1 /* crypto/bn/bn_nist.c */
2 /*
3 * Written by Nils Larsch for the OpenSSL project
4 */
5 /* ====================================================================
6 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
7 *
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
10 * are met:
11 *
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
14 *
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in
17 * the documentation and/or other materials provided with the
18 * distribution.
19 *
20 * 3. All advertising materials mentioning features or use of this
21 * software must display the following acknowledgment:
22 * "This product includes software developed by the OpenSSL Project
23 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
24 *
25 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
26 * endorse or promote products derived from this software without
27 * prior written permission. For written permission, please contact
28 * openssl-core@openssl.org.
29 *
30 * 5. Products derived from this software may not be called "OpenSSL"
31 * nor may "OpenSSL" appear in their names without prior written
32 * permission of the OpenSSL Project.
33 *
34 * 6. Redistributions of any form whatsoever must retain the following
35 * acknowledgment:
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
38 *
39 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
40 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
41 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
42 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
43 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
44 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
45 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
46 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
48 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
49 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
50 * OF THE POSSIBILITY OF SUCH DAMAGE.
51 * ====================================================================
52 *
53 * This product includes cryptographic software written by Eric Young
54 * (eay@cryptsoft.com). This product includes software written by Tim
55 * Hudson (tjh@cryptsoft.com).
56 *
57 */
58
59 #include "bn_lcl.h"
60 #include "cryptlib.h"
61
62
63 #define BN_NIST_192_TOP (192+BN_BITS2-1)/BN_BITS2
64 #define BN_NIST_224_TOP (224+BN_BITS2-1)/BN_BITS2
65 #define BN_NIST_256_TOP (256+BN_BITS2-1)/BN_BITS2
66 #define BN_NIST_384_TOP (384+BN_BITS2-1)/BN_BITS2
67 #define BN_NIST_521_TOP (521+BN_BITS2-1)/BN_BITS2
68
69 /* pre-computed tables are "carry-less" values of modulus*(i+1) */
70 #if BN_BITS2 == 64
71 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
72 {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFFULL},
73 {0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL},
74 {0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFCULL,0xFFFFFFFFFFFFFFFFULL}
75 };
76 static const BN_ULONG _nist_p_192_sqr[] = {
77 0x0000000000000001ULL,0x0000000000000002ULL,0x0000000000000001ULL,
78 0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL
79 };
80 static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
81 {0x0000000000000001ULL,0xFFFFFFFF00000000ULL,
82 0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL},
83 {0x0000000000000002ULL,0xFFFFFFFE00000000ULL,
84 0xFFFFFFFFFFFFFFFFULL,0x00000001FFFFFFFFULL} /* this one is "carry-full" */
85 };
86 static const BN_ULONG _nist_p_224_sqr[] = {
87 0x0000000000000001ULL,0xFFFFFFFE00000000ULL,
88 0xFFFFFFFFFFFFFFFFULL,0x0000000200000000ULL,
89 0x0000000000000000ULL,0xFFFFFFFFFFFFFFFEULL,
90 0xFFFFFFFFFFFFFFFFULL
91 };
92 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
93 {0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL,
94 0x0000000000000000ULL,0xFFFFFFFF00000001ULL},
95 {0xFFFFFFFFFFFFFFFEULL,0x00000001FFFFFFFFULL,
96 0x0000000000000000ULL,0xFFFFFFFE00000002ULL},
97 {0xFFFFFFFFFFFFFFFDULL,0x00000002FFFFFFFFULL,
98 0x0000000000000000ULL,0xFFFFFFFD00000003ULL},
99 {0xFFFFFFFFFFFFFFFCULL,0x00000003FFFFFFFFULL,
100 0x0000000000000000ULL,0xFFFFFFFC00000004ULL},
101 {0xFFFFFFFFFFFFFFFBULL,0x00000004FFFFFFFFULL,
102 0x0000000000000000ULL,0xFFFFFFFB00000005ULL},
103 };
104 static const BN_ULONG _nist_p_256_sqr[] = {
105 0x0000000000000001ULL,0xFFFFFFFE00000000ULL,
106 0xFFFFFFFFFFFFFFFFULL,0x00000001FFFFFFFEULL,
107 0x00000001FFFFFFFEULL,0x00000001FFFFFFFEULL,
108 0xFFFFFFFE00000001ULL,0xFFFFFFFE00000002ULL
109 };
110 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
111 {0x00000000FFFFFFFFULL,0xFFFFFFFF00000000ULL,0xFFFFFFFFFFFFFFFEULL,
112 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
113 {0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
114 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
115 {0x00000002FFFFFFFDULL,0xFFFFFFFD00000000ULL,0xFFFFFFFFFFFFFFFCULL,
116 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
117 {0x00000003FFFFFFFCULL,0xFFFFFFFC00000000ULL,0xFFFFFFFFFFFFFFFBULL,
118 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
119 {0x00000004FFFFFFFBULL,0xFFFFFFFB00000000ULL,0xFFFFFFFFFFFFFFFAULL,
120 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
121 };
122 static const BN_ULONG _nist_p_384_sqr[] = {
123 0xFFFFFFFE00000001ULL,0x0000000200000000ULL,0xFFFFFFFE00000000ULL,
124 0x0000000200000000ULL,0x0000000000000001ULL,0x0000000000000000ULL,
125 0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
126 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL
127 };
128 static const BN_ULONG _nist_p_521[] =
129 {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
130 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
131 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
132 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
133 0x00000000000001FFULL};
134 static const BN_ULONG _nist_p_521_sqr[] = {
135 0x0000000000000001ULL,0x0000000000000000ULL,0x0000000000000000ULL,
136 0x0000000000000000ULL,0x0000000000000000ULL,0x0000000000000000ULL,
137 0x0000000000000000ULL,0x0000000000000000ULL,0xFFFFFFFFFFFFFC00ULL,
138 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
139 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
140 0xFFFFFFFFFFFFFFFFULL,0x000000000003FFFFULL
141 };
142 #elif BN_BITS2 == 32
143 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
144 {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
145 {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
146 {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
147 };
148 static const BN_ULONG _nist_p_192_sqr[] = {
149 0x00000001,0x00000000,0x00000002,0x00000000,0x00000001,0x00000000,
150 0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF
151 };
152 static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
153 {0x00000001,0x00000000,0x00000000,0xFFFFFFFF,
154 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
155 {0x00000002,0x00000000,0x00000000,0xFFFFFFFE,
156 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
157 };
158 static const BN_ULONG _nist_p_224_sqr[] = {
159 0x00000001,0x00000000,0x00000000,0xFFFFFFFE,
160 0xFFFFFFFF,0xFFFFFFFF,0x00000000,0x00000002,
161 0x00000000,0x00000000,0xFFFFFFFE,0xFFFFFFFF,
162 0xFFFFFFFF,0xFFFFFFFF
163 };
164 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
165 {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0x00000000,
166 0x00000000,0x00000000,0x00000001,0xFFFFFFFF},
167 {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0x00000001,
168 0x00000000,0x00000000,0x00000002,0xFFFFFFFE},
169 {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0x00000002,
170 0x00000000,0x00000000,0x00000003,0xFFFFFFFD},
171 {0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0x00000003,
172 0x00000000,0x00000000,0x00000004,0xFFFFFFFC},
173 {0xFFFFFFFB,0xFFFFFFFF,0xFFFFFFFF,0x00000004,
174 0x00000000,0x00000000,0x00000005,0xFFFFFFFB},
175 };
176 static const BN_ULONG _nist_p_256_sqr[] = {
177 0x00000001,0x00000000,0x00000000,0xFFFFFFFE,
178 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0x00000001,
179 0xFFFFFFFE,0x00000001,0xFFFFFFFE,0x00000001,
180 0x00000001,0xFFFFFFFE,0x00000002,0xFFFFFFFE
181 };
182 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
183 {0xFFFFFFFF,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,
184 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
185 {0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,0xFFFFFFFF,
186 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
187 {0xFFFFFFFD,0x00000002,0x00000000,0xFFFFFFFD,0xFFFFFFFC,0xFFFFFFFF,
188 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
189 {0xFFFFFFFC,0x00000003,0x00000000,0xFFFFFFFC,0xFFFFFFFB,0xFFFFFFFF,
190 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
191 {0xFFFFFFFB,0x00000004,0x00000000,0xFFFFFFFB,0xFFFFFFFA,0xFFFFFFFF,
192 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
193 };
194 static const BN_ULONG _nist_p_384_sqr[] = {
195 0x00000001,0xFFFFFFFE,0x00000000,0x00000002,0x00000000,0xFFFFFFFE,
196 0x00000000,0x00000002,0x00000001,0x00000000,0x00000000,0x00000000,
197 0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,0xFFFFFFFF,
198 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF
199 };
200 static const BN_ULONG _nist_p_521[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
201 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
202 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
203 0xFFFFFFFF,0x000001FF};
204 static const BN_ULONG _nist_p_521_sqr[] = {
205 0x00000001,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,
206 0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,
207 0x00000000,0x00000000,0x00000000,0x00000000,0xFFFFFC00,0xFFFFFFFF,
208 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
209 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
210 0xFFFFFFFF,0xFFFFFFFF,0x0003FFFF
211 };
212 #else
213 #error "unsupported BN_BITS2"
214 #endif
215
216
217 static const BIGNUM _bignum_nist_p_192 =
218 {
219 (BN_ULONG *)_nist_p_192[0],
220 BN_NIST_192_TOP,
221 BN_NIST_192_TOP,
222 0,
223 BN_FLG_STATIC_DATA
224 };
225
226 static const BIGNUM _bignum_nist_p_224 =
227 {
228 (BN_ULONG *)_nist_p_224[0],
229 BN_NIST_224_TOP,
230 BN_NIST_224_TOP,
231 0,
232 BN_FLG_STATIC_DATA
233 };
234
235 static const BIGNUM _bignum_nist_p_256 =
236 {
237 (BN_ULONG *)_nist_p_256[0],
238 BN_NIST_256_TOP,
239 BN_NIST_256_TOP,
240 0,
241 BN_FLG_STATIC_DATA
242 };
243
244 static const BIGNUM _bignum_nist_p_384 =
245 {
246 (BN_ULONG *)_nist_p_384[0],
247 BN_NIST_384_TOP,
248 BN_NIST_384_TOP,
249 0,
250 BN_FLG_STATIC_DATA
251 };
252
253 static const BIGNUM _bignum_nist_p_521 =
254 {
255 (BN_ULONG *)_nist_p_521,
256 BN_NIST_521_TOP,
257 BN_NIST_521_TOP,
258 0,
259 BN_FLG_STATIC_DATA
260 };
261
262
BN_get0_nist_prime_192(void)263 const BIGNUM *BN_get0_nist_prime_192(void)
264 {
265 return &_bignum_nist_p_192;
266 }
267
BN_get0_nist_prime_224(void)268 const BIGNUM *BN_get0_nist_prime_224(void)
269 {
270 return &_bignum_nist_p_224;
271 }
272
BN_get0_nist_prime_256(void)273 const BIGNUM *BN_get0_nist_prime_256(void)
274 {
275 return &_bignum_nist_p_256;
276 }
277
BN_get0_nist_prime_384(void)278 const BIGNUM *BN_get0_nist_prime_384(void)
279 {
280 return &_bignum_nist_p_384;
281 }
282
BN_get0_nist_prime_521(void)283 const BIGNUM *BN_get0_nist_prime_521(void)
284 {
285 return &_bignum_nist_p_521;
286 }
287
288
nist_cp_bn_0(BN_ULONG * buf,BN_ULONG * a,int top,int max)289 static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
290 {
291 int i;
292 BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
293
294 #ifdef BN_DEBUG
295 OPENSSL_assert(top <= max);
296 #endif
297 for (i = (top); i != 0; i--)
298 *_tmp1++ = *_tmp2++;
299 for (i = (max) - (top); i != 0; i--)
300 *_tmp1++ = (BN_ULONG) 0;
301 }
302
nist_cp_bn(BN_ULONG * buf,BN_ULONG * a,int top)303 static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
304 {
305 int i;
306 BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
307 for (i = (top); i != 0; i--)
308 *_tmp1++ = *_tmp2++;
309 }
310
311 #if BN_BITS2 == 64
312 #define bn_cp_64(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
313 #define bn_64_set_0(to, n) (to)[n] = (BN_ULONG)0;
314 /*
315 * two following macros are implemented under assumption that they
316 * are called in a sequence with *ascending* n, i.e. as they are...
317 */
318 #define bn_cp_32_naked(to, n, from, m) (((n)&1)?(to[(n)/2]|=((m)&1)?(from[(m)/2]&BN_MASK2h):(from[(m)/2]<<32))\
319 :(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
320 #define bn_32_set_0(to, n) (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
321 #define bn_cp_32(to,n,from,m) ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
322 #else
323 #define bn_cp_64(to, n, from, m) \
324 { \
325 bn_cp_32(to, (n)*2, from, (m)*2); \
326 bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
327 }
328 #define bn_64_set_0(to, n) \
329 { \
330 bn_32_set_0(to, (n)*2); \
331 bn_32_set_0(to, (n)*2+1); \
332 }
333 #if BN_BITS2 == 32
334 #define bn_cp_32(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
335 #define bn_32_set_0(to, n) (to)[n] = (BN_ULONG)0;
336 #endif
337 #endif /* BN_BITS2 != 64 */
338
339
340 #define nist_set_192(to, from, a1, a2, a3) \
341 { \
342 bn_cp_64(to, 0, from, (a3) - 3) \
343 bn_cp_64(to, 1, from, (a2) - 3) \
344 bn_cp_64(to, 2, from, (a1) - 3) \
345 }
346
BN_nist_mod_192(BIGNUM * r,const BIGNUM * a,const BIGNUM * field,BN_CTX * ctx)347 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
348 BN_CTX *ctx)
349 {
350 int top = a->top, i;
351 int carry;
352 register BN_ULONG *r_d, *a_d = a->d;
353 BN_ULONG t_d[BN_NIST_192_TOP],
354 buf[BN_NIST_192_TOP],
355 c_d[BN_NIST_192_TOP],
356 *res;
357 size_t mask;
358 static const BIGNUM _bignum_nist_p_192_sqr = {
359 (BN_ULONG *)_nist_p_192_sqr,
360 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
361 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
362 0,BN_FLG_STATIC_DATA };
363
364 field = &_bignum_nist_p_192; /* just to make sure */
365
366 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_192_sqr)>=0)
367 return BN_nnmod(r, a, field, ctx);
368
369 i = BN_ucmp(field, a);
370 if (i == 0)
371 {
372 BN_zero(r);
373 return 1;
374 }
375 else if (i > 0)
376 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
377
378 if (r != a)
379 {
380 if (!bn_wexpand(r, BN_NIST_192_TOP))
381 return 0;
382 r_d = r->d;
383 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
384 }
385 else
386 r_d = a_d;
387
388 nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
389
390 nist_set_192(t_d, buf, 0, 3, 3);
391 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
392 nist_set_192(t_d, buf, 4, 4, 0);
393 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
394 nist_set_192(t_d, buf, 5, 5, 5)
395 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
396
397 if (carry > 0)
398 carry = (int)bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
399 else
400 carry = 1;
401
402 /*
403 * we need 'if (carry==0 || result>=modulus) result-=modulus;'
404 * as comparison implies subtraction, we can write
405 * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
406 * this is what happens below, but without explicit if:-) a.
407 */
408 mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
409 mask &= 0-(size_t)carry;
410 res = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
411 nist_cp_bn(r_d, res, BN_NIST_192_TOP);
412 r->top = BN_NIST_192_TOP;
413 bn_correct_top(r);
414
415 return 1;
416 }
417
418 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
419
420 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
421 { \
422 bn_cp_32(to, 0, from, (a7) - 7) \
423 bn_cp_32(to, 1, from, (a6) - 7) \
424 bn_cp_32(to, 2, from, (a5) - 7) \
425 bn_cp_32(to, 3, from, (a4) - 7) \
426 bn_cp_32(to, 4, from, (a3) - 7) \
427 bn_cp_32(to, 5, from, (a2) - 7) \
428 bn_cp_32(to, 6, from, (a1) - 7) \
429 }
430
BN_nist_mod_224(BIGNUM * r,const BIGNUM * a,const BIGNUM * field,BN_CTX * ctx)431 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
432 BN_CTX *ctx)
433 {
434 int top = a->top, i;
435 int carry;
436 BN_ULONG *r_d, *a_d = a->d;
437 BN_ULONG t_d[BN_NIST_224_TOP],
438 buf[BN_NIST_224_TOP],
439 c_d[BN_NIST_224_TOP],
440 *res;
441 size_t mask;
442 union { bn_addsub_f f; size_t p; } u;
443 static const BIGNUM _bignum_nist_p_224_sqr = {
444 (BN_ULONG *)_nist_p_224_sqr,
445 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
446 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
447 0,BN_FLG_STATIC_DATA };
448
449
450 field = &_bignum_nist_p_224; /* just to make sure */
451
452 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_224_sqr)>=0)
453 return BN_nnmod(r, a, field, ctx);
454
455 i = BN_ucmp(field, a);
456 if (i == 0)
457 {
458 BN_zero(r);
459 return 1;
460 }
461 else if (i > 0)
462 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
463
464 if (r != a)
465 {
466 if (!bn_wexpand(r, BN_NIST_224_TOP))
467 return 0;
468 r_d = r->d;
469 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
470 }
471 else
472 r_d = a_d;
473
474 #if BN_BITS2==64
475 /* copy upper 256 bits of 448 bit number ... */
476 nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
477 /* ... and right shift by 32 to obtain upper 224 bits */
478 nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8);
479 /* truncate lower part to 224 bits too */
480 r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
481 #else
482 nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
483 #endif
484 nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
485 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
486 nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
487 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
488 nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
489 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
490 nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
491 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
492
493 #if BN_BITS2==64
494 carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
495 #endif
496 u.f = bn_sub_words;
497 if (carry > 0)
498 {
499 carry = (int)bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
500 #if BN_BITS2==64
501 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
502 #endif
503 }
504 else if (carry < 0)
505 {
506 /* it's a bit more comlicated logic in this case.
507 * if bn_add_words yields no carry, then result
508 * has to be adjusted by unconditionally *adding*
509 * the modulus. but if it does, then result has
510 * to be compared to the modulus and conditionally
511 * adjusted by *subtracting* the latter. */
512 carry = (int)bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
513 mask = 0-(size_t)carry;
514 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
515 }
516 else
517 carry = 1;
518
519 /* otherwise it's effectively same as in BN_nist_mod_192... */
520 mask = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
521 mask &= 0-(size_t)carry;
522 res = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
523 nist_cp_bn(r_d, res, BN_NIST_224_TOP);
524 r->top = BN_NIST_224_TOP;
525 bn_correct_top(r);
526
527 return 1;
528 }
529
530 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
531 { \
532 bn_cp_32(to, 0, from, (a8) - 8) \
533 bn_cp_32(to, 1, from, (a7) - 8) \
534 bn_cp_32(to, 2, from, (a6) - 8) \
535 bn_cp_32(to, 3, from, (a5) - 8) \
536 bn_cp_32(to, 4, from, (a4) - 8) \
537 bn_cp_32(to, 5, from, (a3) - 8) \
538 bn_cp_32(to, 6, from, (a2) - 8) \
539 bn_cp_32(to, 7, from, (a1) - 8) \
540 }
541
BN_nist_mod_256(BIGNUM * r,const BIGNUM * a,const BIGNUM * field,BN_CTX * ctx)542 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
543 BN_CTX *ctx)
544 {
545 int i, top = a->top;
546 int carry = 0;
547 register BN_ULONG *a_d = a->d, *r_d;
548 BN_ULONG t_d[BN_NIST_256_TOP],
549 buf[BN_NIST_256_TOP],
550 c_d[BN_NIST_256_TOP],
551 *res;
552 size_t mask;
553 union { bn_addsub_f f; size_t p; } u;
554 static const BIGNUM _bignum_nist_p_256_sqr = {
555 (BN_ULONG *)_nist_p_256_sqr,
556 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
557 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
558 0,BN_FLG_STATIC_DATA };
559
560 field = &_bignum_nist_p_256; /* just to make sure */
561
562 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_256_sqr)>=0)
563 return BN_nnmod(r, a, field, ctx);
564
565 i = BN_ucmp(field, a);
566 if (i == 0)
567 {
568 BN_zero(r);
569 return 1;
570 }
571 else if (i > 0)
572 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
573
574 if (r != a)
575 {
576 if (!bn_wexpand(r, BN_NIST_256_TOP))
577 return 0;
578 r_d = r->d;
579 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
580 }
581 else
582 r_d = a_d;
583
584 nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
585
586 /*S1*/
587 nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
588 /*S2*/
589 nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
590 carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
591 /* left shift */
592 {
593 register BN_ULONG *ap,t,c;
594 ap = t_d;
595 c=0;
596 for (i = BN_NIST_256_TOP; i != 0; --i)
597 {
598 t= *ap;
599 *(ap++)=((t<<1)|c)&BN_MASK2;
600 c=(t & BN_TBIT)?1:0;
601 }
602 carry <<= 1;
603 carry |= c;
604 }
605 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
606 /*S3*/
607 nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
608 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
609 /*S4*/
610 nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
611 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
612 /*D1*/
613 nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
614 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
615 /*D2*/
616 nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
617 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
618 /*D3*/
619 nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
620 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
621 /*D4*/
622 nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
623 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
624
625 /* see BN_nist_mod_224 for explanation */
626 u.f = bn_sub_words;
627 if (carry > 0)
628 carry = (int)bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
629 else if (carry < 0)
630 {
631 carry = (int)bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
632 mask = 0-(size_t)carry;
633 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
634 }
635 else
636 carry = 1;
637
638 mask = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
639 mask &= 0-(size_t)carry;
640 res = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
641 nist_cp_bn(r_d, res, BN_NIST_256_TOP);
642 r->top = BN_NIST_256_TOP;
643 bn_correct_top(r);
644
645 return 1;
646 }
647
648 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
649 { \
650 bn_cp_32(to, 0, from, (a12) - 12) \
651 bn_cp_32(to, 1, from, (a11) - 12) \
652 bn_cp_32(to, 2, from, (a10) - 12) \
653 bn_cp_32(to, 3, from, (a9) - 12) \
654 bn_cp_32(to, 4, from, (a8) - 12) \
655 bn_cp_32(to, 5, from, (a7) - 12) \
656 bn_cp_32(to, 6, from, (a6) - 12) \
657 bn_cp_32(to, 7, from, (a5) - 12) \
658 bn_cp_32(to, 8, from, (a4) - 12) \
659 bn_cp_32(to, 9, from, (a3) - 12) \
660 bn_cp_32(to, 10, from, (a2) - 12) \
661 bn_cp_32(to, 11, from, (a1) - 12) \
662 }
663
BN_nist_mod_384(BIGNUM * r,const BIGNUM * a,const BIGNUM * field,BN_CTX * ctx)664 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
665 BN_CTX *ctx)
666 {
667 int i, top = a->top;
668 int carry = 0;
669 register BN_ULONG *r_d, *a_d = a->d;
670 BN_ULONG t_d[BN_NIST_384_TOP],
671 buf[BN_NIST_384_TOP],
672 c_d[BN_NIST_384_TOP],
673 *res;
674 size_t mask;
675 union { bn_addsub_f f; size_t p; } u;
676 static const BIGNUM _bignum_nist_p_384_sqr = {
677 (BN_ULONG *)_nist_p_384_sqr,
678 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
679 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
680 0,BN_FLG_STATIC_DATA };
681
682
683 field = &_bignum_nist_p_384; /* just to make sure */
684
685 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_384_sqr)>=0)
686 return BN_nnmod(r, a, field, ctx);
687
688 i = BN_ucmp(field, a);
689 if (i == 0)
690 {
691 BN_zero(r);
692 return 1;
693 }
694 else if (i > 0)
695 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
696
697 if (r != a)
698 {
699 if (!bn_wexpand(r, BN_NIST_384_TOP))
700 return 0;
701 r_d = r->d;
702 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
703 }
704 else
705 r_d = a_d;
706
707 nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
708
709 /*S1*/
710 nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
711 /* left shift */
712 {
713 register BN_ULONG *ap,t,c;
714 ap = t_d;
715 c=0;
716 for (i = 3; i != 0; --i)
717 {
718 t= *ap;
719 *(ap++)=((t<<1)|c)&BN_MASK2;
720 c=(t & BN_TBIT)?1:0;
721 }
722 *ap=c;
723 }
724 carry = (int)bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
725 t_d, BN_NIST_256_TOP);
726 /*S2 */
727 carry += (int)bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
728 /*S3*/
729 nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
730 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
731 /*S4*/
732 nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
733 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
734 /*S5*/
735 nist_set_384(t_d, buf,0,0,0,0,23,22,21,20,0,0,0,0);
736 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
737 /*S6*/
738 nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
739 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
740 /*D1*/
741 nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
742 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
743 /*D2*/
744 nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
745 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
746 /*D3*/
747 nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
748 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
749
750 /* see BN_nist_mod_224 for explanation */
751 u.f = bn_sub_words;
752 if (carry > 0)
753 carry = (int)bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
754 else if (carry < 0)
755 {
756 carry = (int)bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
757 mask = 0-(size_t)carry;
758 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
759 }
760 else
761 carry = 1;
762
763 mask = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
764 mask &= 0-(size_t)carry;
765 res = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
766 nist_cp_bn(r_d, res, BN_NIST_384_TOP);
767 r->top = BN_NIST_384_TOP;
768 bn_correct_top(r);
769
770 return 1;
771 }
772
773 #define BN_NIST_521_RSHIFT (521%BN_BITS2)
774 #define BN_NIST_521_LSHIFT (BN_BITS2-BN_NIST_521_RSHIFT)
775 #define BN_NIST_521_TOP_MASK ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
776
BN_nist_mod_521(BIGNUM * r,const BIGNUM * a,const BIGNUM * field,BN_CTX * ctx)777 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
778 BN_CTX *ctx)
779 {
780 int top = a->top, i;
781 BN_ULONG *r_d, *a_d = a->d,
782 t_d[BN_NIST_521_TOP],
783 val,tmp,*res;
784 size_t mask;
785 static const BIGNUM _bignum_nist_p_521_sqr = {
786 (BN_ULONG *)_nist_p_521_sqr,
787 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
788 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
789 0,BN_FLG_STATIC_DATA };
790
791 field = &_bignum_nist_p_521; /* just to make sure */
792
793 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_521_sqr)>=0)
794 return BN_nnmod(r, a, field, ctx);
795
796 i = BN_ucmp(field, a);
797 if (i == 0)
798 {
799 BN_zero(r);
800 return 1;
801 }
802 else if (i > 0)
803 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
804
805 if (r != a)
806 {
807 if (!bn_wexpand(r,BN_NIST_521_TOP))
808 return 0;
809 r_d = r->d;
810 nist_cp_bn(r_d,a_d, BN_NIST_521_TOP);
811 }
812 else
813 r_d = a_d;
814
815 /* upper 521 bits, copy ... */
816 nist_cp_bn_0(t_d,a_d + (BN_NIST_521_TOP-1), top - (BN_NIST_521_TOP-1),BN_NIST_521_TOP);
817 /* ... and right shift */
818 for (val=t_d[0],i=0; i<BN_NIST_521_TOP-1; i++)
819 {
820 tmp = val>>BN_NIST_521_RSHIFT;
821 val = t_d[i+1];
822 t_d[i] = (tmp | val<<BN_NIST_521_LSHIFT) & BN_MASK2;
823 }
824 t_d[i] = val>>BN_NIST_521_RSHIFT;
825 /* lower 521 bits */
826 r_d[i] &= BN_NIST_521_TOP_MASK;
827
828 bn_add_words(r_d,r_d,t_d,BN_NIST_521_TOP);
829 mask = 0-(size_t)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
830 res = (BN_ULONG *)(((size_t)t_d&~mask) | ((size_t)r_d&mask));
831 nist_cp_bn(r_d,res,BN_NIST_521_TOP);
832 r->top = BN_NIST_521_TOP;
833 bn_correct_top(r);
834
835 return 1;
836 }
837