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