716dc81825379c258b7e75b88ae44ac3d96d2ce9
[openssl.git] / crypto / bn / bn_nist.c
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_224[][BN_NIST_224_TOP] = {
77         {0x0000000000000001ULL,0xFFFFFFFF00000000ULL,
78          0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL},
79         {0x0000000000000002ULL,0xFFFFFFFE00000000ULL,
80          0xFFFFFFFFFFFFFFFFULL,0x00000001FFFFFFFFULL} /* this one is "carry-full" */
81         };
82 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
83         {0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL,
84          0x0000000000000000ULL,0xFFFFFFFF00000001ULL},
85         {0xFFFFFFFFFFFFFFFEULL,0x00000001FFFFFFFFULL,
86          0x0000000000000000ULL,0xFFFFFFFE00000002ULL},
87         {0xFFFFFFFFFFFFFFFDULL,0x00000002FFFFFFFFULL,
88          0x0000000000000000ULL,0xFFFFFFFD00000003ULL},
89         {0xFFFFFFFFFFFFFFFCULL,0x00000003FFFFFFFFULL,
90          0x0000000000000000ULL,0xFFFFFFFC00000004ULL},
91         {0xFFFFFFFFFFFFFFFBULL,0x00000004FFFFFFFFULL,
92          0x0000000000000000ULL,0xFFFFFFFB00000005ULL},
93         };
94 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
95         {0x00000000FFFFFFFFULL,0xFFFFFFFF00000000ULL,0xFFFFFFFFFFFFFFFEULL,
96          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
97         {0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
98          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
99         {0x00000002FFFFFFFDULL,0xFFFFFFFD00000000ULL,0xFFFFFFFFFFFFFFFCULL,
100          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
101         {0x00000003FFFFFFFCULL,0xFFFFFFFC00000000ULL,0xFFFFFFFFFFFFFFFBULL,
102          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
103         {0x00000004FFFFFFFBULL,0xFFFFFFFB00000000ULL,0xFFFFFFFFFFFFFFFAULL,
104          0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
105         };
106 static const BN_ULONG _nist_p_521[] =
107         {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
108         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
109         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
110         0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
111         0x00000000000001FFULL};
112 #elif BN_BITS2 == 32
113 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
114         {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
115         {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
116         {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
117         };
118 static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
119         {0x00000001,0x00000000,0x00000000,0xFFFFFFFF,
120          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
121         {0x00000002,0x00000000,0x00000000,0xFFFFFFFE,
122          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
123         };
124 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
125         {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0x00000000,
126          0x00000000,0x00000000,0x00000001,0xFFFFFFFF},
127         {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0x00000001,
128          0x00000000,0x00000000,0x00000002,0xFFFFFFFE},
129         {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0x00000002,
130          0x00000000,0x00000000,0x00000003,0xFFFFFFFD},
131         {0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0x00000003,
132          0x00000000,0x00000000,0x00000004,0xFFFFFFFC},
133         {0xFFFFFFFB,0xFFFFFFFF,0xFFFFFFFF,0x00000004,
134          0x00000000,0x00000000,0x00000005,0xFFFFFFFB},
135         };
136 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
137         {0xFFFFFFFF,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,
138          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
139         {0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,0xFFFFFFFF,
140          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
141         {0xFFFFFFFD,0x00000002,0x00000000,0xFFFFFFFD,0xFFFFFFFC,0xFFFFFFFF,
142          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
143         {0xFFFFFFFC,0x00000003,0x00000000,0xFFFFFFFC,0xFFFFFFFB,0xFFFFFFFF,
144          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
145         {0xFFFFFFFB,0x00000004,0x00000000,0xFFFFFFFB,0xFFFFFFFA,0xFFFFFFFF,
146          0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
147         };
148 static const BN_ULONG _nist_p_521[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
149         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
150         0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
151         0xFFFFFFFF,0x000001FF};
152 #else
153 #error "unsupported BN_BITS2"
154 #endif
155
156
157 static const BIGNUM _bignum_nist_p_192 =
158         {
159         (BN_ULONG *)_nist_p_192[0],
160         BN_NIST_192_TOP,
161         BN_NIST_192_TOP,
162         0,
163         BN_FLG_STATIC_DATA
164         };
165
166 static const BIGNUM _bignum_nist_p_224 =
167         {
168         (BN_ULONG *)_nist_p_224[0],
169         BN_NIST_224_TOP,
170         BN_NIST_224_TOP,
171         0,
172         BN_FLG_STATIC_DATA
173         };
174
175 static const BIGNUM _bignum_nist_p_256 =
176         {
177         (BN_ULONG *)_nist_p_256[0],
178         BN_NIST_256_TOP,
179         BN_NIST_256_TOP,
180         0,
181         BN_FLG_STATIC_DATA
182         };
183
184 static const BIGNUM _bignum_nist_p_384 =
185         {
186         (BN_ULONG *)_nist_p_384[0],
187         BN_NIST_384_TOP,
188         BN_NIST_384_TOP,
189         0,
190         BN_FLG_STATIC_DATA
191         };
192
193 static const BIGNUM _bignum_nist_p_521 =
194         {
195         (BN_ULONG *)_nist_p_521,
196         BN_NIST_521_TOP,
197         BN_NIST_521_TOP,
198         0,
199         BN_FLG_STATIC_DATA
200         };
201
202
203 const BIGNUM *BN_get0_nist_prime_192(void)
204         {
205         return &_bignum_nist_p_192;
206         }
207
208 const BIGNUM *BN_get0_nist_prime_224(void)
209         {
210         return &_bignum_nist_p_224;
211         }
212
213 const BIGNUM *BN_get0_nist_prime_256(void)
214         {
215         return &_bignum_nist_p_256;
216         }
217
218 const BIGNUM *BN_get0_nist_prime_384(void)
219         {
220         return &_bignum_nist_p_384;
221         }
222
223 const BIGNUM *BN_get0_nist_prime_521(void)
224         {
225         return &_bignum_nist_p_521;
226         }
227
228
229 static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
230         {
231         int i;
232         BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
233
234         OPENSSL_assert(top <= max);
235         for (i = (top); i != 0; i--)
236                 *_tmp1++ = *_tmp2++;
237         for (i = (max) - (top); i != 0; i--)
238                 *_tmp1++ = (BN_ULONG) 0;
239         }
240
241 static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
242         { 
243         int i;
244         BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
245         for (i = (top); i != 0; i--)
246                 *_tmp1++ = *_tmp2++;
247         }
248
249 #if BN_BITS2 == 64
250 #define bn_cp_64(to, n, from, m)        (to)[n] = (m>=0)?((from)[m]):0;
251 #define bn_64_set_0(to, n)              (to)[n] = (BN_ULONG)0;
252 /*
253  * two following macros are implemented under assumption that they
254  * are called in a sequence with *ascending* n, i.e. as they are...
255  */
256 #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))\
257                                                 :(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
258 #define bn_32_set_0(to, n)              (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
259 #define bn_cp_32(to,n,from,m)           ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
260 #else
261 #define bn_cp_64(to, n, from, m) \
262         { \
263         bn_cp_32(to, (n)*2, from, (m)*2); \
264         bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
265         }
266 #define bn_64_set_0(to, n) \
267         { \
268         bn_32_set_0(to, (n)*2); \
269         bn_32_set_0(to, (n)*2+1); \
270         }
271 #if BN_BITS2 == 32
272 #define bn_cp_32(to, n, from, m)        (to)[n] = (m>=0)?((from)[m]):0;
273 #define bn_32_set_0(to, n)              (to)[n] = (BN_ULONG)0;
274 #endif
275 #endif /* BN_BITS2 != 64 */
276
277
278 #define nist_set_192(to, from, a1, a2, a3) \
279         { \
280         bn_cp_64(to, 0, from, (a3) - 3) \
281         bn_cp_64(to, 1, from, (a2) - 3) \
282         bn_cp_64(to, 2, from, (a1) - 3) \
283         }
284
285 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
286         BN_CTX *ctx)
287         {
288         int      top = a->top, i;
289         int      carry;
290         register BN_ULONG *r_d, *a_d = a->d;
291         BN_ULONG t_d[BN_NIST_192_TOP],
292                  buf[BN_NIST_192_TOP],
293                  c_d[BN_NIST_192_TOP],
294                 *res;
295         size_t   mask;
296
297         field = &_bignum_nist_p_192; /* just to make sure */
298
299         if (BN_is_negative(a) || a->top > 2*BN_NIST_192_TOP)
300                 return BN_nnmod(r, field, a, ctx);
301
302         i = BN_ucmp(field, a);
303         if (i == 0)
304                 {
305                 BN_zero(r);
306                 return 1;
307                 }
308         else if (i > 0)
309                 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
310
311         if (r != a)
312                 {
313                 if (!bn_wexpand(r, BN_NIST_192_TOP))
314                         return 0;
315                 r_d = r->d;
316                 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
317                 }
318         else
319                 r_d = a_d;
320
321         nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
322
323         nist_set_192(t_d, buf, 0, 3, 3);
324         carry = bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
325         nist_set_192(t_d, buf, 4, 4, 0);
326         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
327         nist_set_192(t_d, buf, 5, 5, 5)
328         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
329
330         if (carry > 0)
331                 carry = bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
332         else
333                 carry = 1;
334
335         /*
336          * we need 'if (carry==0 || result>=modulus) result-=modulus;'
337          * as comparison implies subtraction, we can write
338          * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
339          * this is what happens below, but without explicit if:-) a.
340          */
341         mask  = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
342         mask &= 0-(size_t)carry;
343         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
344         nist_cp_bn(r_d, res, BN_NIST_192_TOP);
345         r->top = BN_NIST_192_TOP;
346         bn_correct_top(r);
347
348         return 1;
349         }
350
351 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
352
353 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
354         { \
355         bn_cp_32(to, 0, from, (a7) - 7) \
356         bn_cp_32(to, 1, from, (a6) - 7) \
357         bn_cp_32(to, 2, from, (a5) - 7) \
358         bn_cp_32(to, 3, from, (a4) - 7) \
359         bn_cp_32(to, 4, from, (a3) - 7) \
360         bn_cp_32(to, 5, from, (a2) - 7) \
361         bn_cp_32(to, 6, from, (a1) - 7) \
362         }
363
364 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
365         BN_CTX *ctx)
366         {
367         int     top = a->top, i;
368         int     carry;
369         BN_ULONG *r_d, *a_d = a->d;
370         BN_ULONG t_d[BN_NIST_224_TOP],
371                  buf[BN_NIST_224_TOP],
372                  c_d[BN_NIST_224_TOP],
373                 *res;
374         size_t   mask;
375         union { bn_addsub_f f; size_t p; } u;
376
377         field = &_bignum_nist_p_224; /* just to make sure */
378
379         if (BN_is_negative(a) || a->top > (2*224+BN_BITS2-1)/BN_BITS2)
380                 return BN_nnmod(r, field, a, ctx);
381
382         i = BN_ucmp(field, a);
383         if (i == 0)
384                 {
385                 BN_zero(r);
386                 return 1;
387                 }
388         else if (i > 0)
389                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
390
391         if (r != a)
392                 {
393                 if (!bn_wexpand(r, BN_NIST_224_TOP))
394                         return 0;
395                 r_d = r->d;
396                 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
397                 }
398         else
399                 r_d = a_d;
400
401 #if BN_BITS2==64
402         /* copy upper 256 bits of 448 bit number ... */
403         nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
404         /* ... and right shift by 32 to obtain upper 224 bits */
405         nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8);
406         /* truncate lower part to 224 bits too */
407         r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
408 #else
409         nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
410 #endif
411         nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
412         carry = bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
413         nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
414         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
415         nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
416         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
417         nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
418         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
419
420 #if BN_BITS2==64
421         carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
422 #endif
423         u.f = bn_sub_words;
424         if (carry > 0)
425                 {
426                 carry = bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
427 #if BN_BITS2==64
428                 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
429 #endif
430                 }
431         else if (carry < 0)
432                 {
433                 /* it's a bit more comlicated logic in this case.
434                  * if bn_add_words yields no carry, then result
435                  * has to be adjusted by unconditionally *adding*
436                  * the modulus. but if it does, then result has
437                  * to be compared to the modulus and conditionally
438                  * adjusted by *subtracting* the latter. */
439                 carry = bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
440                 mask = 0-(size_t)carry;
441                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
442                 }
443         else
444                 carry = 1;
445
446         /* otherwise it's effectively same as in BN_nist_mod_192... */
447         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
448         mask &= 0-(size_t)carry;
449         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
450         nist_cp_bn(r_d, res, BN_NIST_224_TOP);
451         r->top = BN_NIST_224_TOP;
452         bn_correct_top(r);
453
454         return 1;
455         }
456
457 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
458         { \
459         bn_cp_32(to, 0, from, (a8) - 8) \
460         bn_cp_32(to, 1, from, (a7) - 8) \
461         bn_cp_32(to, 2, from, (a6) - 8) \
462         bn_cp_32(to, 3, from, (a5) - 8) \
463         bn_cp_32(to, 4, from, (a4) - 8) \
464         bn_cp_32(to, 5, from, (a3) - 8) \
465         bn_cp_32(to, 6, from, (a2) - 8) \
466         bn_cp_32(to, 7, from, (a1) - 8) \
467         }
468
469 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
470         BN_CTX *ctx)
471         {
472         int     i, top = a->top;
473         int     carry = 0;
474         register BN_ULONG *a_d = a->d, *r_d;
475         BN_ULONG t_d[BN_NIST_256_TOP],
476                  buf[BN_NIST_256_TOP],
477                  c_d[BN_NIST_256_TOP],
478                 *res;
479         size_t   mask;
480         union { bn_addsub_f f; size_t p; } u;
481
482         field = &_bignum_nist_p_256; /* just to make sure */
483
484         if (BN_is_negative(a) || a->top > 2*BN_NIST_256_TOP)
485                 return BN_nnmod(r, field, a, ctx);
486
487         i = BN_ucmp(field, a);
488         if (i == 0)
489                 {
490                 BN_zero(r);
491                 return 1;
492                 }
493         else if (i > 0)
494                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
495
496         if (r != a)
497                 {
498                 if (!bn_wexpand(r, BN_NIST_256_TOP))
499                         return 0;
500                 r_d = r->d;
501                 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
502                 }
503         else
504                 r_d = a_d;
505
506         nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
507
508         /*S1*/
509         nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
510         /*S2*/
511         nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
512         carry = bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
513         /* left shift */
514                 {
515                 register BN_ULONG *ap,t,c;
516                 ap = t_d;
517                 c=0;
518                 for (i = BN_NIST_256_TOP; i != 0; --i)
519                         {
520                         t= *ap;
521                         *(ap++)=((t<<1)|c)&BN_MASK2;
522                         c=(t & BN_TBIT)?1:0;
523                         }
524                 carry <<= 1;
525                 carry  |= c;
526                 }
527         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
528         /*S3*/
529         nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
530         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
531         /*S4*/
532         nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
533         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
534         /*D1*/
535         nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
536         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
537         /*D2*/
538         nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
539         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
540         /*D3*/
541         nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
542         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
543         /*D4*/
544         nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
545         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
546
547         /* see BN_nist_mod_224 for explanation */
548         u.f = bn_sub_words;
549         if (carry > 0)
550                 carry = bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
551         else if (carry < 0)
552                 {
553                 carry = bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
554                 mask = 0-(size_t)carry;
555                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
556                 }
557         else
558                 carry = 1;
559
560         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
561         mask &= 0-(size_t)carry;
562         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
563         nist_cp_bn(r_d, res, BN_NIST_256_TOP);
564         r->top = BN_NIST_256_TOP;
565         bn_correct_top(r);
566
567         return 1;
568         }
569
570 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
571         { \
572         bn_cp_32(to, 0, from,  (a12) - 12) \
573         bn_cp_32(to, 1, from,  (a11) - 12) \
574         bn_cp_32(to, 2, from,  (a10) - 12) \
575         bn_cp_32(to, 3, from,  (a9) - 12)  \
576         bn_cp_32(to, 4, from,  (a8) - 12)  \
577         bn_cp_32(to, 5, from,  (a7) - 12)  \
578         bn_cp_32(to, 6, from,  (a6) - 12)  \
579         bn_cp_32(to, 7, from,  (a5) - 12)  \
580         bn_cp_32(to, 8, from,  (a4) - 12)  \
581         bn_cp_32(to, 9, from,  (a3) - 12)  \
582         bn_cp_32(to, 10, from, (a2) - 12)  \
583         bn_cp_32(to, 11, from, (a1) - 12)  \
584         }
585
586 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
587         BN_CTX *ctx)
588         {
589         int     i, top = a->top;
590         int     carry = 0;
591         register BN_ULONG *r_d, *a_d = a->d;
592         BN_ULONG t_d[BN_NIST_384_TOP],
593                  buf[BN_NIST_384_TOP],
594                  c_d[BN_NIST_384_TOP],
595                 *res;
596         size_t   mask;
597         union { bn_addsub_f f; size_t p; } u;
598
599         field = &_bignum_nist_p_384; /* just to make sure */
600
601         if (BN_is_negative(a) || a->top > 2*BN_NIST_384_TOP)
602                 return BN_nnmod(r, field, a, ctx);
603
604         i = BN_ucmp(field, a);
605         if (i == 0)
606                 {
607                 BN_zero(r);
608                 return 1;
609                 }
610         else if (i > 0)
611                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
612
613         if (r != a)
614                 {
615                 if (!bn_wexpand(r, BN_NIST_384_TOP))
616                         return 0;
617                 r_d = r->d;
618                 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
619                 }
620         else
621                 r_d = a_d;
622
623         nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
624
625         /*S1*/
626         nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
627                 /* left shift */
628                 {
629                 register BN_ULONG *ap,t,c;
630                 ap = t_d;
631                 c=0;
632                 for (i = 3; i != 0; --i)
633                         {
634                         t= *ap;
635                         *(ap++)=((t<<1)|c)&BN_MASK2;
636                         c=(t & BN_TBIT)?1:0;
637                         }
638                 *ap=c;
639                 }
640         carry = bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2), 
641                 t_d, BN_NIST_256_TOP);
642         /*S2 */
643         carry += bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
644         /*S3*/
645         nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
646         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
647         /*S4*/
648         nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
649         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
650         /*S5*/
651         nist_set_384(t_d, buf,0,0,0,0,23,22,21,20,0,0,0,0);
652         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
653         /*S6*/
654         nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
655         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
656         /*D1*/
657         nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
658         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
659         /*D2*/
660         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
661         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
662         /*D3*/
663         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
664         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
665
666         /* see BN_nist_mod_224 for explanation */
667         u.f = bn_sub_words;
668         if (carry > 0)
669                 carry = bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
670         else if (carry < 0)
671                 {
672                 carry = bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
673                 mask = 0-(size_t)carry;
674                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
675                 }
676         else
677                 carry = 1;
678
679         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
680         mask &= 0-(size_t)carry;
681         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
682         nist_cp_bn(r_d, res, BN_NIST_384_TOP);
683         r->top = BN_NIST_384_TOP;
684         bn_correct_top(r);
685
686         return 1;
687         }
688
689 #define BN_NIST_521_RSHIFT      (521%BN_BITS2)
690 #define BN_NIST_521_LSHIFT      (BN_BITS2-BN_NIST_521_RSHIFT)
691 #define BN_NIST_521_TOP_MASK    ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
692
693 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
694         BN_CTX *ctx)
695         {
696         int     top = a->top, i;
697         BN_ULONG *r_d, *a_d = a->d,
698                  t_d[BN_NIST_521_TOP],
699                  val,tmp,*res;
700         size_t  mask;
701
702         field = &_bignum_nist_p_521; /* just to make sure */
703
704         if (BN_is_negative(a) || BN_num_bits(a)>2*521)
705                 return BN_nnmod(r, field, a, ctx);
706
707         i = BN_ucmp(field, a);
708         if (i == 0)
709                 {
710                 BN_zero(r);
711                 return 1;
712                 }
713         else if (i > 0)
714                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
715
716         if (r != a)
717                 {
718                 if (!bn_wexpand(r,BN_NIST_521_TOP))
719                         return 0;
720                 r_d = r->d;
721                 nist_cp_bn(r_d,a_d, BN_NIST_521_TOP);
722                 }
723         else
724                 r_d = a_d;
725
726         /* upper 521 bits, copy ... */
727         nist_cp_bn_0(t_d,a_d + (BN_NIST_521_TOP-1), top - (BN_NIST_521_TOP-1),BN_NIST_521_TOP);
728         /* ... and right shift */
729         for (val=t_d[0],i=0; i<BN_NIST_521_TOP-1; i++)
730                 {
731                 tmp = val>>BN_NIST_521_RSHIFT;
732                 val = t_d[i+1];
733                 t_d[i] = (tmp | val<<BN_NIST_521_LSHIFT) & BN_MASK2;
734                 }
735         t_d[i] = val>>BN_NIST_521_RSHIFT;
736         /* lower 521 bits */
737         r_d[i] &= BN_NIST_521_TOP_MASK;
738
739         bn_add_words(r_d,r_d,t_d,BN_NIST_521_TOP);
740         mask = 0-(size_t)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
741         res  = (BN_ULONG *)(((size_t)t_d&~mask) | ((size_t)r_d&mask));
742         nist_cp_bn(r_d,res,BN_NIST_521_TOP);
743         r->top = BN_NIST_521_TOP;
744         bn_correct_top(r);
745
746         return 1;
747         }