ret = 0; | |
1027 | const int max = BN_num_bits(p) + 1; | |
1028 | int *arr = NULL; | |
1029 | bn_check_top(a); | |
1030 | bn_check_top(b); | |
1031 | bn_check_top(p); | |
b4faea50 | 1032 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL) |
0f113f3e MC |
1033 | goto err; |
1034 | ret = BN_GF2m_poly2arr(p, arr, max); | |
1035 | if (!ret || ret > max) { | |
1036 | BNerr(BN_F_BN_GF2M_MOD_EXP, BN_R_INVALID_LENGTH); | |
1037 | goto err; | |
1038 | } | |
1039 | ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx); | |
1040 | bn_check_top(r); | |
1041 | err: | |
b548a1f1 | 1042 | OPENSSL_free(arr); |
0f113f3e MC |
1043 | return ret; |
1044 | } | |
1045 | ||
1046 | /* | |
1047 | * Compute the square root of a, reduce modulo p, and store the result in r. | |
1048 | * r could be a. Uses exponentiation as in algorithm A.4.1 from IEEE P1363. | |
1dc920c8 | 1049 | */ |
0f113f3e MC |
1050 | int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[], |
1051 | BN_CTX *ctx) | |
1052 | { | |
1053 | int ret = 0; | |
1054 | BIGNUM *u; | |
1055 | ||
1056 | bn_check_top(a); | |
1057 | ||
1058 | if (!p[0]) { | |
1059 | /* reduction mod 1 => return 0 */ | |
1060 | BN_zero(r); | |
1061 | return 1; | |
1062 | } | |
1063 | ||
1064 | BN_CTX_start(ctx); | |
1065 | if ((u = BN_CTX_get(ctx)) == NULL) | |
1066 | goto err; | |
1067 | ||
1068 | if (!BN_set_bit(u, p[0] - 1)) | |
1069 | goto err; | |
1070 | ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx); | |
1071 | bn_check_top(r); | |
1072 | ||
1073 | err: | |
1074 | BN_CTX_end(ctx); | |
1075 | return ret; | |
1076 | } | |
1077 | ||
1078 | /* | |
1079 | * Compute the square root of a, reduce modulo p, and store the result in r. | |
1080 | * r could be a. This function calls down to the BN_GF2m_mod_sqrt_arr | |
1081 | * implementation; this wrapper function is only provided for convenience; | |
1082 | * for best performance, use the BN_GF2m_mod_sqrt_arr function. | |
1dc920c8 BM |
1083 | */ |
1084 | int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) | |
0f113f3e MC |
1085 | { |
1086 | int ret = 0; | |
1087 | const int max = BN_num_bits(p) + 1; | |
1088 | int *arr = NULL; | |
1089 | bn_check_top(a); | |
1090 | bn_check_top(p); | |
b4faea50 | 1091 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL) |
0f113f3e MC |
1092 | goto err; |
1093 | ret = BN_GF2m_poly2arr(p, arr, max); | |
1094 | if (!ret || ret > max) { | |
1095 | BNerr(BN_F_BN_GF2M_MOD_SQRT, BN_R_INVALID_LENGTH); | |
1096 | goto err; | |
1097 | } | |
1098 | ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx); | |
1099 | bn_check_top(r); | |
1100 | err: | |
b548a1f1 | 1101 | OPENSSL_free(arr); |
0f113f3e MC |
1102 | return ret; |
1103 | } | |
1104 | ||
1105 | /* | |
1106 | * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns | |
1107 | * 0. Uses algorithms A.4.7 and A.4.6 from IEEE P1363. | |
1dc920c8 | 1108 | */ |
0f113f3e MC |
1109 | int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[], |
1110 | BN_CTX *ctx) | |
1111 | { | |
1112 | int ret = 0, count = 0, j; | |
1113 | BIGNUM *a, *z, *rho, *w, *w2, *tmp; | |
1114 | ||
1115 | bn_check_top(a_); | |
1116 | ||
1117 | if (!p[0]) { | |
1118 | /* reduction mod 1 => return 0 */ | |
1119 | BN_zero(r); | |
1120 | return 1; | |
1121 | } | |
1122 | ||
1123 | BN_CTX_start(ctx); | |
1124 | a = BN_CTX_get(ctx); | |
1125 | z = BN_CTX_get(ctx); | |
1126 | w = BN_CTX_get(ctx); | |
1127 | if (w == NULL) | |
1128 | goto err; | |
1129 | ||
1130 | if (!BN_GF2m_mod_arr(a, a_, p)) | |
1131 | goto err; | |
1132 | ||
1133 | if (BN_is_zero(a)) { | |
1134 | BN_zero(r); | |
1135 | ret = 1; | |
1136 | goto err; | |
1137 | } | |
1138 | ||
1139 | if (p[0] & 0x1) { /* m is odd */ | |
1140 | /* compute half-trace of a */ | |
1141 | if (!BN_copy(z, a)) | |
1142 | goto err; | |
1143 | for (j = 1; j <= (p[0] - 1) / 2; j++) { | |
1144 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) | |
1145 | goto err; | |
1146 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) | |
1147 | goto err; | |
1148 | if (!BN_GF2m_add(z, z, a)) | |
1149 | goto err; | |
1150 | } | |
1151 | ||
1152 | } else { /* m is even */ | |
1153 | ||
1154 | rho = BN_CTX_get(ctx); | |
1155 | w2 = BN_CTX_get(ctx); | |
1156 | tmp = BN_CTX_get(ctx); | |
1157 | if (tmp == NULL) | |
1158 | goto err; | |
1159 | do { | |
1160 | if (!BN_rand(rho, p[0], 0, 0)) | |
1161 | goto err; | |
1162 | if (!BN_GF2m_mod_arr(rho, rho, p)) | |
1163 | goto err; | |
1164 | BN_zero(z); | |
1165 | if (!BN_copy(w, rho)) | |
1166 | goto err; | |
1167 | for (j = 1; j <= p[0] - 1; j++) { | |
1168 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) | |
1169 | goto err; | |
1170 | if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx)) | |
1171 | goto err; | |
1172 | if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx)) | |
1173 | goto err; | |
1174 | if (!BN_GF2m_add(z, z, tmp)) | |
1175 | goto err; | |
1176 | if (!BN_GF2m_add(w, w2, rho)) | |
1177 | goto err; | |
1178 | } | |
1179 | count++; | |
1180 | } while (BN_is_zero(w) && (count < MAX_ITERATIONS)); | |
1181 | if (BN_is_zero(w)) { | |
1182 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_TOO_MANY_ITERATIONS); | |
1183 | goto err; | |
1184 | } | |
1185 | } | |
1186 | ||
1187 | if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx)) | |
1188 | goto err; | |
1189 | if (!BN_GF2m_add(w, z, w)) | |
1190 | goto err; | |
1191 | if (BN_GF2m_cmp(w, a)) { | |
1192 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_NO_SOLUTION); | |
1193 | goto err; | |
1194 | } | |
1195 | ||
1196 | if (!BN_copy(r, z)) | |
1197 | goto err; | |
1198 | bn_check_top(r); | |
1199 | ||
1200 | ret = 1; | |
1201 | ||
1202 | err: | |
1203 | BN_CTX_end(ctx); | |
1204 | return ret; | |
1205 | } | |
1206 | ||
1207 | /* | |
1208 | * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns | |
1209 | * 0. This function calls down to the BN_GF2m_mod_solve_quad_arr | |
1210 | * implementation; this wrapper function is only provided for convenience; | |
1211 | * for best performance, use the BN_GF2m_mod_solve_quad_arr function. | |
1dc920c8 | 1212 | */ |
0f113f3e MC |
1213 | int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
1214 | BN_CTX *ctx) | |
1215 | { | |
1216 | int ret = 0; | |
1217 | const int max = BN_num_bits(p) + 1; | |
1218 | int *arr = NULL; | |
1219 | bn_check_top(a); | |
1220 | bn_check_top(p); | |
b4faea50 | 1221 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL) |
0f113f3e MC |
1222 | goto err; |
1223 | ret = BN_GF2m_poly2arr(p, arr, max); | |
1224 | if (!ret || ret > max) { | |
1225 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD, BN_R_INVALID_LENGTH); | |
1226 | goto err; | |
1227 | } | |
1228 | ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx); | |
1229 | bn_check_top(r); | |
1230 | err: | |
b548a1f1 | 1231 | OPENSSL_free(arr); |
0f113f3e MC |
1232 | return ret; |
1233 | } | |
1234 | ||
1235 | /* | |
1236 | * Convert the bit-string representation of a polynomial ( \sum_{i=0}^n a_i * | |
1237 | * x^i) into an array of integers corresponding to the bits with non-zero | |
1238 | * coefficient. Array is terminated with -1. Up to max elements of the array | |
1239 | * will be filled. Return value is total number of array elements that would | |
1240 | * be filled if array was large enough. | |
1dc920c8 | 1241 | */ |
c4e7870a | 1242 | int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max) |
0f113f3e MC |
1243 | { |
1244 | int i, j, k = 0; | |
1245 | BN_ULONG mask; | |
1246 | ||
1247 | if (BN_is_zero(a)) | |
1248 | return 0; | |
1249 | ||
1250 | for (i = a->top - 1; i >= 0; i--) { | |
1251 | if (!a->d[i]) | |
1252 | /* skip word if a->d[i] == 0 */ | |
1253 | continue; | |
1254 | mask = BN_TBIT; | |
1255 | for (j = BN_BITS2 - 1; j >= 0; j--) { | |
1256 | if (a->d[i] & mask) { | |
1257 | if (k < max) | |
1258 | p[k] = BN_BITS2 * i + j; | |
1259 | k++; | |
1260 | } | |
1261 | mask >>= 1; | |
1262 | } | |
1263 | } | |
1264 | ||
1265 | if (k < max) { | |
1266 | p[k] = -1; | |
1267 | k++; | |
1268 | } | |
1269 | ||
1270 | return k; | |
1271 | } | |
1272 | ||
1273 | /* | |
1274 | * Convert the coefficient array representation of a polynomial to a | |
c4e7870a | 1275 | * bit-string. The array must be terminated by -1. |
1dc920c8 | 1276 | */ |
c4e7870a | 1277 | int BN_GF2m_arr2poly(const int p[], BIGNUM *a) |
0f113f3e MC |
1278 | { |
1279 | int i; | |
1280 | ||
1281 | bn_check_top(a); | |
1282 | BN_zero(a); | |
1283 | for (i = 0; p[i] != -1; i++) { | |
1284 | if (BN_set_bit(a, p[i]) == 0) | |
1285 | return 0; | |
1286 | } | |
1287 | bn_check_top(a); | |
1288 | ||
1289 | return 1; | |
1290 | } | |
1dc920c8 | 1291 | |
b3310161 | 1292 | #endif |