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[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         if (BN_ucmp(field, r) <= 0)
349                 {
350                 if (!BN_usub(r, r, field)) return 0;
351                 }
352
353         return 1;
354         }
355
356 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
357
358 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
359         { \
360         bn_cp_32(to, 0, from, (a7) - 7) \
361         bn_cp_32(to, 1, from, (a6) - 7) \
362         bn_cp_32(to, 2, from, (a5) - 7) \
363         bn_cp_32(to, 3, from, (a4) - 7) \
364         bn_cp_32(to, 4, from, (a3) - 7) \
365         bn_cp_32(to, 5, from, (a2) - 7) \
366         bn_cp_32(to, 6, from, (a1) - 7) \
367         }
368
369 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
370         BN_CTX *ctx)
371         {
372         int     top = a->top, i;
373         int     carry;
374         BN_ULONG *r_d, *a_d = a->d;
375         BN_ULONG t_d[BN_NIST_224_TOP],
376                  buf[BN_NIST_224_TOP],
377                  c_d[BN_NIST_224_TOP],
378                 *res;
379         size_t   mask;
380         union { bn_addsub_f f; size_t p; } u;
381
382         field = &_bignum_nist_p_224; /* just to make sure */
383
384         if (BN_is_negative(a) || a->top > 2*BN_NIST_224_TOP)
385                 return BN_nnmod(r, field, a, ctx);
386
387         i = BN_ucmp(field, a);
388         if (i == 0)
389                 {
390                 BN_zero(r);
391                 return 1;
392                 }
393         else if (i > 0)
394                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
395
396         if (r != a)
397                 {
398                 if (!bn_wexpand(r, BN_NIST_224_TOP))
399                         return 0;
400                 r_d = r->d;
401                 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
402                 }
403         else
404                 r_d = a_d;
405
406 #if BN_BITS2==64
407         /* copy upper 256 bits of 448 bit number ... */
408         nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
409         /* ... and right shift by 32 to obtain upper 224 bits */
410         nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8);
411         /* truncate lower part to 224 bits too */
412         r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
413 #else
414         nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
415 #endif
416         nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
417         carry = bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
418         nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
419         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
420         nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
421         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
422         nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
423         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
424
425 #if BN_BITS2==64
426         carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
427 #endif
428         u.f = bn_sub_words;
429         if (carry > 0)
430                 {
431                 carry = bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
432 #if BN_BITS2==64
433                 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
434 #endif
435                 }
436         else if (carry < 0)
437                 {
438                 /* it's a bit more comlicated logic in this case.
439                  * if bn_add_words yields no carry, then result
440                  * has to be adjusted by unconditionally *adding*
441                  * the modulus. but if it does, then result has
442                  * to be compared to the modulus and conditionally
443                  * adjusted by *subtracting* the latter. */
444                 carry = bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
445                 mask = 0-(size_t)carry;
446                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
447                 }
448         else
449                 carry = 1;
450
451         /* otherwise it's effectively same as in BN_nist_mod_192... */
452         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
453         mask &= 0-(size_t)carry;
454         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
455         nist_cp_bn(r_d, res, BN_NIST_224_TOP);
456         r->top = BN_NIST_224_TOP;
457         bn_correct_top(r);
458
459         if (BN_ucmp(field, r) <= 0)
460                 {
461                 if (!BN_usub(r, r, field)) return 0;
462                 }
463
464         return 1;
465         }
466
467 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
468         { \
469         bn_cp_32(to, 0, from, (a8) - 8) \
470         bn_cp_32(to, 1, from, (a7) - 8) \
471         bn_cp_32(to, 2, from, (a6) - 8) \
472         bn_cp_32(to, 3, from, (a5) - 8) \
473         bn_cp_32(to, 4, from, (a4) - 8) \
474         bn_cp_32(to, 5, from, (a3) - 8) \
475         bn_cp_32(to, 6, from, (a2) - 8) \
476         bn_cp_32(to, 7, from, (a1) - 8) \
477         }
478
479 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
480         BN_CTX *ctx)
481         {
482         int     i, top = a->top;
483         int     carry = 0;
484         register BN_ULONG *a_d = a->d, *r_d;
485         BN_ULONG t_d[BN_NIST_256_TOP],
486                  buf[BN_NIST_256_TOP],
487                  c_d[BN_NIST_256_TOP],
488                 *res;
489         size_t   mask;
490         union { bn_addsub_f f; size_t p; } u;
491
492         field = &_bignum_nist_p_256; /* just to make sure */
493
494         if (BN_is_negative(a) || a->top > 2*BN_NIST_256_TOP)
495                 return BN_nnmod(r, field, a, ctx);
496
497         i = BN_ucmp(field, a);
498         if (i == 0)
499                 {
500                 BN_zero(r);
501                 return 1;
502                 }
503         else if (i > 0)
504                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
505
506         if (r != a)
507                 {
508                 if (!bn_wexpand(r, BN_NIST_256_TOP))
509                         return 0;
510                 r_d = r->d;
511                 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
512                 }
513         else
514                 r_d = a_d;
515
516         nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
517
518         /*S1*/
519         nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
520         /*S2*/
521         nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
522         carry = bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
523         /* left shift */
524                 {
525                 register BN_ULONG *ap,t,c;
526                 ap = t_d;
527                 c=0;
528                 for (i = BN_NIST_256_TOP; i != 0; --i)
529                         {
530                         t= *ap;
531                         *(ap++)=((t<<1)|c)&BN_MASK2;
532                         c=(t & BN_TBIT)?1:0;
533                         }
534                 carry <<= 1;
535                 carry  |= c;
536                 }
537         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
538         /*S3*/
539         nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
540         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
541         /*S4*/
542         nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
543         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
544         /*D1*/
545         nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
546         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
547         /*D2*/
548         nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
549         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
550         /*D3*/
551         nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
552         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
553         /*D4*/
554         nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
555         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
556
557         /* see BN_nist_mod_224 for explanation */
558         u.f = bn_sub_words;
559         if (carry > 0)
560                 carry = bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
561         else if (carry < 0)
562                 {
563                 carry = bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
564                 mask = 0-(size_t)carry;
565                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
566                 }
567         else
568                 carry = 1;
569
570         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
571         mask &= 0-(size_t)carry;
572         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
573         nist_cp_bn(r_d, res, BN_NIST_256_TOP);
574         r->top = BN_NIST_256_TOP;
575         bn_correct_top(r);
576
577         if (BN_ucmp(field, r) <= 0)
578                 {
579                 if (!BN_usub(r, r, field)) return 0;
580                 }
581
582         return 1;
583         }
584
585 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
586         { \
587         bn_cp_32(to, 0, from,  (a12) - 12) \
588         bn_cp_32(to, 1, from,  (a11) - 12) \
589         bn_cp_32(to, 2, from,  (a10) - 12) \
590         bn_cp_32(to, 3, from,  (a9) - 12)  \
591         bn_cp_32(to, 4, from,  (a8) - 12)  \
592         bn_cp_32(to, 5, from,  (a7) - 12)  \
593         bn_cp_32(to, 6, from,  (a6) - 12)  \
594         bn_cp_32(to, 7, from,  (a5) - 12)  \
595         bn_cp_32(to, 8, from,  (a4) - 12)  \
596         bn_cp_32(to, 9, from,  (a3) - 12)  \
597         bn_cp_32(to, 10, from, (a2) - 12)  \
598         bn_cp_32(to, 11, from, (a1) - 12)  \
599         }
600
601 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
602         BN_CTX *ctx)
603         {
604         int     i, top = a->top;
605         int     carry = 0;
606         register BN_ULONG *r_d, *a_d = a->d;
607         BN_ULONG t_d[BN_NIST_384_TOP],
608                  buf[BN_NIST_384_TOP],
609                  c_d[BN_NIST_384_TOP],
610                 *res;
611         size_t   mask;
612         union { bn_addsub_f f; size_t p; } u;
613
614         field = &_bignum_nist_p_384; /* just to make sure */
615
616         if (BN_is_negative(a) || a->top > 2*BN_NIST_384_TOP)
617                 return BN_nnmod(r, field, a, ctx);
618
619         i = BN_ucmp(field, a);
620         if (i == 0)
621                 {
622                 BN_zero(r);
623                 return 1;
624                 }
625         else if (i > 0)
626                 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
627
628         if (r != a)
629                 {
630                 if (!bn_wexpand(r, BN_NIST_384_TOP))
631                         return 0;
632                 r_d = r->d;
633                 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
634                 }
635         else
636                 r_d = a_d;
637
638         nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
639
640         /*S1*/
641         nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
642                 /* left shift */
643                 {
644                 register BN_ULONG *ap,t,c;
645                 ap = t_d;
646                 c=0;
647                 for (i = 3; i != 0; --i)
648                         {
649                         t= *ap;
650                         *(ap++)=((t<<1)|c)&BN_MASK2;
651                         c=(t & BN_TBIT)?1:0;
652                         }
653                 *ap=c;
654                 }
655         carry = bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2), 
656                 t_d, BN_NIST_256_TOP);
657         /*S2 */
658         carry += bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
659         /*S3*/
660         nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
661         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
662         /*S4*/
663         nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
664         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
665         /*S5*/
666         nist_set_384(t_d, buf,0,0,0,0,23,22,21,20,0,0,0,0);
667         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
668         /*S6*/
669         nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
670         carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
671         /*D1*/
672         nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
673         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
674         /*D2*/
675         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
676         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
677         /*D3*/
678         nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
679         carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
680
681         /* see BN_nist_mod_224 for explanation */
682         u.f = bn_sub_words;
683         if (carry > 0)
684                 carry = bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
685         else if (carry < 0)
686                 {
687                 carry = bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
688                 mask = 0-(size_t)carry;
689                 u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
690                 }
691         else
692                 carry = 1;
693
694         mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
695         mask &= 0-(size_t)carry;
696         res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
697         nist_cp_bn(r_d, res, BN_NIST_384_TOP);
698         r->top = BN_NIST_384_TOP;
699         bn_correct_top(r);
700
701         if (BN_ucmp(field, r) <= 0)
702                 {
703                 if (!BN_usub(r, r, field)) return 0;
704                 }
705
706         return 1;
707         }
708
709 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
710         BN_CTX *ctx)
711         {
712 #if BN_BITS2 == 64
713 #define BN_NIST_521_TOP_MASK    (BN_ULONG)0x1FF
714 #elif BN_BITS2 == 32
715 #define BN_NIST_521_TOP_MASK    (BN_ULONG)0x1FF
716 #endif
717         int     top, ret = 0;
718         BN_ULONG *r_d;
719         BIGNUM  *tmp;
720
721         field = &_bignum_nist_p_521; /* just to make sure */
722
723         if (BN_is_negative(a))
724                 return BN_nnmod(r, field, a, ctx);
725
726         /* check whether a reduction is necessary */
727         top = a->top;
728         if (top < BN_NIST_521_TOP  || ( top == BN_NIST_521_TOP &&
729             (!(a->d[BN_NIST_521_TOP-1] & ~(BN_NIST_521_TOP_MASK)))))
730                 {
731                 int i = BN_ucmp(field, a);
732                 if (i == 0)
733                         {
734                         BN_zero(r);
735                         return 1;
736                         }
737                 else
738                         {
739 #ifdef BN_DEBUG
740                         OPENSSL_assert(i > 0); /* because 'field' is 1111...1111 */
741 #endif
742                         return (r == a)? 1 : (BN_copy(r ,a) != NULL);
743                         }
744                 }
745
746         if (BN_num_bits(a) > 2*521)
747                 return BN_nnmod(r, field, a, ctx);
748
749         BN_CTX_start(ctx);
750         tmp = BN_CTX_get(ctx);
751         if (!tmp)
752                 goto err;
753
754         if (!bn_wexpand(tmp, BN_NIST_521_TOP))
755                 goto err;
756         nist_cp_bn(tmp->d, a->d, BN_NIST_521_TOP);
757
758         tmp->top = BN_NIST_521_TOP;
759         tmp->d[BN_NIST_521_TOP-1]  &= BN_NIST_521_TOP_MASK;
760         bn_correct_top(tmp);
761
762         if (!BN_rshift(r, a, 521))
763                 goto err;
764
765         if (!BN_uadd(r, tmp, r))
766                 goto err;
767
768         if (BN_ucmp(field, r) <= 0)
769                 {
770                 if (!BN_usub(r, r, field)) goto err;
771                 }
772
773         ret = 1;
774 err:
775         BN_CTX_end(ctx);
776
777         bn_check_top(r);
778         return ret;
779         }