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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 | ||
6c950e0d BM |
30 | /* NOTE: This file is licensed pursuant to the OpenSSL license below |
31 | * and may be modified; but after modifications, the above covenant | |
32 | * may no longer apply! In such cases, the corresponding paragraph | |
33 | * ["In addition, Sun covenants ... causes the infringement."] and | |
34 | * this note can be edited out; but please keep the Sun copyright | |
35 | * notice and attribution. */ | |
36 | ||
1dc920c8 BM |
37 | /* ==================================================================== |
38 | * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. | |
39 | * | |
40 | * Redistribution and use in source and binary forms, with or without | |
41 | * modification, are permitted provided that the following conditions | |
42 | * are met: | |
43 | * | |
44 | * 1. Redistributions of source code must retain the above copyright | |
45 | * notice, this list of conditions and the following disclaimer. | |
46 | * | |
47 | * 2. Redistributions in binary form must reproduce the above copyright | |
48 | * notice, this list of conditions and the following disclaimer in | |
49 | * the documentation and/or other materials provided with the | |
50 | * distribution. | |
51 | * | |
52 | * 3. All advertising materials mentioning features or use of this | |
53 | * software must display the following acknowledgment: | |
54 | * "This product includes software developed by the OpenSSL Project | |
55 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |
56 | * | |
57 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |
58 | * endorse or promote products derived from this software without | |
59 | * prior written permission. For written permission, please contact | |
60 | * openssl-core@openssl.org. | |
61 | * | |
62 | * 5. Products derived from this software may not be called "OpenSSL" | |
63 | * nor may "OpenSSL" appear in their names without prior written | |
64 | * permission of the OpenSSL Project. | |
65 | * | |
66 | * 6. Redistributions of any form whatsoever must retain the following | |
67 | * acknowledgment: | |
68 | * "This product includes software developed by the OpenSSL Project | |
69 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |
70 | * | |
71 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |
72 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
73 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |
74 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |
75 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |
76 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
77 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |
78 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
79 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |
80 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |
81 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |
82 | * OF THE POSSIBILITY OF SUCH DAMAGE. | |
83 | * ==================================================================== | |
84 | * | |
85 | * This product includes cryptographic software written by Eric Young | |
86 | * (eay@cryptsoft.com). This product includes software written by Tim | |
87 | * Hudson (tjh@cryptsoft.com). | |
88 | * | |
89 | */ | |
90 | ||
73e45b2d | 91 | |
fe26d066 | 92 | |
1dc920c8 BM |
93 | #include <assert.h> |
94 | #include <limits.h> | |
95 | #include <stdio.h> | |
96 | #include "cryptlib.h" | |
97 | #include "bn_lcl.h" | |
98 | ||
b3310161 DSH |
99 | #ifndef OPENSSL_NO_EC2M |
100 | ||
1dc920c8 BM |
101 | /* Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should fail. */ |
102 | #define MAX_ITERATIONS 50 | |
103 | ||
104 | static const BN_ULONG SQR_tb[16] = | |
105 | { 0, 1, 4, 5, 16, 17, 20, 21, | |
106 | 64, 65, 68, 69, 80, 81, 84, 85 }; | |
107 | /* Platform-specific macros to accelerate squaring. */ | |
108 | #if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) | |
109 | #define SQR1(w) \ | |
110 | SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \ | |
111 | SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \ | |
112 | SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \ | |
113 | SQR_tb[(w) >> 36 & 0xF] << 8 | SQR_tb[(w) >> 32 & 0xF] | |
114 | #define SQR0(w) \ | |
115 | SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \ | |
116 | SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \ | |
117 | SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \ | |
118 | SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF] | |
119 | #endif | |
120 | #ifdef THIRTY_TWO_BIT | |
121 | #define SQR1(w) \ | |
122 | SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \ | |
123 | SQR_tb[(w) >> 20 & 0xF] << 8 | SQR_tb[(w) >> 16 & 0xF] | |
124 | #define SQR0(w) \ | |
125 | SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \ | |
126 | SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF] | |
127 | #endif | |
1dc920c8 | 128 | |
925596f8 | 129 | #if !defined(OPENSSL_BN_ASM_GF2m) |
1dc920c8 BM |
130 | /* Product of two polynomials a, b each with degree < BN_BITS2 - 1, |
131 | * result is a polynomial r with degree < 2 * BN_BITS - 1 | |
132 | * The caller MUST ensure that the variables have the right amount | |
133 | * of space allocated. | |
134 | */ | |
1dc920c8 BM |
135 | #ifdef THIRTY_TWO_BIT |
136 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b) | |
137 | { | |
138 | register BN_ULONG h, l, s; | |
139 | BN_ULONG tab[8], top2b = a >> 30; | |
140 | register BN_ULONG a1, a2, a4; | |
141 | ||
142 | a1 = a & (0x3FFFFFFF); a2 = a1 << 1; a4 = a2 << 1; | |
143 | ||
144 | tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2; | |
145 | tab[4] = a4; tab[5] = a1^a4; tab[6] = a2^a4; tab[7] = a1^a2^a4; | |
146 | ||
147 | s = tab[b & 0x7]; l = s; | |
148 | s = tab[b >> 3 & 0x7]; l ^= s << 3; h = s >> 29; | |
149 | s = tab[b >> 6 & 0x7]; l ^= s << 6; h ^= s >> 26; | |
150 | s = tab[b >> 9 & 0x7]; l ^= s << 9; h ^= s >> 23; | |
151 | s = tab[b >> 12 & 0x7]; l ^= s << 12; h ^= s >> 20; | |
152 | s = tab[b >> 15 & 0x7]; l ^= s << 15; h ^= s >> 17; | |
153 | s = tab[b >> 18 & 0x7]; l ^= s << 18; h ^= s >> 14; | |
154 | s = tab[b >> 21 & 0x7]; l ^= s << 21; h ^= s >> 11; | |
155 | s = tab[b >> 24 & 0x7]; l ^= s << 24; h ^= s >> 8; | |
156 | s = tab[b >> 27 & 0x7]; l ^= s << 27; h ^= s >> 5; | |
157 | s = tab[b >> 30 ]; l ^= s << 30; h ^= s >> 2; | |
158 | ||
159 | /* compensate for the top two bits of a */ | |
160 | ||
161 | if (top2b & 01) { l ^= b << 30; h ^= b >> 2; } | |
162 | if (top2b & 02) { l ^= b << 31; h ^= b >> 1; } | |
163 | ||
164 | *r1 = h; *r0 = l; | |
165 | } | |
166 | #endif | |
167 | #if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) | |
168 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b) | |
169 | { | |
170 | register BN_ULONG h, l, s; | |
171 | BN_ULONG tab[16], top3b = a >> 61; | |
172 | register BN_ULONG a1, a2, a4, a8; | |
173 | ||
27b2b78f | 174 | a1 = a & (0x1FFFFFFFFFFFFFFFULL); a2 = a1 << 1; a4 = a2 << 1; a8 = a4 << 1; |
1dc920c8 BM |
175 | |
176 | tab[ 0] = 0; tab[ 1] = a1; tab[ 2] = a2; tab[ 3] = a1^a2; | |
177 | tab[ 4] = a4; tab[ 5] = a1^a4; tab[ 6] = a2^a4; tab[ 7] = a1^a2^a4; | |
178 | tab[ 8] = a8; tab[ 9] = a1^a8; tab[10] = a2^a8; tab[11] = a1^a2^a8; | |
179 | tab[12] = a4^a8; tab[13] = a1^a4^a8; tab[14] = a2^a4^a8; tab[15] = a1^a2^a4^a8; | |
180 | ||
181 | s = tab[b & 0xF]; l = s; | |
182 | s = tab[b >> 4 & 0xF]; l ^= s << 4; h = s >> 60; | |
183 | s = tab[b >> 8 & 0xF]; l ^= s << 8; h ^= s >> 56; | |
184 | s = tab[b >> 12 & 0xF]; l ^= s << 12; h ^= s >> 52; | |
185 | s = tab[b >> 16 & 0xF]; l ^= s << 16; h ^= s >> 48; | |
186 | s = tab[b >> 20 & 0xF]; l ^= s << 20; h ^= s >> 44; | |
187 | s = tab[b >> 24 & 0xF]; l ^= s << 24; h ^= s >> 40; | |
188 | s = tab[b >> 28 & 0xF]; l ^= s << 28; h ^= s >> 36; | |
189 | s = tab[b >> 32 & 0xF]; l ^= s << 32; h ^= s >> 32; | |
190 | s = tab[b >> 36 & 0xF]; l ^= s << 36; h ^= s >> 28; | |
191 | s = tab[b >> 40 & 0xF]; l ^= s << 40; h ^= s >> 24; | |
192 | s = tab[b >> 44 & 0xF]; l ^= s << 44; h ^= s >> 20; | |
193 | s = tab[b >> 48 & 0xF]; l ^= s << 48; h ^= s >> 16; | |
194 | s = tab[b >> 52 & 0xF]; l ^= s << 52; h ^= s >> 12; | |
195 | s = tab[b >> 56 & 0xF]; l ^= s << 56; h ^= s >> 8; | |
196 | s = tab[b >> 60 ]; l ^= s << 60; h ^= s >> 4; | |
197 | ||
198 | /* compensate for the top three bits of a */ | |
199 | ||
200 | if (top3b & 01) { l ^= b << 61; h ^= b >> 3; } | |
201 | if (top3b & 02) { l ^= b << 62; h ^= b >> 2; } | |
202 | if (top3b & 04) { l ^= b << 63; h ^= b >> 1; } | |
203 | ||
204 | *r1 = h; *r0 = l; | |
205 | } | |
206 | #endif | |
207 | ||
208 | /* Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1, | |
209 | * result is a polynomial r with degree < 4 * BN_BITS2 - 1 | |
210 | * The caller MUST ensure that the variables have the right amount | |
211 | * of space allocated. | |
212 | */ | |
213 | static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0, const BN_ULONG b1, const BN_ULONG b0) | |
214 | { | |
215 | BN_ULONG m1, m0; | |
216 | /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */ | |
217 | bn_GF2m_mul_1x1(r+3, r+2, a1, b1); | |
218 | bn_GF2m_mul_1x1(r+1, r, a0, b0); | |
219 | bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1); | |
220 | /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */ | |
221 | r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */ | |
222 | r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */ | |
223 | } | |
925596f8 AP |
224 | #else |
225 | void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1, BN_ULONG b0); | |
226 | #endif | |
1dc920c8 BM |
227 | |
228 | /* Add polynomials a and b and store result in r; r could be a or b, a and b | |
229 | * could be equal; r is the bitwise XOR of a and b. | |
230 | */ | |
231 | int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) | |
232 | { | |
233 | int i; | |
234 | const BIGNUM *at, *bt; | |
235 | ||
e7e5fe47 GT |
236 | bn_check_top(a); |
237 | bn_check_top(b); | |
238 | ||
1dc920c8 BM |
239 | if (a->top < b->top) { at = b; bt = a; } |
240 | else { at = a; bt = b; } | |
241 | ||
2d9dcd4f BM |
242 | if(bn_wexpand(r, at->top) == NULL) |
243 | return 0; | |
1dc920c8 BM |
244 | |
245 | for (i = 0; i < bt->top; i++) | |
246 | { | |
247 | r->d[i] = at->d[i] ^ bt->d[i]; | |
248 | } | |
249 | for (; i < at->top; i++) | |
250 | { | |
251 | r->d[i] = at->d[i]; | |
252 | } | |
253 | ||
254 | r->top = at->top; | |
d870740c | 255 | bn_correct_top(r); |
1dc920c8 BM |
256 | |
257 | return 1; | |
258 | } | |
259 | ||
260 | ||
c80fd6b2 MC |
261 | /*- |
262 | * Some functions allow for representation of the irreducible polynomials | |
1dc920c8 BM |
263 | * as an int[], say p. The irreducible f(t) is then of the form: |
264 | * t^p[0] + t^p[1] + ... + t^p[k] | |
265 | * where m = p[0] > p[1] > ... > p[k] = 0. | |
266 | */ | |
267 | ||
268 | ||
269 | /* Performs modular reduction of a and store result in r. r could be a. */ | |
c4e7870a | 270 | int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]) |
1dc920c8 BM |
271 | { |
272 | int j, k; | |
273 | int n, dN, d0, d1; | |
274 | BN_ULONG zz, *z; | |
e7e5fe47 GT |
275 | |
276 | bn_check_top(a); | |
277 | ||
e1064adf | 278 | if (!p[0]) |
b6358c89 | 279 | { |
e1064adf | 280 | /* reduction mod 1 => return 0 */ |
b6358c89 GT |
281 | BN_zero(r); |
282 | return 1; | |
283 | } | |
e1064adf GT |
284 | |
285 | /* Since the algorithm does reduction in the r value, if a != r, copy | |
286 | * the contents of a into r so we can do reduction in r. | |
1dc920c8 | 287 | */ |
7a8645d1 | 288 | if (a != r) |
1dc920c8 BM |
289 | { |
290 | if (!bn_wexpand(r, a->top)) return 0; | |
291 | for (j = 0; j < a->top; j++) | |
292 | { | |
293 | r->d[j] = a->d[j]; | |
294 | } | |
295 | r->top = a->top; | |
296 | } | |
297 | z = r->d; | |
298 | ||
299 | /* start reduction */ | |
300 | dN = p[0] / BN_BITS2; | |
301 | for (j = r->top - 1; j > dN;) | |
302 | { | |
303 | zz = z[j]; | |
304 | if (z[j] == 0) { j--; continue; } | |
305 | z[j] = 0; | |
306 | ||
e1064adf | 307 | for (k = 1; p[k] != 0; k++) |
1dc920c8 BM |
308 | { |
309 | /* reducing component t^p[k] */ | |
310 | n = p[0] - p[k]; | |
311 | d0 = n % BN_BITS2; d1 = BN_BITS2 - d0; | |
312 | n /= BN_BITS2; | |
313 | z[j-n] ^= (zz>>d0); | |
314 | if (d0) z[j-n-1] ^= (zz<<d1); | |
315 | } | |
316 | ||
317 | /* reducing component t^0 */ | |
318 | n = dN; | |
319 | d0 = p[0] % BN_BITS2; | |
320 | d1 = BN_BITS2 - d0; | |
321 | z[j-n] ^= (zz >> d0); | |
322 | if (d0) z[j-n-1] ^= (zz << d1); | |
323 | } | |
324 | ||
325 | /* final round of reduction */ | |
326 | while (j == dN) | |
327 | { | |
328 | ||
329 | d0 = p[0] % BN_BITS2; | |
330 | zz = z[dN] >> d0; | |
331 | if (zz == 0) break; | |
332 | d1 = BN_BITS2 - d0; | |
333 | ||
8228fd89 BM |
334 | /* clear up the top d1 bits */ |
335 | if (d0) | |
336 | z[dN] = (z[dN] << d1) >> d1; | |
337 | else | |
338 | z[dN] = 0; | |
1dc920c8 BM |
339 | z[0] ^= zz; /* reduction t^0 component */ |
340 | ||
e1064adf | 341 | for (k = 1; p[k] != 0; k++) |
1dc920c8 | 342 | { |
c237de05 BM |
343 | BN_ULONG tmp_ulong; |
344 | ||
1dc920c8 BM |
345 | /* reducing component t^p[k]*/ |
346 | n = p[k] / BN_BITS2; | |
347 | d0 = p[k] % BN_BITS2; | |
348 | d1 = BN_BITS2 - d0; | |
349 | z[n] ^= (zz << d0); | |
c237de05 BM |
350 | tmp_ulong = zz >> d1; |
351 | if (d0 && tmp_ulong) | |
352 | z[n+1] ^= tmp_ulong; | |
1dc920c8 BM |
353 | } |
354 | ||
355 | ||
356 | } | |
357 | ||
d870740c | 358 | bn_correct_top(r); |
1dc920c8 BM |
359 | return 1; |
360 | } | |
361 | ||
362 | /* Performs modular reduction of a by p and store result in r. r could be a. | |
363 | * | |
364 | * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper | |
365 | * function is only provided for convenience; for best performance, use the | |
366 | * BN_GF2m_mod_arr function. | |
367 | */ | |
368 | int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p) | |
369 | { | |
444c3a84 | 370 | int ret = 0; |
034688ec | 371 | int arr[6]; |
e7e5fe47 GT |
372 | bn_check_top(a); |
373 | bn_check_top(p); | |
034688ec | 374 | ret = BN_GF2m_poly2arr(p, arr, sizeof(arr)/sizeof(arr[0])); |
8d3cdd5b | 375 | if (!ret || ret > (int)(sizeof(arr)/sizeof(arr[0]))) |
1dc920c8 BM |
376 | { |
377 | BNerr(BN_F_BN_GF2M_MOD,BN_R_INVALID_LENGTH); | |
034688ec | 378 | return 0; |
1dc920c8 BM |
379 | } |
380 | ret = BN_GF2m_mod_arr(r, a, arr); | |
d870740c | 381 | bn_check_top(r); |
1dc920c8 BM |
382 | return ret; |
383 | } | |
384 | ||
385 | ||
386 | /* Compute the product of two polynomials a and b, reduce modulo p, and store | |
387 | * the result in r. r could be a or b; a could be b. | |
388 | */ | |
c4e7870a | 389 | int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const int p[], BN_CTX *ctx) |
1dc920c8 BM |
390 | { |
391 | int zlen, i, j, k, ret = 0; | |
392 | BIGNUM *s; | |
393 | BN_ULONG x1, x0, y1, y0, zz[4]; | |
e7e5fe47 GT |
394 | |
395 | bn_check_top(a); | |
396 | bn_check_top(b); | |
397 | ||
1dc920c8 BM |
398 | if (a == b) |
399 | { | |
400 | return BN_GF2m_mod_sqr_arr(r, a, p, ctx); | |
401 | } | |
1dc920c8 BM |
402 | |
403 | BN_CTX_start(ctx); | |
404 | if ((s = BN_CTX_get(ctx)) == NULL) goto err; | |
405 | ||
7a8645d1 | 406 | zlen = a->top + b->top + 4; |
1dc920c8 BM |
407 | if (!bn_wexpand(s, zlen)) goto err; |
408 | s->top = zlen; | |
409 | ||
410 | for (i = 0; i < zlen; i++) s->d[i] = 0; | |
411 | ||
412 | for (j = 0; j < b->top; j += 2) | |
413 | { | |
414 | y0 = b->d[j]; | |
415 | y1 = ((j+1) == b->top) ? 0 : b->d[j+1]; | |
416 | for (i = 0; i < a->top; i += 2) | |
417 | { | |
418 | x0 = a->d[i]; | |
419 | x1 = ((i+1) == a->top) ? 0 : a->d[i+1]; | |
420 | bn_GF2m_mul_2x2(zz, x1, x0, y1, y0); | |
421 | for (k = 0; k < 4; k++) s->d[i+j+k] ^= zz[k]; | |
422 | } | |
423 | } | |
424 | ||
d870740c | 425 | bn_correct_top(s); |
e1064adf GT |
426 | if (BN_GF2m_mod_arr(r, s, p)) |
427 | ret = 1; | |
d870740c | 428 | bn_check_top(r); |
1dc920c8 | 429 | |
e7e5fe47 | 430 | err: |
1dc920c8 BM |
431 | BN_CTX_end(ctx); |
432 | return ret; | |
1dc920c8 BM |
433 | } |
434 | ||
435 | /* Compute the product of two polynomials a and b, reduce modulo p, and store | |
436 | * the result in r. r could be a or b; a could equal b. | |
437 | * | |
438 | * This function calls down to the BN_GF2m_mod_mul_arr implementation; this wrapper | |
439 | * function is only provided for convenience; for best performance, use the | |
440 | * BN_GF2m_mod_mul_arr function. | |
441 | */ | |
442 | int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx) | |
443 | { | |
444c3a84 | 444 | int ret = 0; |
c4e7870a BM |
445 | const int max = BN_num_bits(p) + 1; |
446 | int *arr=NULL; | |
e7e5fe47 GT |
447 | bn_check_top(a); |
448 | bn_check_top(b); | |
449 | bn_check_top(p); | |
c4e7870a | 450 | if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err; |
e1064adf GT |
451 | ret = BN_GF2m_poly2arr(p, arr, max); |
452 | if (!ret || ret > max) | |
1dc920c8 BM |
453 | { |
454 | BNerr(BN_F_BN_GF2M_MOD_MUL,BN_R_INVALID_LENGTH); | |
455 | goto err; | |
456 | } | |
457 | ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx); | |
d870740c | 458 | bn_check_top(r); |
e7e5fe47 | 459 | err: |
1dc920c8 BM |
460 | if (arr) OPENSSL_free(arr); |
461 | return ret; | |
462 | } | |
463 | ||
464 | ||
465 | /* Square a, reduce the result mod p, and store it in a. r could be a. */ | |
c4e7870a | 466 | int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[], BN_CTX *ctx) |
1dc920c8 BM |
467 | { |
468 | int i, ret = 0; | |
469 | BIGNUM *s; | |
e7e5fe47 GT |
470 | |
471 | bn_check_top(a); | |
1dc920c8 BM |
472 | BN_CTX_start(ctx); |
473 | if ((s = BN_CTX_get(ctx)) == NULL) return 0; | |
474 | if (!bn_wexpand(s, 2 * a->top)) goto err; | |
475 | ||
476 | for (i = a->top - 1; i >= 0; i--) | |
477 | { | |
478 | s->d[2*i+1] = SQR1(a->d[i]); | |
479 | s->d[2*i ] = SQR0(a->d[i]); | |
480 | } | |
481 | ||
482 | s->top = 2 * a->top; | |
d870740c | 483 | bn_correct_top(s); |
1dc920c8 | 484 | if (!BN_GF2m_mod_arr(r, s, p)) goto err; |
d870740c | 485 | bn_check_top(r); |
1dc920c8 | 486 | ret = 1; |
e7e5fe47 | 487 | err: |
1dc920c8 BM |
488 | BN_CTX_end(ctx); |
489 | return ret; | |
490 | } | |
491 | ||
492 | /* Square a, reduce the result mod p, and store it in a. r could be a. | |
493 | * | |
494 | * This function calls down to the BN_GF2m_mod_sqr_arr implementation; this wrapper | |
495 | * function is only provided for convenience; for best performance, use the | |
496 | * BN_GF2m_mod_sqr_arr function. | |
497 | */ | |
498 | int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) | |
499 | { | |
444c3a84 | 500 | int ret = 0; |
c4e7870a BM |
501 | const int max = BN_num_bits(p) + 1; |
502 | int *arr=NULL; | |
e7e5fe47 GT |
503 | |
504 | bn_check_top(a); | |
505 | bn_check_top(p); | |
c4e7870a | 506 | if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err; |
e1064adf GT |
507 | ret = BN_GF2m_poly2arr(p, arr, max); |
508 | if (!ret || ret > max) | |
1dc920c8 BM |
509 | { |
510 | BNerr(BN_F_BN_GF2M_MOD_SQR,BN_R_INVALID_LENGTH); | |
511 | goto err; | |
512 | } | |
513 | ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx); | |
d870740c | 514 | bn_check_top(r); |
e7e5fe47 | 515 | err: |
1dc920c8 BM |
516 | if (arr) OPENSSL_free(arr); |
517 | return ret; | |
518 | } | |
519 | ||
520 | ||
521 | /* Invert a, reduce modulo p, and store the result in r. r could be a. | |
522 | * Uses Modified Almost Inverse Algorithm (Algorithm 10) from | |
523 | * Hankerson, D., Hernandez, J.L., and Menezes, A. "Software Implementation | |
524 | * of Elliptic Curve Cryptography Over Binary Fields". | |
525 | */ | |
526 | int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) | |
527 | { | |
e166891e | 528 | BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp; |
1dc920c8 BM |
529 | int ret = 0; |
530 | ||
e7e5fe47 GT |
531 | bn_check_top(a); |
532 | bn_check_top(p); | |
533 | ||
1dc920c8 BM |
534 | BN_CTX_start(ctx); |
535 | ||
034688ec AP |
536 | if ((b = BN_CTX_get(ctx))==NULL) goto err; |
537 | if ((c = BN_CTX_get(ctx))==NULL) goto err; | |
538 | if ((u = BN_CTX_get(ctx))==NULL) goto err; | |
539 | if ((v = BN_CTX_get(ctx))==NULL) goto err; | |
1dc920c8 | 540 | |
1dc920c8 | 541 | if (!BN_GF2m_mod(u, a, p)) goto err; |
1dc920c8 BM |
542 | if (BN_is_zero(u)) goto err; |
543 | ||
034688ec | 544 | if (!BN_copy(v, p)) goto err; |
dd83d0f4 | 545 | #if 0 |
034688ec AP |
546 | if (!BN_one(b)) goto err; |
547 | ||
1dc920c8 BM |
548 | while (1) |
549 | { | |
550 | while (!BN_is_odd(u)) | |
551 | { | |
8038e7e4 | 552 | if (BN_is_zero(u)) goto err; |
1dc920c8 BM |
553 | if (!BN_rshift1(u, u)) goto err; |
554 | if (BN_is_odd(b)) | |
555 | { | |
556 | if (!BN_GF2m_add(b, b, p)) goto err; | |
557 | } | |
558 | if (!BN_rshift1(b, b)) goto err; | |
559 | } | |
560 | ||
e1064adf | 561 | if (BN_abs_is_word(u, 1)) break; |
1dc920c8 BM |
562 | |
563 | if (BN_num_bits(u) < BN_num_bits(v)) | |
564 | { | |
565 | tmp = u; u = v; v = tmp; | |
566 | tmp = b; b = c; c = tmp; | |
567 | } | |
568 | ||
569 | if (!BN_GF2m_add(u, u, v)) goto err; | |
570 | if (!BN_GF2m_add(b, b, c)) goto err; | |
571 | } | |
034688ec AP |
572 | #else |
573 | { | |
574 | int i, ubits = BN_num_bits(u), | |
575 | vbits = BN_num_bits(v), /* v is copy of p */ | |
576 | top = p->top; | |
577 | BN_ULONG *udp,*bdp,*vdp,*cdp; | |
578 | ||
579 | bn_wexpand(u,top); udp = u->d; | |
580 | for (i=u->top;i<top;i++) udp[i] = 0; | |
581 | u->top = top; | |
582 | bn_wexpand(b,top); bdp = b->d; | |
583 | bdp[0] = 1; | |
584 | for (i=1;i<top;i++) bdp[i] = 0; | |
585 | b->top = top; | |
586 | bn_wexpand(c,top); cdp = c->d; | |
587 | for (i=0;i<top;i++) cdp[i] = 0; | |
588 | c->top = top; | |
589 | vdp = v->d; /* It pays off to "cache" *->d pointers, because | |
590 | * it allows optimizer to be more aggressive. | |
591 | * But we don't have to "cache" p->d, because *p | |
592 | * is declared 'const'... */ | |
593 | while (1) | |
594 | { | |
595 | while (ubits && !(udp[0]&1)) | |
596 | { | |
597 | BN_ULONG u0,u1,b0,b1,mask; | |
598 | ||
599 | u0 = udp[0]; | |
600 | b0 = bdp[0]; | |
601 | mask = (BN_ULONG)0-(b0&1); | |
602 | b0 ^= p->d[0]&mask; | |
603 | for (i=0;i<top-1;i++) | |
604 | { | |
605 | u1 = udp[i+1]; | |
606 | udp[i] = ((u0>>1)|(u1<<(BN_BITS2-1)))&BN_MASK2; | |
607 | u0 = u1; | |
608 | b1 = bdp[i+1]^(p->d[i+1]&mask); | |
609 | bdp[i] = ((b0>>1)|(b1<<(BN_BITS2-1)))&BN_MASK2; | |
610 | b0 = b1; | |
611 | } | |
612 | udp[i] = u0>>1; | |
613 | bdp[i] = b0>>1; | |
614 | ubits--; | |
615 | } | |
1dc920c8 | 616 | |
034688ec AP |
617 | if (ubits<=BN_BITS2 && udp[0]==1) break; |
618 | ||
619 | if (ubits<vbits) | |
620 | { | |
621 | i = ubits; ubits = vbits; vbits = i; | |
622 | tmp = u; u = v; v = tmp; | |
623 | tmp = b; b = c; c = tmp; | |
624 | udp = vdp; vdp = v->d; | |
625 | bdp = cdp; cdp = c->d; | |
626 | } | |
627 | for(i=0;i<top;i++) | |
628 | { | |
629 | udp[i] ^= vdp[i]; | |
630 | bdp[i] ^= cdp[i]; | |
631 | } | |
632 | if (ubits==vbits) | |
633 | { | |
d3379de5 | 634 | BN_ULONG ul; |
4736eab9 AP |
635 | int utop = (ubits-1)/BN_BITS2; |
636 | ||
d3379de5 DSH |
637 | while ((ul=udp[utop])==0 && utop) utop--; |
638 | ubits = utop*BN_BITS2 + BN_num_bits_word(ul); | |
034688ec AP |
639 | } |
640 | } | |
dd83d0f4 | 641 | bn_correct_top(b); |
034688ec AP |
642 | } |
643 | #endif | |
1dc920c8 BM |
644 | |
645 | if (!BN_copy(r, b)) goto err; | |
d870740c | 646 | bn_check_top(r); |
1dc920c8 BM |
647 | ret = 1; |
648 | ||
e7e5fe47 | 649 | err: |
0a06ad76 BM |
650 | #ifdef BN_DEBUG /* BN_CTX_end would complain about the expanded form */ |
651 | bn_correct_top(c); | |
4f201574 BM |
652 | bn_correct_top(u); |
653 | bn_correct_top(v); | |
0a06ad76 | 654 | #endif |
1dc920c8 BM |
655 | BN_CTX_end(ctx); |
656 | return ret; | |
657 | } | |
658 | ||
659 | /* Invert xx, reduce modulo p, and store the result in r. r could be xx. | |
660 | * | |
661 | * This function calls down to the BN_GF2m_mod_inv implementation; this wrapper | |
662 | * function is only provided for convenience; for best performance, use the | |
663 | * BN_GF2m_mod_inv function. | |
664 | */ | |
c4e7870a | 665 | int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[], BN_CTX *ctx) |
1dc920c8 BM |
666 | { |
667 | BIGNUM *field; | |
668 | int ret = 0; | |
669 | ||
e7e5fe47 | 670 | bn_check_top(xx); |
1dc920c8 BM |
671 | BN_CTX_start(ctx); |
672 | if ((field = BN_CTX_get(ctx)) == NULL) goto err; | |
673 | if (!BN_GF2m_arr2poly(p, field)) goto err; | |
674 | ||
675 | ret = BN_GF2m_mod_inv(r, xx, field, ctx); | |
d870740c | 676 | bn_check_top(r); |
1dc920c8 | 677 | |
e7e5fe47 | 678 | err: |
1dc920c8 BM |
679 | BN_CTX_end(ctx); |
680 | return ret; | |
681 | } | |
682 | ||
683 | ||
909abce8 | 684 | #ifndef OPENSSL_SUN_GF2M_DIV |
1dc920c8 BM |
685 | /* Divide y by x, reduce modulo p, and store the result in r. r could be x |
686 | * or y, x could equal y. | |
687 | */ | |
688 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p, BN_CTX *ctx) | |
689 | { | |
690 | BIGNUM *xinv = NULL; | |
691 | int ret = 0; | |
e7e5fe47 GT |
692 | |
693 | bn_check_top(y); | |
694 | bn_check_top(x); | |
695 | bn_check_top(p); | |
696 | ||
1dc920c8 BM |
697 | BN_CTX_start(ctx); |
698 | xinv = BN_CTX_get(ctx); | |
699 | if (xinv == NULL) goto err; | |
700 | ||
701 | if (!BN_GF2m_mod_inv(xinv, x, p, ctx)) goto err; | |
702 | if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx)) goto err; | |
d870740c | 703 | bn_check_top(r); |
1dc920c8 BM |
704 | ret = 1; |
705 | ||
e7e5fe47 | 706 | err: |
1dc920c8 BM |
707 | BN_CTX_end(ctx); |
708 | return ret; | |
709 | } | |
710 | #else | |
711 | /* Divide y by x, reduce modulo p, and store the result in r. r could be x | |
712 | * or y, x could equal y. | |
713 | * Uses algorithm Modular_Division_GF(2^m) from | |
714 | * Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to | |
715 | * the Great Divide". | |
716 | */ | |
717 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p, BN_CTX *ctx) | |
718 | { | |
719 | BIGNUM *a, *b, *u, *v; | |
720 | int ret = 0; | |
721 | ||
e7e5fe47 GT |
722 | bn_check_top(y); |
723 | bn_check_top(x); | |
724 | bn_check_top(p); | |
725 | ||
1dc920c8 BM |
726 | BN_CTX_start(ctx); |
727 | ||
728 | a = BN_CTX_get(ctx); | |
729 | b = BN_CTX_get(ctx); | |
730 | u = BN_CTX_get(ctx); | |
731 | v = BN_CTX_get(ctx); | |
732 | if (v == NULL) goto err; | |
733 | ||
734 | /* reduce x and y mod p */ | |
735 | if (!BN_GF2m_mod(u, y, p)) goto err; | |
736 | if (!BN_GF2m_mod(a, x, p)) goto err; | |
737 | if (!BN_copy(b, p)) goto err; | |
1dc920c8 | 738 | |
1dc920c8 BM |
739 | while (!BN_is_odd(a)) |
740 | { | |
741 | if (!BN_rshift1(a, a)) goto err; | |
742 | if (BN_is_odd(u)) if (!BN_GF2m_add(u, u, p)) goto err; | |
743 | if (!BN_rshift1(u, u)) goto err; | |
744 | } | |
745 | ||
746 | do | |
747 | { | |
748 | if (BN_GF2m_cmp(b, a) > 0) | |
749 | { | |
750 | if (!BN_GF2m_add(b, b, a)) goto err; | |
751 | if (!BN_GF2m_add(v, v, u)) goto err; | |
752 | do | |
753 | { | |
754 | if (!BN_rshift1(b, b)) goto err; | |
755 | if (BN_is_odd(v)) if (!BN_GF2m_add(v, v, p)) goto err; | |
756 | if (!BN_rshift1(v, v)) goto err; | |
757 | } while (!BN_is_odd(b)); | |
758 | } | |
e1064adf | 759 | else if (BN_abs_is_word(a, 1)) |
1dc920c8 BM |
760 | break; |
761 | else | |
762 | { | |
763 | if (!BN_GF2m_add(a, a, b)) goto err; | |
764 | if (!BN_GF2m_add(u, u, v)) goto err; | |
765 | do | |
766 | { | |
767 | if (!BN_rshift1(a, a)) goto err; | |
768 | if (BN_is_odd(u)) if (!BN_GF2m_add(u, u, p)) goto err; | |
769 | if (!BN_rshift1(u, u)) goto err; | |
770 | } while (!BN_is_odd(a)); | |
771 | } | |
772 | } while (1); | |
773 | ||
774 | if (!BN_copy(r, u)) goto err; | |
d870740c | 775 | bn_check_top(r); |
1dc920c8 BM |
776 | ret = 1; |
777 | ||
e7e5fe47 | 778 | err: |
1dc920c8 BM |
779 | BN_CTX_end(ctx); |
780 | return ret; | |
781 | } | |
782 | #endif | |
783 | ||
784 | /* Divide yy by xx, reduce modulo p, and store the result in r. r could be xx | |
785 | * or yy, xx could equal yy. | |
786 | * | |
787 | * This function calls down to the BN_GF2m_mod_div implementation; this wrapper | |
788 | * function is only provided for convenience; for best performance, use the | |
789 | * BN_GF2m_mod_div function. | |
790 | */ | |
c4e7870a | 791 | int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx, const int p[], BN_CTX *ctx) |
1dc920c8 BM |
792 | { |
793 | BIGNUM *field; | |
794 | int ret = 0; | |
795 | ||
e7e5fe47 GT |
796 | bn_check_top(yy); |
797 | bn_check_top(xx); | |
798 | ||
1dc920c8 BM |
799 | BN_CTX_start(ctx); |
800 | if ((field = BN_CTX_get(ctx)) == NULL) goto err; | |
801 | if (!BN_GF2m_arr2poly(p, field)) goto err; | |
802 | ||
803 | ret = BN_GF2m_mod_div(r, yy, xx, field, ctx); | |
d870740c | 804 | bn_check_top(r); |
1dc920c8 | 805 | |
e7e5fe47 | 806 | err: |
1dc920c8 BM |
807 | BN_CTX_end(ctx); |
808 | return ret; | |
809 | } | |
810 | ||
811 | ||
812 | /* Compute the bth power of a, reduce modulo p, and store | |
813 | * the result in r. r could be a. | |
814 | * Uses simple square-and-multiply algorithm A.5.1 from IEEE P1363. | |
815 | */ | |
c4e7870a | 816 | int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const int p[], BN_CTX *ctx) |
1dc920c8 BM |
817 | { |
818 | int ret = 0, i, n; | |
819 | BIGNUM *u; | |
e7e5fe47 GT |
820 | |
821 | bn_check_top(a); | |
822 | bn_check_top(b); | |
823 | ||
1dc920c8 | 824 | if (BN_is_zero(b)) |
1dc920c8 | 825 | return(BN_one(r)); |
e1064adf GT |
826 | |
827 | if (BN_abs_is_word(b, 1)) | |
828 | return (BN_copy(r, a) != NULL); | |
1dc920c8 BM |
829 | |
830 | BN_CTX_start(ctx); | |
831 | if ((u = BN_CTX_get(ctx)) == NULL) goto err; | |
832 | ||
833 | if (!BN_GF2m_mod_arr(u, a, p)) goto err; | |
834 | ||
835 | n = BN_num_bits(b) - 1; | |
836 | for (i = n - 1; i >= 0; i--) | |
837 | { | |
838 | if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx)) goto err; | |
839 | if (BN_is_bit_set(b, i)) | |
840 | { | |
841 | if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx)) goto err; | |
842 | } | |
843 | } | |
844 | if (!BN_copy(r, u)) goto err; | |
d870740c | 845 | bn_check_top(r); |
1dc920c8 | 846 | ret = 1; |
e7e5fe47 | 847 | err: |
1dc920c8 BM |
848 | BN_CTX_end(ctx); |
849 | return ret; | |
850 | } | |
851 | ||
852 | /* Compute the bth power of a, reduce modulo p, and store | |
853 | * the result in r. r could be a. | |
854 | * | |
855 | * This function calls down to the BN_GF2m_mod_exp_arr implementation; this wrapper | |
856 | * function is only provided for convenience; for best performance, use the | |
857 | * BN_GF2m_mod_exp_arr function. | |
858 | */ | |
859 | int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx) | |
860 | { | |
444c3a84 | 861 | int ret = 0; |
c4e7870a BM |
862 | const int max = BN_num_bits(p) + 1; |
863 | int *arr=NULL; | |
e7e5fe47 GT |
864 | bn_check_top(a); |
865 | bn_check_top(b); | |
866 | bn_check_top(p); | |
c4e7870a | 867 | if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err; |
e1064adf GT |
868 | ret = BN_GF2m_poly2arr(p, arr, max); |
869 | if (!ret || ret > max) | |
1dc920c8 BM |
870 | { |
871 | BNerr(BN_F_BN_GF2M_MOD_EXP,BN_R_INVALID_LENGTH); | |
872 | goto err; | |
873 | } | |
874 | ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx); | |
d870740c | 875 | bn_check_top(r); |
e7e5fe47 | 876 | err: |
1dc920c8 BM |
877 | if (arr) OPENSSL_free(arr); |
878 | return ret; | |
879 | } | |
880 | ||
881 | /* Compute the square root of a, reduce modulo p, and store | |
882 | * the result in r. r could be a. | |
883 | * Uses exponentiation as in algorithm A.4.1 from IEEE P1363. | |
884 | */ | |
c4e7870a | 885 | int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[], BN_CTX *ctx) |
1dc920c8 BM |
886 | { |
887 | int ret = 0; | |
888 | BIGNUM *u; | |
e1064adf | 889 | |
e7e5fe47 GT |
890 | bn_check_top(a); |
891 | ||
e1064adf | 892 | if (!p[0]) |
b6358c89 | 893 | { |
e1064adf | 894 | /* reduction mod 1 => return 0 */ |
b6358c89 GT |
895 | BN_zero(r); |
896 | return 1; | |
897 | } | |
e7e5fe47 | 898 | |
1dc920c8 BM |
899 | BN_CTX_start(ctx); |
900 | if ((u = BN_CTX_get(ctx)) == NULL) goto err; | |
901 | ||
1dc920c8 BM |
902 | if (!BN_set_bit(u, p[0] - 1)) goto err; |
903 | ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx); | |
d870740c | 904 | bn_check_top(r); |
1dc920c8 | 905 | |
e7e5fe47 | 906 | err: |
1dc920c8 BM |
907 | BN_CTX_end(ctx); |
908 | return ret; | |
909 | } | |
910 | ||
911 | /* Compute the square root of a, reduce modulo p, and store | |
912 | * the result in r. r could be a. | |
913 | * | |
914 | * This function calls down to the BN_GF2m_mod_sqrt_arr implementation; this wrapper | |
915 | * function is only provided for convenience; for best performance, use the | |
916 | * BN_GF2m_mod_sqrt_arr function. | |
917 | */ | |
918 | int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) | |
919 | { | |
444c3a84 | 920 | int ret = 0; |
c4e7870a BM |
921 | const int max = BN_num_bits(p) + 1; |
922 | int *arr=NULL; | |
e7e5fe47 GT |
923 | bn_check_top(a); |
924 | bn_check_top(p); | |
c4e7870a | 925 | if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err; |
e1064adf GT |
926 | ret = BN_GF2m_poly2arr(p, arr, max); |
927 | if (!ret || ret > max) | |
1dc920c8 | 928 | { |
aa4ce731 | 929 | BNerr(BN_F_BN_GF2M_MOD_SQRT,BN_R_INVALID_LENGTH); |
1dc920c8 BM |
930 | goto err; |
931 | } | |
932 | ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx); | |
d870740c | 933 | bn_check_top(r); |
e7e5fe47 | 934 | err: |
1dc920c8 BM |
935 | if (arr) OPENSSL_free(arr); |
936 | return ret; | |
937 | } | |
938 | ||
939 | /* Find r such that r^2 + r = a mod p. r could be a. If no r exists returns 0. | |
940 | * Uses algorithms A.4.7 and A.4.6 from IEEE P1363. | |
941 | */ | |
c4e7870a | 942 | int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[], BN_CTX *ctx) |
1dc920c8 | 943 | { |
1a4e245f | 944 | int ret = 0, count = 0, j; |
1dc920c8 | 945 | BIGNUM *a, *z, *rho, *w, *w2, *tmp; |
e1064adf | 946 | |
e7e5fe47 GT |
947 | bn_check_top(a_); |
948 | ||
e1064adf | 949 | if (!p[0]) |
b6358c89 | 950 | { |
e1064adf | 951 | /* reduction mod 1 => return 0 */ |
b6358c89 GT |
952 | BN_zero(r); |
953 | return 1; | |
954 | } | |
e1064adf | 955 | |
1dc920c8 BM |
956 | BN_CTX_start(ctx); |
957 | a = BN_CTX_get(ctx); | |
958 | z = BN_CTX_get(ctx); | |
959 | w = BN_CTX_get(ctx); | |
960 | if (w == NULL) goto err; | |
961 | ||
962 | if (!BN_GF2m_mod_arr(a, a_, p)) goto err; | |
963 | ||
964 | if (BN_is_zero(a)) | |
965 | { | |
b6358c89 GT |
966 | BN_zero(r); |
967 | ret = 1; | |
1dc920c8 BM |
968 | goto err; |
969 | } | |
970 | ||
971 | if (p[0] & 0x1) /* m is odd */ | |
972 | { | |
973 | /* compute half-trace of a */ | |
974 | if (!BN_copy(z, a)) goto err; | |
821385ad | 975 | for (j = 1; j <= (p[0] - 1) / 2; j++) |
1dc920c8 BM |
976 | { |
977 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err; | |
978 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err; | |
979 | if (!BN_GF2m_add(z, z, a)) goto err; | |
980 | } | |
981 | ||
982 | } | |
983 | else /* m is even */ | |
984 | { | |
985 | rho = BN_CTX_get(ctx); | |
986 | w2 = BN_CTX_get(ctx); | |
987 | tmp = BN_CTX_get(ctx); | |
988 | if (tmp == NULL) goto err; | |
989 | do | |
990 | { | |
991 | if (!BN_rand(rho, p[0], 0, 0)) goto err; | |
992 | if (!BN_GF2m_mod_arr(rho, rho, p)) goto err; | |
b6358c89 | 993 | BN_zero(z); |
1dc920c8 | 994 | if (!BN_copy(w, rho)) goto err; |
821385ad | 995 | for (j = 1; j <= p[0] - 1; j++) |
1dc920c8 BM |
996 | { |
997 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err; | |
998 | if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx)) goto err; | |
999 | if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx)) goto err; | |
1000 | if (!BN_GF2m_add(z, z, tmp)) goto err; | |
1001 | if (!BN_GF2m_add(w, w2, rho)) goto err; | |
1002 | } | |
1003 | count++; | |
1004 | } while (BN_is_zero(w) && (count < MAX_ITERATIONS)); | |
1005 | if (BN_is_zero(w)) | |
1006 | { | |
1007 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR,BN_R_TOO_MANY_ITERATIONS); | |
1008 | goto err; | |
1009 | } | |
1010 | } | |
1011 | ||
1012 | if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx)) goto err; | |
1013 | if (!BN_GF2m_add(w, z, w)) goto err; | |
ace3ebd6 GT |
1014 | if (BN_GF2m_cmp(w, a)) |
1015 | { | |
1016 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_NO_SOLUTION); | |
1017 | goto err; | |
1018 | } | |
1dc920c8 BM |
1019 | |
1020 | if (!BN_copy(r, z)) goto err; | |
d870740c | 1021 | bn_check_top(r); |
1dc920c8 BM |
1022 | |
1023 | ret = 1; | |
1024 | ||
e7e5fe47 | 1025 | err: |
1dc920c8 BM |
1026 | BN_CTX_end(ctx); |
1027 | return ret; | |
1028 | } | |
1029 | ||
1030 | /* Find r such that r^2 + r = a mod p. r could be a. If no r exists returns 0. | |
1031 | * | |
1032 | * This function calls down to the BN_GF2m_mod_solve_quad_arr implementation; this wrapper | |
1033 | * function is only provided for convenience; for best performance, use the | |
1034 | * BN_GF2m_mod_solve_quad_arr function. | |
1035 | */ | |
1036 | int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) | |
1037 | { | |
444c3a84 | 1038 | int ret = 0; |
c4e7870a BM |
1039 | const int max = BN_num_bits(p) + 1; |
1040 | int *arr=NULL; | |
e7e5fe47 GT |
1041 | bn_check_top(a); |
1042 | bn_check_top(p); | |
c4e7870a | 1043 | if ((arr = (int *)OPENSSL_malloc(sizeof(int) * |
444c3a84 | 1044 | max)) == NULL) goto err; |
e1064adf GT |
1045 | ret = BN_GF2m_poly2arr(p, arr, max); |
1046 | if (!ret || ret > max) | |
1dc920c8 BM |
1047 | { |
1048 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD,BN_R_INVALID_LENGTH); | |
1049 | goto err; | |
1050 | } | |
1051 | ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx); | |
d870740c | 1052 | bn_check_top(r); |
e7e5fe47 | 1053 | err: |
1dc920c8 BM |
1054 | if (arr) OPENSSL_free(arr); |
1055 | return ret; | |
1056 | } | |
1057 | ||
e1064adf | 1058 | /* Convert the bit-string representation of a polynomial |
c4e7870a BM |
1059 | * ( \sum_{i=0}^n a_i * x^i) into an array of integers corresponding |
1060 | * to the bits with non-zero coefficient. Array is terminated with -1. | |
1dc920c8 | 1061 | * Up to max elements of the array will be filled. Return value is total |
c4e7870a | 1062 | * number of array elements that would be filled if array was large enough. |
1dc920c8 | 1063 | */ |
c4e7870a | 1064 | int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max) |
1dc920c8 | 1065 | { |
e1064adf | 1066 | int i, j, k = 0; |
1dc920c8 BM |
1067 | BN_ULONG mask; |
1068 | ||
c4e7870a | 1069 | if (BN_is_zero(a)) |
e1064adf | 1070 | return 0; |
1dc920c8 BM |
1071 | |
1072 | for (i = a->top - 1; i >= 0; i--) | |
1073 | { | |
e1064adf GT |
1074 | if (!a->d[i]) |
1075 | /* skip word if a->d[i] == 0 */ | |
1076 | continue; | |
1dc920c8 BM |
1077 | mask = BN_TBIT; |
1078 | for (j = BN_BITS2 - 1; j >= 0; j--) | |
1079 | { | |
1080 | if (a->d[i] & mask) | |
1081 | { | |
1082 | if (k < max) p[k] = BN_BITS2 * i + j; | |
1083 | k++; | |
1084 | } | |
1085 | mask >>= 1; | |
1086 | } | |
1087 | } | |
1088 | ||
c4e7870a BM |
1089 | if (k < max) { |
1090 | p[k] = -1; | |
1091 | k++; | |
1092 | } | |
1093 | ||
1dc920c8 BM |
1094 | return k; |
1095 | } | |
1096 | ||
1097 | /* Convert the coefficient array representation of a polynomial to a | |
c4e7870a | 1098 | * bit-string. The array must be terminated by -1. |
1dc920c8 | 1099 | */ |
c4e7870a | 1100 | int BN_GF2m_arr2poly(const int p[], BIGNUM *a) |
1dc920c8 BM |
1101 | { |
1102 | int i; | |
1103 | ||
e7e5fe47 | 1104 | bn_check_top(a); |
1dc920c8 | 1105 | BN_zero(a); |
c4e7870a | 1106 | for (i = 0; p[i] != -1; i++) |
1dc920c8 | 1107 | { |
8c5a2bd6 NL |
1108 | if (BN_set_bit(a, p[i]) == 0) |
1109 | return 0; | |
1dc920c8 | 1110 | } |
d870740c | 1111 | bn_check_top(a); |
e7e5fe47 | 1112 | |
1dc920c8 BM |
1113 | return 1; |
1114 | } | |
1115 | ||
b3310161 | 1116 | #endif |