1 /* crypto/bn/bn_nist.c */
3 * Written by Nils Larsch for the OpenSSL project
5 /* ====================================================================
6 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
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9 * modification, are permitted provided that the following conditions
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13 * notice, this list of conditions and the following disclaimer.
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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/)"
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36 * "This product includes software developed by the OpenSSL Project
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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
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51 * ====================================================================
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).
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
69 /* pre-computed tables are "carry-less" values of modulus*(i+1) */
72 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
73 {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFFULL},
74 {0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL},
75 {0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFCULL,0xFFFFFFFFFFFFFFFFULL}
78 static const BN_ULONG _nist_p_192_sqr[] = {
79 0x0000000000000001ULL,0x0000000000000002ULL,0x0000000000000001ULL,
80 0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL
83 static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
84 {0x0000000000000001ULL,0xFFFFFFFF00000000ULL,
85 0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL},
86 {0x0000000000000002ULL,0xFFFFFFFE00000000ULL,
87 0xFFFFFFFFFFFFFFFFULL,0x00000001FFFFFFFFULL} /* this one is "carry-full" */
90 static const BN_ULONG _nist_p_224_sqr[] = {
91 0x0000000000000001ULL,0xFFFFFFFE00000000ULL,
92 0xFFFFFFFFFFFFFFFFULL,0x0000000200000000ULL,
93 0x0000000000000000ULL,0xFFFFFFFFFFFFFFFEULL,
97 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
98 {0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL,
99 0x0000000000000000ULL,0xFFFFFFFF00000001ULL},
100 {0xFFFFFFFFFFFFFFFEULL,0x00000001FFFFFFFFULL,
101 0x0000000000000000ULL,0xFFFFFFFE00000002ULL},
102 {0xFFFFFFFFFFFFFFFDULL,0x00000002FFFFFFFFULL,
103 0x0000000000000000ULL,0xFFFFFFFD00000003ULL},
104 {0xFFFFFFFFFFFFFFFCULL,0x00000003FFFFFFFFULL,
105 0x0000000000000000ULL,0xFFFFFFFC00000004ULL},
106 {0xFFFFFFFFFFFFFFFBULL,0x00000004FFFFFFFFULL,
107 0x0000000000000000ULL,0xFFFFFFFB00000005ULL},
110 static const BN_ULONG _nist_p_256_sqr[] = {
111 0x0000000000000001ULL,0xFFFFFFFE00000000ULL,
112 0xFFFFFFFFFFFFFFFFULL,0x00000001FFFFFFFEULL,
113 0x00000001FFFFFFFEULL,0x00000001FFFFFFFEULL,
114 0xFFFFFFFE00000001ULL,0xFFFFFFFE00000002ULL
117 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
118 {0x00000000FFFFFFFFULL,0xFFFFFFFF00000000ULL,0xFFFFFFFFFFFFFFFEULL,
119 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
120 {0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
121 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
122 {0x00000002FFFFFFFDULL,0xFFFFFFFD00000000ULL,0xFFFFFFFFFFFFFFFCULL,
123 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
124 {0x00000003FFFFFFFCULL,0xFFFFFFFC00000000ULL,0xFFFFFFFFFFFFFFFBULL,
125 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
126 {0x00000004FFFFFFFBULL,0xFFFFFFFB00000000ULL,0xFFFFFFFFFFFFFFFAULL,
127 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
130 static const BN_ULONG _nist_p_384_sqr[] = {
131 0xFFFFFFFE00000001ULL,0x0000000200000000ULL,0xFFFFFFFE00000000ULL,
132 0x0000000200000000ULL,0x0000000000000001ULL,0x0000000000000000ULL,
133 0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
134 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL
137 static const BN_ULONG _nist_p_521[] =
138 {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
139 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
140 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
141 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
142 0x00000000000001FFULL};
144 static const BN_ULONG _nist_p_521_sqr[] = {
145 0x0000000000000001ULL,0x0000000000000000ULL,0x0000000000000000ULL,
146 0x0000000000000000ULL,0x0000000000000000ULL,0x0000000000000000ULL,
147 0x0000000000000000ULL,0x0000000000000000ULL,0xFFFFFFFFFFFFFC00ULL,
148 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
149 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
150 0xFFFFFFFFFFFFFFFFULL,0x000000000003FFFFULL
154 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
155 {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
156 {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
157 {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
160 static const BN_ULONG _nist_p_192_sqr[] = {
161 0x00000001,0x00000000,0x00000002,0x00000000,0x00000001,0x00000000,
162 0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF
165 static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
166 {0x00000001,0x00000000,0x00000000,0xFFFFFFFF,
167 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
168 {0x00000002,0x00000000,0x00000000,0xFFFFFFFE,
169 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
172 static const BN_ULONG _nist_p_224_sqr[] = {
173 0x00000001,0x00000000,0x00000000,0xFFFFFFFE,
174 0xFFFFFFFF,0xFFFFFFFF,0x00000000,0x00000002,
175 0x00000000,0x00000000,0xFFFFFFFE,0xFFFFFFFF,
176 0xFFFFFFFF,0xFFFFFFFF
179 static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
180 {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0x00000000,
181 0x00000000,0x00000000,0x00000001,0xFFFFFFFF},
182 {0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0x00000001,
183 0x00000000,0x00000000,0x00000002,0xFFFFFFFE},
184 {0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0x00000002,
185 0x00000000,0x00000000,0x00000003,0xFFFFFFFD},
186 {0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0x00000003,
187 0x00000000,0x00000000,0x00000004,0xFFFFFFFC},
188 {0xFFFFFFFB,0xFFFFFFFF,0xFFFFFFFF,0x00000004,
189 0x00000000,0x00000000,0x00000005,0xFFFFFFFB},
192 static const BN_ULONG _nist_p_256_sqr[] = {
193 0x00000001,0x00000000,0x00000000,0xFFFFFFFE,
194 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0x00000001,
195 0xFFFFFFFE,0x00000001,0xFFFFFFFE,0x00000001,
196 0x00000001,0xFFFFFFFE,0x00000002,0xFFFFFFFE
199 static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
200 {0xFFFFFFFF,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,
201 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
202 {0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,0xFFFFFFFF,
203 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
204 {0xFFFFFFFD,0x00000002,0x00000000,0xFFFFFFFD,0xFFFFFFFC,0xFFFFFFFF,
205 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
206 {0xFFFFFFFC,0x00000003,0x00000000,0xFFFFFFFC,0xFFFFFFFB,0xFFFFFFFF,
207 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
208 {0xFFFFFFFB,0x00000004,0x00000000,0xFFFFFFFB,0xFFFFFFFA,0xFFFFFFFF,
209 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
212 static const BN_ULONG _nist_p_384_sqr[] = {
213 0x00000001,0xFFFFFFFE,0x00000000,0x00000002,0x00000000,0xFFFFFFFE,
214 0x00000000,0x00000002,0x00000001,0x00000000,0x00000000,0x00000000,
215 0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,0xFFFFFFFF,
216 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF
219 static const BN_ULONG _nist_p_521[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
220 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
221 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
222 0xFFFFFFFF,0x000001FF};
224 static const BN_ULONG _nist_p_521_sqr[] = {
225 0x00000001,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,
226 0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,
227 0x00000000,0x00000000,0x00000000,0x00000000,0xFFFFFC00,0xFFFFFFFF,
228 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
229 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
230 0xFFFFFFFF,0xFFFFFFFF,0x0003FFFF
233 #error "unsupported BN_BITS2"
237 static const BIGNUM _bignum_nist_p_192 =
239 (BN_ULONG *)_nist_p_192[0],
246 static const BIGNUM _bignum_nist_p_224 =
248 (BN_ULONG *)_nist_p_224[0],
255 static const BIGNUM _bignum_nist_p_256 =
257 (BN_ULONG *)_nist_p_256[0],
264 static const BIGNUM _bignum_nist_p_384 =
266 (BN_ULONG *)_nist_p_384[0],
273 static const BIGNUM _bignum_nist_p_521 =
275 (BN_ULONG *)_nist_p_521,
283 const BIGNUM *BN_get0_nist_prime_192(void)
285 return &_bignum_nist_p_192;
288 const BIGNUM *BN_get0_nist_prime_224(void)
290 return &_bignum_nist_p_224;
293 const BIGNUM *BN_get0_nist_prime_256(void)
295 return &_bignum_nist_p_256;
298 const BIGNUM *BN_get0_nist_prime_384(void)
300 return &_bignum_nist_p_384;
303 const BIGNUM *BN_get0_nist_prime_521(void)
305 return &_bignum_nist_p_521;
309 static void nist_cp_bn_0(BN_ULONG *buf, const BN_ULONG *a, int top, int max)
312 BN_ULONG *_tmp1 = (buf);
313 const BN_ULONG *_tmp2 = (a);
316 OPENSSL_assert(top <= max);
318 for (i = (top); i != 0; i--)
320 for (i = (max) - (top); i != 0; i--)
321 *_tmp1++ = (BN_ULONG) 0;
324 static void nist_cp_bn(BN_ULONG *buf, const BN_ULONG *a, int top)
327 BN_ULONG *_tmp1 = (buf);
328 const BN_ULONG *_tmp2 = (a);
330 for (i = (top); i != 0; i--)
335 #define bn_cp_64(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
336 #define bn_64_set_0(to, n) (to)[n] = (BN_ULONG)0;
338 * two following macros are implemented under assumption that they
339 * are called in a sequence with *ascending* n, i.e. as they are...
341 #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))\
342 :(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
343 #define bn_32_set_0(to, n) (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
344 #define bn_cp_32(to,n,from,m) ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
345 # if defined(L_ENDIAN)
346 # if defined(__arch64__)
347 # define NIST_INT64 long
349 # define NIST_INT64 long long
353 #define bn_cp_64(to, n, from, m) \
355 bn_cp_32(to, (n)*2, from, (m)*2); \
356 bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
358 #define bn_64_set_0(to, n) \
360 bn_32_set_0(to, (n)*2); \
361 bn_32_set_0(to, (n)*2+1); \
363 #define bn_cp_32(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
364 #define bn_32_set_0(to, n) (to)[n] = (BN_ULONG)0;
365 # if defined(_WIN32) && !defined(__GNUC__)
366 # define NIST_INT64 __int64
367 # elif defined(BN_LLONG)
368 # define NIST_INT64 long long
370 #endif /* BN_BITS2 != 64 */
372 #define nist_set_192(to, from, a1, a2, a3) \
374 bn_cp_64(to, 0, from, (a3) - 3) \
375 bn_cp_64(to, 1, from, (a2) - 3) \
376 bn_cp_64(to, 2, from, (a1) - 3) \
379 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
384 register BN_ULONG *r_d, *a_d = a->d;
386 BN_ULONG bn[BN_NIST_192_TOP];
387 unsigned int ui[BN_NIST_192_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
389 BN_ULONG c_d[BN_NIST_192_TOP],
392 static const BIGNUM _bignum_nist_p_192_sqr = {
393 (BN_ULONG *)_nist_p_192_sqr,
394 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
395 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
396 0,BN_FLG_STATIC_DATA };
398 field = &_bignum_nist_p_192; /* just to make sure */
400 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_192_sqr)>=0)
401 return BN_nnmod(r, a, field, ctx);
403 i = BN_ucmp(field, a);
410 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
414 if (!bn_wexpand(r, BN_NIST_192_TOP))
417 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
422 nist_cp_bn_0(buf.bn, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
424 #if defined(NIST_INT64)
426 NIST_INT64 acc; /* accumulator */
427 unsigned int *rp=(unsigned int *)r_d;
428 const unsigned int *bp=(const unsigned int *)buf.ui;
430 acc = rp[0]; acc += bp[3*2-6];
431 acc += bp[5*2-6]; rp[0] = (unsigned int)acc; acc >>= 32;
433 acc += rp[1]; acc += bp[3*2-5];
434 acc += bp[5*2-5]; rp[1] = (unsigned int)acc; acc >>= 32;
436 acc += rp[2]; acc += bp[3*2-6];
438 acc += bp[5*2-6]; rp[2] = (unsigned int)acc; acc >>= 32;
440 acc += rp[3]; acc += bp[3*2-5];
442 acc += bp[5*2-5]; rp[3] = (unsigned int)acc; acc >>= 32;
444 acc += rp[4]; acc += bp[4*2-6];
445 acc += bp[5*2-6]; rp[4] = (unsigned int)acc; acc >>= 32;
447 acc += rp[5]; acc += bp[4*2-5];
448 acc += bp[5*2-5]; rp[5] = (unsigned int)acc;
450 carry = (int)(acc>>32);
454 BN_ULONG t_d[BN_NIST_192_TOP];
456 nist_set_192(t_d, buf.bn, 0, 3, 3);
457 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
458 nist_set_192(t_d, buf.bn, 4, 4, 0);
459 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
460 nist_set_192(t_d, buf.bn, 5, 5, 5)
461 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
465 carry = (int)bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
470 * we need 'if (carry==0 || result>=modulus) result-=modulus;'
471 * as comparison implies subtraction, we can write
472 * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
473 * this is what happens below, but without explicit if:-) a.
475 mask = 0-(PTR_SIZE_INT)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
476 mask &= 0-(PTR_SIZE_INT)carry;
479 (((PTR_SIZE_INT)res&~mask) | ((PTR_SIZE_INT)r_d&mask));
480 nist_cp_bn(r_d, res, BN_NIST_192_TOP);
481 r->top = BN_NIST_192_TOP;
487 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
489 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
491 bn_cp_32(to, 0, from, (a7) - 7) \
492 bn_cp_32(to, 1, from, (a6) - 7) \
493 bn_cp_32(to, 2, from, (a5) - 7) \
494 bn_cp_32(to, 3, from, (a4) - 7) \
495 bn_cp_32(to, 4, from, (a3) - 7) \
496 bn_cp_32(to, 5, from, (a2) - 7) \
497 bn_cp_32(to, 6, from, (a1) - 7) \
500 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
505 BN_ULONG *r_d, *a_d = a->d;
507 BN_ULONG bn[BN_NIST_224_TOP];
508 unsigned int ui[BN_NIST_224_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
510 BN_ULONG c_d[BN_NIST_224_TOP],
513 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
514 static const BIGNUM _bignum_nist_p_224_sqr = {
515 (BN_ULONG *)_nist_p_224_sqr,
516 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
517 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
518 0,BN_FLG_STATIC_DATA };
521 field = &_bignum_nist_p_224; /* just to make sure */
523 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_224_sqr)>=0)
524 return BN_nnmod(r, a, field, ctx);
526 i = BN_ucmp(field, a);
533 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
537 if (!bn_wexpand(r, BN_NIST_224_TOP))
540 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
546 /* copy upper 256 bits of 448 bit number ... */
547 nist_cp_bn_0(c_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
548 /* ... and right shift by 32 to obtain upper 224 bits */
549 nist_set_224(buf.bn, c_d, 14, 13, 12, 11, 10, 9, 8);
550 /* truncate lower part to 224 bits too */
551 r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
553 nist_cp_bn_0(buf.bn, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
556 #if defined(NIST_INT64) && BN_BITS2!=64
558 NIST_INT64 acc; /* accumulator */
559 unsigned int *rp=(unsigned int *)r_d;
560 const unsigned int *bp=(const unsigned int *)buf.ui;
562 acc = rp[0]; acc -= bp[7-7];
563 acc -= bp[11-7]; rp[0] = (unsigned int)acc; acc >>= 32;
565 acc += rp[1]; acc -= bp[8-7];
566 acc -= bp[12-7]; rp[1] = (unsigned int)acc; acc >>= 32;
568 acc += rp[2]; acc -= bp[9-7];
569 acc -= bp[13-7]; rp[2] = (unsigned int)acc; acc >>= 32;
571 acc += rp[3]; acc += bp[7-7];
573 acc -= bp[10-7]; rp[3] = (unsigned int)acc; acc>>= 32;
575 acc += rp[4]; acc += bp[8-7];
577 acc -= bp[11-7]; rp[4] = (unsigned int)acc; acc >>= 32;
579 acc += rp[5]; acc += bp[9-7];
581 acc -= bp[12-7]; rp[5] = (unsigned int)acc; acc >>= 32;
583 acc += rp[6]; acc += bp[10-7];
584 acc -= bp[13-7]; rp[6] = (unsigned int)acc;
586 carry = (int)(acc>>32);
593 BN_ULONG t_d[BN_NIST_224_TOP];
595 nist_set_224(t_d, buf.bn, 10, 9, 8, 7, 0, 0, 0);
596 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
597 nist_set_224(t_d, buf.bn, 0, 13, 12, 11, 0, 0, 0);
598 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
599 nist_set_224(t_d, buf.bn, 13, 12, 11, 10, 9, 8, 7);
600 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
601 nist_set_224(t_d, buf.bn, 0, 0, 0, 0, 13, 12, 11);
602 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
605 carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
612 carry = (int)bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
614 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
619 /* it's a bit more comlicated logic in this case.
620 * if bn_add_words yields no carry, then result
621 * has to be adjusted by unconditionally *adding*
622 * the modulus. but if it does, then result has
623 * to be compared to the modulus and conditionally
624 * adjusted by *subtracting* the latter. */
625 carry = (int)bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
626 mask = 0-(PTR_SIZE_INT)carry;
627 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
628 ((PTR_SIZE_INT)bn_add_words&~mask);
633 /* otherwise it's effectively same as in BN_nist_mod_192... */
634 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
635 mask &= 0-(PTR_SIZE_INT)carry;
637 res = (BN_ULONG *)(((PTR_SIZE_INT)res&~mask) |
638 ((PTR_SIZE_INT)r_d&mask));
639 nist_cp_bn(r_d, res, BN_NIST_224_TOP);
640 r->top = BN_NIST_224_TOP;
646 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
648 bn_cp_32(to, 0, from, (a8) - 8) \
649 bn_cp_32(to, 1, from, (a7) - 8) \
650 bn_cp_32(to, 2, from, (a6) - 8) \
651 bn_cp_32(to, 3, from, (a5) - 8) \
652 bn_cp_32(to, 4, from, (a4) - 8) \
653 bn_cp_32(to, 5, from, (a3) - 8) \
654 bn_cp_32(to, 6, from, (a2) - 8) \
655 bn_cp_32(to, 7, from, (a1) - 8) \
658 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
663 register BN_ULONG *a_d = a->d, *r_d;
665 BN_ULONG bn[BN_NIST_256_TOP];
666 unsigned int ui[BN_NIST_256_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
668 BN_ULONG c_d[BN_NIST_256_TOP],
671 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
672 static const BIGNUM _bignum_nist_p_256_sqr = {
673 (BN_ULONG *)_nist_p_256_sqr,
674 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
675 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
676 0,BN_FLG_STATIC_DATA };
678 field = &_bignum_nist_p_256; /* just to make sure */
680 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_256_sqr)>=0)
681 return BN_nnmod(r, a, field, ctx);
683 i = BN_ucmp(field, a);
690 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
694 if (!bn_wexpand(r, BN_NIST_256_TOP))
697 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
702 nist_cp_bn_0(buf.bn, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
704 #if defined(NIST_INT64)
706 NIST_INT64 acc; /* accumulator */
707 unsigned int *rp=(unsigned int *)r_d;
708 const unsigned int *bp=(const unsigned int *)buf.ui;
710 acc = rp[0]; acc += bp[8-8];
715 acc -= bp[14-8]; rp[0] = (unsigned int)acc; acc >>= 32;
717 acc += rp[1]; acc += bp[9-8];
722 acc -= bp[15-8]; rp[1] = (unsigned int)acc; acc >>= 32;
724 acc += rp[2]; acc += bp[10-8];
728 acc -= bp[15-8]; rp[2] = (unsigned int)acc; acc >>= 32;
730 acc += rp[3]; acc += bp[11-8];
737 acc -= bp[9-8]; rp[3] = (unsigned int)acc; acc >>= 32;
739 acc += rp[4]; acc += bp[12-8];
745 acc -= bp[10-8]; rp[4] = (unsigned int)acc; acc >>= 32;
747 acc += rp[5]; acc += bp[13-8];
753 acc -= bp[11-8]; rp[5] = (unsigned int)acc; acc >>= 32;
755 acc += rp[6]; acc += bp[14-8];
762 acc -= bp[9-8]; rp[6] = (unsigned int)acc; acc >>= 32;
764 acc += rp[7]; acc += bp[15-8];
771 acc -= bp[13-8]; rp[7] = (unsigned int)acc;
773 carry = (int)(acc>>32);
777 BN_ULONG t_d[BN_NIST_256_TOP];
780 nist_set_256(t_d, buf.bn, 15, 14, 13, 12, 11, 0, 0, 0);
782 nist_set_256(c_d, buf.bn, 0, 15, 14, 13, 12, 0, 0, 0);
783 carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
786 register BN_ULONG *ap,t,c;
789 for (i = BN_NIST_256_TOP; i != 0; --i)
792 *(ap++)=((t<<1)|c)&BN_MASK2;
798 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
800 nist_set_256(t_d, buf.bn, 15, 14, 0, 0, 0, 10, 9, 8);
801 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
803 nist_set_256(t_d, buf.bn, 8, 13, 15, 14, 13, 11, 10, 9);
804 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
806 nist_set_256(t_d, buf.bn, 10, 8, 0, 0, 0, 13, 12, 11);
807 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
809 nist_set_256(t_d, buf.bn, 11, 9, 0, 0, 15, 14, 13, 12);
810 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
812 nist_set_256(t_d, buf.bn, 12, 0, 10, 9, 8, 15, 14, 13);
813 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
815 nist_set_256(t_d, buf.bn, 13, 0, 11, 10, 9, 0, 15, 14);
816 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
820 /* see BN_nist_mod_224 for explanation */
823 carry = (int)bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
826 carry = (int)bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
827 mask = 0-(PTR_SIZE_INT)carry;
828 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
829 ((PTR_SIZE_INT)bn_add_words&~mask);
834 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
835 mask &= 0-(PTR_SIZE_INT)carry;
837 res = (BN_ULONG *)(((PTR_SIZE_INT)res&~mask) |
838 ((PTR_SIZE_INT)r_d&mask));
839 nist_cp_bn(r_d, res, BN_NIST_256_TOP);
840 r->top = BN_NIST_256_TOP;
846 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
848 bn_cp_32(to, 0, from, (a12) - 12) \
849 bn_cp_32(to, 1, from, (a11) - 12) \
850 bn_cp_32(to, 2, from, (a10) - 12) \
851 bn_cp_32(to, 3, from, (a9) - 12) \
852 bn_cp_32(to, 4, from, (a8) - 12) \
853 bn_cp_32(to, 5, from, (a7) - 12) \
854 bn_cp_32(to, 6, from, (a6) - 12) \
855 bn_cp_32(to, 7, from, (a5) - 12) \
856 bn_cp_32(to, 8, from, (a4) - 12) \
857 bn_cp_32(to, 9, from, (a3) - 12) \
858 bn_cp_32(to, 10, from, (a2) - 12) \
859 bn_cp_32(to, 11, from, (a1) - 12) \
862 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
867 register BN_ULONG *r_d, *a_d = a->d;
869 BN_ULONG bn[BN_NIST_384_TOP];
870 unsigned int ui[BN_NIST_384_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
872 BN_ULONG c_d[BN_NIST_384_TOP],
875 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
876 static const BIGNUM _bignum_nist_p_384_sqr = {
877 (BN_ULONG *)_nist_p_384_sqr,
878 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
879 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
880 0,BN_FLG_STATIC_DATA };
883 field = &_bignum_nist_p_384; /* just to make sure */
885 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_384_sqr)>=0)
886 return BN_nnmod(r, a, field, ctx);
888 i = BN_ucmp(field, a);
895 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
899 if (!bn_wexpand(r, BN_NIST_384_TOP))
902 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
907 nist_cp_bn_0(buf.bn, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
909 #if defined(NIST_INT64)
911 NIST_INT64 acc; /* accumulator */
912 unsigned int *rp=(unsigned int *)r_d;
913 const unsigned int *bp=(const unsigned int *)buf.ui;
915 acc = rp[0]; acc += bp[12-12];
918 acc -= bp[23-12]; rp[0] = (unsigned int)acc; acc >>= 32;
920 acc += rp[1]; acc += bp[13-12];
924 acc -= bp[20-12]; rp[1] = (unsigned int)acc; acc >>= 32;
926 acc += rp[2]; acc += bp[14-12];
929 acc -= bp[21-12]; rp[2] = (unsigned int)acc; acc >>= 32;
931 acc += rp[3]; acc += bp[15-12];
937 acc -= bp[23-12]; rp[3] = (unsigned int)acc; acc >>= 32;
939 acc += rp[4]; acc += bp[21-12];
948 acc -= bp[23-12]; rp[4] = (unsigned int)acc; acc >>= 32;
950 acc += rp[5]; acc += bp[22-12];
957 acc -= bp[16-12]; rp[5] = (unsigned int)acc; acc >>= 32;
959 acc += rp[6]; acc += bp[23-12];
965 acc -= bp[17-12]; rp[6] = (unsigned int)acc; acc >>= 32;
967 acc += rp[7]; acc += bp[19-12];
971 acc -= bp[18-12]; rp[7] = (unsigned int)acc; acc >>= 32;
973 acc += rp[8]; acc += bp[20-12];
976 acc -= bp[19-12]; rp[8] = (unsigned int)acc; acc >>= 32;
978 acc += rp[9]; acc += bp[21-12];
981 acc -= bp[20-12]; rp[9] = (unsigned int)acc; acc >>= 32;
983 acc += rp[10]; acc += bp[22-12];
986 acc -= bp[21-12]; rp[10] = (unsigned int)acc; acc >>= 32;
988 acc += rp[11]; acc += bp[23-12];
991 acc -= bp[22-12]; rp[11] = (unsigned int)acc;
993 carry = (int)(acc>>32);
997 BN_ULONG t_d[BN_NIST_384_TOP];
1000 nist_set_256(t_d, buf.bn, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
1003 register BN_ULONG *ap,t,c;
1006 for (i = 3; i != 0; --i)
1009 *(ap++)=((t<<1)|c)&BN_MASK2;
1010 c=(t & BN_TBIT)?1:0;
1014 carry = (int)bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
1015 t_d, BN_NIST_256_TOP);
1017 carry += (int)bn_add_words(r_d, r_d, buf.bn, BN_NIST_384_TOP);
1019 nist_set_384(t_d,buf.bn,20,19,18,17,16,15,14,13,12,23,22,21);
1020 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1022 nist_set_384(t_d,buf.bn,19,18,17,16,15,14,13,12,20,0,23,0);
1023 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1025 nist_set_384(t_d, buf.bn,0,0,0,0,23,22,21,20,0,0,0,0);
1026 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1028 nist_set_384(t_d,buf.bn,0,0,0,0,0,0,23,22,21,0,0,20);
1029 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1031 nist_set_384(t_d,buf.bn,22,21,20,19,18,17,16,15,14,13,12,23);
1032 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1034 nist_set_384(t_d,buf.bn,0,0,0,0,0,0,0,23,22,21,20,0);
1035 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1037 nist_set_384(t_d,buf.bn,0,0,0,0,0,0,0,23,23,0,0,0);
1038 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1042 /* see BN_nist_mod_224 for explanation */
1045 carry = (int)bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
1048 carry = (int)bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
1049 mask = 0-(PTR_SIZE_INT)carry;
1050 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
1051 ((PTR_SIZE_INT)bn_add_words&~mask);
1056 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
1057 mask &= 0-(PTR_SIZE_INT)carry;
1059 res = (BN_ULONG *)(((PTR_SIZE_INT)res&~mask) |
1060 ((PTR_SIZE_INT)r_d&mask));
1061 nist_cp_bn(r_d, res, BN_NIST_384_TOP);
1062 r->top = BN_NIST_384_TOP;
1068 #define BN_NIST_521_RSHIFT (521%BN_BITS2)
1069 #define BN_NIST_521_LSHIFT (BN_BITS2-BN_NIST_521_RSHIFT)
1070 #define BN_NIST_521_TOP_MASK ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
1072 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
1075 int top = a->top, i;
1076 BN_ULONG *r_d, *a_d = a->d,
1077 t_d[BN_NIST_521_TOP],
1080 static const BIGNUM _bignum_nist_p_521_sqr = {
1081 (BN_ULONG *)_nist_p_521_sqr,
1082 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
1083 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
1084 0,BN_FLG_STATIC_DATA };
1086 field = &_bignum_nist_p_521; /* just to make sure */
1088 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_521_sqr)>=0)
1089 return BN_nnmod(r, a, field, ctx);
1091 i = BN_ucmp(field, a);
1098 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
1102 if (!bn_wexpand(r,BN_NIST_521_TOP))
1105 nist_cp_bn(r_d,a_d, BN_NIST_521_TOP);
1110 /* upper 521 bits, copy ... */
1111 nist_cp_bn_0(t_d,a_d + (BN_NIST_521_TOP-1), top - (BN_NIST_521_TOP-1),BN_NIST_521_TOP);
1112 /* ... and right shift */
1113 for (val=t_d[0],i=0; i<BN_NIST_521_TOP-1; i++)
1115 tmp = val>>BN_NIST_521_RSHIFT;
1117 t_d[i] = (tmp | val<<BN_NIST_521_LSHIFT) & BN_MASK2;
1119 t_d[i] = val>>BN_NIST_521_RSHIFT;
1120 /* lower 521 bits */
1121 r_d[i] &= BN_NIST_521_TOP_MASK;
1123 bn_add_words(r_d,r_d,t_d,BN_NIST_521_TOP);
1124 mask = 0-(PTR_SIZE_INT)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
1126 res = (BN_ULONG *)(((PTR_SIZE_INT)res&~mask) |
1127 ((PTR_SIZE_INT)r_d&mask));
1128 nist_cp_bn(r_d,res,BN_NIST_521_TOP);
1129 r->top = BN_NIST_521_TOP;
1135 int (*BN_nist_mod_func(const BIGNUM *p))(BIGNUM *r, const BIGNUM *a, const BIGNUM *field, BN_CTX *ctx)
1137 if (BN_ucmp(&_bignum_nist_p_192, p) == 0)
1138 return BN_nist_mod_192;
1139 if (BN_ucmp(&_bignum_nist_p_224, p) == 0)
1140 return BN_nist_mod_224;
1141 if (BN_ucmp(&_bignum_nist_p_256, p) == 0)
1142 return BN_nist_mod_256;
1143 if (BN_ucmp(&_bignum_nist_p_384, p) == 0)
1144 return BN_nist_mod_384;
1145 if (BN_ucmp(&_bignum_nist_p_521, p) == 0)
1146 return BN_nist_mod_521;