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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21 * software must display the following acknowledgment:
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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) */
71 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
72 {0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFFULL},
73 {0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL},
74 {0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFCULL,0xFFFFFFFFFFFFFFFFULL}
76 static const BN_ULONG _nist_p_192_sqr[] = {
77 0x0000000000000001ULL,0x0000000000000002ULL,0x0000000000000001ULL,
78 0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL
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" */
86 static const BN_ULONG _nist_p_224_sqr[] = {
87 0x0000000000000001ULL,0xFFFFFFFE00000000ULL,
88 0xFFFFFFFFFFFFFFFFULL,0x0000000200000000ULL,
89 0x0000000000000000ULL,0xFFFFFFFFFFFFFFFEULL,
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},
104 static const BN_ULONG _nist_p_256_sqr[] = {
105 0x0000000000000001ULL,0xFFFFFFFE00000000ULL,
106 0xFFFFFFFFFFFFFFFFULL,0x00000001FFFFFFFEULL,
107 0x00000001FFFFFFFEULL,0x00000001FFFFFFFEULL,
108 0xFFFFFFFE00000001ULL,0xFFFFFFFE00000002ULL
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},
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
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
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}
148 static const BN_ULONG _nist_p_192_sqr[] = {
149 0x00000001,0x00000000,0x00000002,0x00000000,0x00000001,0x00000000,
150 0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF
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}
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
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},
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
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},
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
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
213 #error "unsupported BN_BITS2"
217 static const BIGNUM _bignum_nist_p_192 =
219 (BN_ULONG *)_nist_p_192[0],
226 static const BIGNUM _bignum_nist_p_224 =
228 (BN_ULONG *)_nist_p_224[0],
235 static const BIGNUM _bignum_nist_p_256 =
237 (BN_ULONG *)_nist_p_256[0],
244 static const BIGNUM _bignum_nist_p_384 =
246 (BN_ULONG *)_nist_p_384[0],
253 static const BIGNUM _bignum_nist_p_521 =
255 (BN_ULONG *)_nist_p_521,
263 const BIGNUM *BN_get0_nist_prime_192(void)
265 return &_bignum_nist_p_192;
268 const BIGNUM *BN_get0_nist_prime_224(void)
270 return &_bignum_nist_p_224;
273 const BIGNUM *BN_get0_nist_prime_256(void)
275 return &_bignum_nist_p_256;
278 const BIGNUM *BN_get0_nist_prime_384(void)
280 return &_bignum_nist_p_384;
283 const BIGNUM *BN_get0_nist_prime_521(void)
285 return &_bignum_nist_p_521;
289 static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max)
292 BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
295 OPENSSL_assert(top <= max);
297 for (i = (top); i != 0; i--)
299 for (i = (max) - (top); i != 0; i--)
300 *_tmp1++ = (BN_ULONG) 0;
303 static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
306 BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
307 for (i = (top); i != 0; i--)
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;
315 * two following macros are implemented under assumption that they
316 * are called in a sequence with *ascending* n, i.e. as they are...
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 # if defined(L_ENDIAN)
323 # if defined(__arch64__)
324 # define NIST_INT64 long
326 # define NIST_INT64 long long
330 #define bn_cp_64(to, n, from, m) \
332 bn_cp_32(to, (n)*2, from, (m)*2); \
333 bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
335 #define bn_64_set_0(to, n) \
337 bn_32_set_0(to, (n)*2); \
338 bn_32_set_0(to, (n)*2+1); \
340 #define bn_cp_32(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
341 #define bn_32_set_0(to, n) (to)[n] = (BN_ULONG)0;
342 # if defined(_WIN32) && !defined(__GNUC__)
343 # define NIST_INT64 __int64
345 # define NIST_INT64 long long
347 #endif /* BN_BITS2 != 64 */
350 #define nist_set_192(to, from, a1, a2, a3) \
352 bn_cp_64(to, 0, from, (a3) - 3) \
353 bn_cp_64(to, 1, from, (a2) - 3) \
354 bn_cp_64(to, 2, from, (a1) - 3) \
357 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
362 register BN_ULONG *r_d, *a_d = a->d;
363 BN_ULONG buf[BN_NIST_192_TOP],
364 c_d[BN_NIST_192_TOP],
367 static const BIGNUM _bignum_nist_p_192_sqr = {
368 (BN_ULONG *)_nist_p_192_sqr,
369 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
370 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
371 0,BN_FLG_STATIC_DATA };
373 field = &_bignum_nist_p_192; /* just to make sure */
375 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_192_sqr)>=0)
376 return BN_nnmod(r, a, field, ctx);
378 i = BN_ucmp(field, a);
385 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
389 if (!bn_wexpand(r, BN_NIST_192_TOP))
392 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
397 nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
399 #if defined(NIST_INT64)
401 NIST_INT64 acc; /* accumulator */
402 unsigned int *rp=(unsigned int *)r_d;
403 const unsigned int *bp=(const unsigned int *)buf;
405 acc = rp[0]; acc += bp[3*2-6];
406 acc += bp[5*2-6]; rp[0] = (unsigned int)acc; acc >>= 32;
408 acc += rp[1]; acc += bp[3*2-5];
409 acc += bp[5*2-5]; rp[1] = (unsigned int)acc; acc >>= 32;
411 acc += rp[2]; acc += bp[3*2-6];
413 acc += bp[5*2-6]; rp[2] = (unsigned int)acc; acc >>= 32;
415 acc += rp[3]; acc += bp[3*2-5];
417 acc += bp[5*2-5]; rp[3] = (unsigned int)acc; acc >>= 32;
419 acc += rp[4]; acc += bp[4*2-6];
420 acc += bp[5*2-6]; rp[4] = (unsigned int)acc; acc >>= 32;
422 acc += rp[5]; acc += bp[4*2-5];
423 acc += bp[5*2-5]; rp[5] = (unsigned int)acc;
425 carry = (int)(acc>>32);
429 BN_ULONG t_d[BN_NIST_192_TOP];
431 nist_set_192(t_d, buf, 0, 3, 3);
432 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
433 nist_set_192(t_d, buf, 4, 4, 0);
434 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
435 nist_set_192(t_d, buf, 5, 5, 5)
436 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
440 carry = (int)bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
445 * we need 'if (carry==0 || result>=modulus) result-=modulus;'
446 * as comparison implies subtraction, we can write
447 * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
448 * this is what happens below, but without explicit if:-) a.
450 mask = 0-(PTR_SIZE_INT)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
451 mask &= 0-(PTR_SIZE_INT)carry;
453 (((PTR_SIZE_INT)c_d&~mask) | ((PTR_SIZE_INT)r_d&mask));
454 nist_cp_bn(r_d, res, BN_NIST_192_TOP);
455 r->top = BN_NIST_192_TOP;
461 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
463 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
465 bn_cp_32(to, 0, from, (a7) - 7) \
466 bn_cp_32(to, 1, from, (a6) - 7) \
467 bn_cp_32(to, 2, from, (a5) - 7) \
468 bn_cp_32(to, 3, from, (a4) - 7) \
469 bn_cp_32(to, 4, from, (a3) - 7) \
470 bn_cp_32(to, 5, from, (a2) - 7) \
471 bn_cp_32(to, 6, from, (a1) - 7) \
474 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
479 BN_ULONG *r_d, *a_d = a->d;
480 BN_ULONG buf[BN_NIST_224_TOP],
481 c_d[BN_NIST_224_TOP],
484 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
485 static const BIGNUM _bignum_nist_p_224_sqr = {
486 (BN_ULONG *)_nist_p_224_sqr,
487 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
488 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
489 0,BN_FLG_STATIC_DATA };
492 field = &_bignum_nist_p_224; /* just to make sure */
494 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_224_sqr)>=0)
495 return BN_nnmod(r, a, field, ctx);
497 i = BN_ucmp(field, a);
504 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
508 if (!bn_wexpand(r, BN_NIST_224_TOP))
511 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
517 /* copy upper 256 bits of 448 bit number ... */
518 nist_cp_bn_0(c_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
519 /* ... and right shift by 32 to obtain upper 224 bits */
520 nist_set_224(buf, c_d, 14, 13, 12, 11, 10, 9, 8);
521 /* truncate lower part to 224 bits too */
522 r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
524 nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
527 #if defined(NIST_INT64) && BN_BITS2!=64
529 NIST_INT64 acc; /* accumulator */
530 unsigned int *rp=(unsigned int *)r_d;
531 const unsigned int *bp=(const unsigned int *)buf;
533 acc = rp[0]; acc -= bp[7-7];
534 acc -= bp[11-7]; rp[0] = (unsigned int)acc; acc >>= 32;
536 acc += rp[1]; acc -= bp[8-7];
537 acc -= bp[12-7]; rp[1] = (unsigned int)acc; acc >>= 32;
539 acc += rp[2]; acc -= bp[9-7];
540 acc -= bp[13-7]; rp[2] = (unsigned int)acc; acc >>= 32;
542 acc += rp[3]; acc += bp[7-7];
544 acc -= bp[10-7]; rp[3] = (unsigned int)acc; acc>>= 32;
546 acc += rp[4]; acc += bp[8-7];
548 acc -= bp[11-7]; rp[4] = (unsigned int)acc; acc >>= 32;
550 acc += rp[5]; acc += bp[9-7];
552 acc -= bp[12-7]; rp[5] = (unsigned int)acc; acc >>= 32;
554 acc += rp[6]; acc += bp[10-7];
555 acc -= bp[13-7]; rp[6] = (unsigned int)acc;
557 carry = (int)(acc>>32);
564 BN_ULONG t_d[BN_NIST_224_TOP];
566 nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
567 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
568 nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
569 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
570 nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
571 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
572 nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
573 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
576 carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
583 carry = (int)bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
585 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
590 /* it's a bit more comlicated logic in this case.
591 * if bn_add_words yields no carry, then result
592 * has to be adjusted by unconditionally *adding*
593 * the modulus. but if it does, then result has
594 * to be compared to the modulus and conditionally
595 * adjusted by *subtracting* the latter. */
596 carry = (int)bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
597 mask = 0-(PTR_SIZE_INT)carry;
598 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
599 ((PTR_SIZE_INT)bn_add_words&~mask);
604 /* otherwise it's effectively same as in BN_nist_mod_192... */
605 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
606 mask &= 0-(PTR_SIZE_INT)carry;
607 res = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
608 ((PTR_SIZE_INT)r_d&mask));
609 nist_cp_bn(r_d, res, BN_NIST_224_TOP);
610 r->top = BN_NIST_224_TOP;
616 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
618 bn_cp_32(to, 0, from, (a8) - 8) \
619 bn_cp_32(to, 1, from, (a7) - 8) \
620 bn_cp_32(to, 2, from, (a6) - 8) \
621 bn_cp_32(to, 3, from, (a5) - 8) \
622 bn_cp_32(to, 4, from, (a4) - 8) \
623 bn_cp_32(to, 5, from, (a3) - 8) \
624 bn_cp_32(to, 6, from, (a2) - 8) \
625 bn_cp_32(to, 7, from, (a1) - 8) \
628 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
633 register BN_ULONG *a_d = a->d, *r_d;
634 BN_ULONG buf[BN_NIST_256_TOP],
635 c_d[BN_NIST_256_TOP],
638 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
639 static const BIGNUM _bignum_nist_p_256_sqr = {
640 (BN_ULONG *)_nist_p_256_sqr,
641 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
642 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
643 0,BN_FLG_STATIC_DATA };
645 field = &_bignum_nist_p_256; /* just to make sure */
647 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_256_sqr)>=0)
648 return BN_nnmod(r, a, field, ctx);
650 i = BN_ucmp(field, a);
657 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
661 if (!bn_wexpand(r, BN_NIST_256_TOP))
664 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
669 nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
671 #if defined(NIST_INT64)
673 NIST_INT64 acc; /* accumulator */
674 unsigned int *rp=(unsigned int *)r_d;
675 const unsigned int *bp=(const unsigned int *)buf;
677 acc = rp[0]; acc += bp[8-8];
682 acc -= bp[14-8]; rp[0] = (unsigned int)acc; acc >>= 32;
684 acc += rp[1]; acc += bp[9-8];
689 acc -= bp[15-8]; rp[1] = (unsigned int)acc; acc >>= 32;
691 acc += rp[2]; acc += bp[10-8];
695 acc -= bp[15-8]; rp[2] = (unsigned int)acc; acc >>= 32;
697 acc += rp[3]; acc += bp[11-8];
704 acc -= bp[9-8]; rp[3] = (unsigned int)acc; acc >>= 32;
706 acc += rp[4]; acc += bp[12-8];
712 acc -= bp[10-8]; rp[4] = (unsigned int)acc; acc >>= 32;
714 acc += rp[5]; acc += bp[13-8];
720 acc -= bp[11-8]; rp[5] = (unsigned int)acc; acc >>= 32;
722 acc += rp[6]; acc += bp[14-8];
729 acc -= bp[9-8]; rp[6] = (unsigned int)acc; acc >>= 32;
731 acc += rp[7]; acc += bp[15-8];
738 acc -= bp[13-8]; rp[7] = (unsigned int)acc;
740 carry = (int)(acc>>32);
744 BN_ULONG t_d[BN_NIST_256_TOP];
747 nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
749 nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
750 carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
753 register BN_ULONG *ap,t,c;
756 for (i = BN_NIST_256_TOP; i != 0; --i)
759 *(ap++)=((t<<1)|c)&BN_MASK2;
765 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
767 nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
768 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
770 nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
771 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
773 nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
774 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
776 nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
777 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
779 nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
780 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
782 nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
783 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
787 /* see BN_nist_mod_224 for explanation */
790 carry = (int)bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
793 carry = (int)bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
794 mask = 0-(PTR_SIZE_INT)carry;
795 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
796 ((PTR_SIZE_INT)bn_add_words&~mask);
801 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
802 mask &= 0-(PTR_SIZE_INT)carry;
803 res = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
804 ((PTR_SIZE_INT)r_d&mask));
805 nist_cp_bn(r_d, res, BN_NIST_256_TOP);
806 r->top = BN_NIST_256_TOP;
812 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
814 bn_cp_32(to, 0, from, (a12) - 12) \
815 bn_cp_32(to, 1, from, (a11) - 12) \
816 bn_cp_32(to, 2, from, (a10) - 12) \
817 bn_cp_32(to, 3, from, (a9) - 12) \
818 bn_cp_32(to, 4, from, (a8) - 12) \
819 bn_cp_32(to, 5, from, (a7) - 12) \
820 bn_cp_32(to, 6, from, (a6) - 12) \
821 bn_cp_32(to, 7, from, (a5) - 12) \
822 bn_cp_32(to, 8, from, (a4) - 12) \
823 bn_cp_32(to, 9, from, (a3) - 12) \
824 bn_cp_32(to, 10, from, (a2) - 12) \
825 bn_cp_32(to, 11, from, (a1) - 12) \
828 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
833 register BN_ULONG *r_d, *a_d = a->d;
834 BN_ULONG buf[BN_NIST_384_TOP],
835 c_d[BN_NIST_384_TOP],
838 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
839 static const BIGNUM _bignum_nist_p_384_sqr = {
840 (BN_ULONG *)_nist_p_384_sqr,
841 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
842 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
843 0,BN_FLG_STATIC_DATA };
846 field = &_bignum_nist_p_384; /* just to make sure */
848 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_384_sqr)>=0)
849 return BN_nnmod(r, a, field, ctx);
851 i = BN_ucmp(field, a);
858 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
862 if (!bn_wexpand(r, BN_NIST_384_TOP))
865 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
870 nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
872 #if defined(NIST_INT64)
874 NIST_INT64 acc; /* accumulator */
875 unsigned int *rp=(unsigned int *)r_d;
876 const unsigned int *bp=(const unsigned int *)buf;
878 acc = rp[0]; acc += bp[12-12];
881 acc -= bp[23-12]; rp[0] = (unsigned int)acc; acc >>= 32;
883 acc += rp[1]; acc += bp[13-12];
887 acc -= bp[20-12]; rp[1] = (unsigned int)acc; acc >>= 32;
889 acc += rp[2]; acc += bp[14-12];
892 acc -= bp[21-12]; rp[2] = (unsigned int)acc; acc >>= 32;
894 acc += rp[3]; acc += bp[15-12];
900 acc -= bp[23-12]; rp[3] = (unsigned int)acc; acc >>= 32;
902 acc += rp[4]; acc += bp[21-12];
911 acc -= bp[23-12]; rp[4] = (unsigned int)acc; acc >>= 32;
913 acc += rp[5]; acc += bp[22-12];
920 acc -= bp[16-12]; rp[5] = (unsigned int)acc; acc >>= 32;
922 acc += rp[6]; acc += bp[23-12];
928 acc -= bp[17-12]; rp[6] = (unsigned int)acc; acc >>= 32;
930 acc += rp[7]; acc += bp[19-12];
934 acc -= bp[18-12]; rp[7] = (unsigned int)acc; acc >>= 32;
936 acc += rp[8]; acc += bp[20-12];
939 acc -= bp[19-12]; rp[8] = (unsigned int)acc; acc >>= 32;
941 acc += rp[9]; acc += bp[21-12];
944 acc -= bp[20-12]; rp[9] = (unsigned int)acc; acc >>= 32;
946 acc += rp[10]; acc += bp[22-12];
949 acc -= bp[21-12]; rp[10] = (unsigned int)acc; acc >>= 32;
951 acc += rp[11]; acc += bp[23-12];
954 acc -= bp[22-12]; rp[11] = (unsigned int)acc;
956 carry = (int)(acc>>32);
960 BN_ULONG t_d[BN_NIST_384_TOP];
963 nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
966 register BN_ULONG *ap,t,c;
969 for (i = 3; i != 0; --i)
972 *(ap++)=((t<<1)|c)&BN_MASK2;
977 carry = (int)bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
978 t_d, BN_NIST_256_TOP);
980 carry += (int)bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
982 nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
983 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
985 nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
986 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
988 nist_set_384(t_d, buf,0,0,0,0,23,22,21,20,0,0,0,0);
989 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
991 nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
992 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
994 nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
995 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
997 nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
998 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1000 nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
1001 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1005 /* see BN_nist_mod_224 for explanation */
1008 carry = (int)bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
1011 carry = (int)bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
1012 mask = 0-(PTR_SIZE_INT)carry;
1013 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
1014 ((PTR_SIZE_INT)bn_add_words&~mask);
1019 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
1020 mask &= 0-(PTR_SIZE_INT)carry;
1021 res = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
1022 ((PTR_SIZE_INT)r_d&mask));
1023 nist_cp_bn(r_d, res, BN_NIST_384_TOP);
1024 r->top = BN_NIST_384_TOP;
1030 #define BN_NIST_521_RSHIFT (521%BN_BITS2)
1031 #define BN_NIST_521_LSHIFT (BN_BITS2-BN_NIST_521_RSHIFT)
1032 #define BN_NIST_521_TOP_MASK ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
1034 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
1037 int top = a->top, i;
1038 BN_ULONG *r_d, *a_d = a->d,
1039 t_d[BN_NIST_521_TOP],
1042 static const BIGNUM _bignum_nist_p_521_sqr = {
1043 (BN_ULONG *)_nist_p_521_sqr,
1044 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
1045 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
1046 0,BN_FLG_STATIC_DATA };
1048 field = &_bignum_nist_p_521; /* just to make sure */
1050 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_521_sqr)>=0)
1051 return BN_nnmod(r, a, field, ctx);
1053 i = BN_ucmp(field, a);
1060 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
1064 if (!bn_wexpand(r,BN_NIST_521_TOP))
1067 nist_cp_bn(r_d,a_d, BN_NIST_521_TOP);
1072 /* upper 521 bits, copy ... */
1073 nist_cp_bn_0(t_d,a_d + (BN_NIST_521_TOP-1), top - (BN_NIST_521_TOP-1),BN_NIST_521_TOP);
1074 /* ... and right shift */
1075 for (val=t_d[0],i=0; i<BN_NIST_521_TOP-1; i++)
1077 tmp = val>>BN_NIST_521_RSHIFT;
1079 t_d[i] = (tmp | val<<BN_NIST_521_LSHIFT) & BN_MASK2;
1081 t_d[i] = val>>BN_NIST_521_RSHIFT;
1082 /* lower 521 bits */
1083 r_d[i] &= BN_NIST_521_TOP_MASK;
1085 bn_add_words(r_d,r_d,t_d,BN_NIST_521_TOP);
1086 mask = 0-(PTR_SIZE_INT)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
1087 res = (BN_ULONG *)(((PTR_SIZE_INT)t_d&~mask) |
1088 ((PTR_SIZE_INT)r_d&mask));
1089 nist_cp_bn(r_d,res,BN_NIST_521_TOP);
1090 r->top = BN_NIST_521_TOP;
1096 int (*BN_nist_mod_func(const BIGNUM *p))(BIGNUM *r, const BIGNUM *a, const BIGNUM *field, BN_CTX *ctx)
1098 if (BN_ucmp(&_bignum_nist_p_192, p) == 0)
1099 return BN_nist_mod_192;
1100 if (BN_ucmp(&_bignum_nist_p_224, p) == 0)
1101 return BN_nist_mod_224;
1102 if (BN_ucmp(&_bignum_nist_p_256, p) == 0)
1103 return BN_nist_mod_256;
1104 if (BN_ucmp(&_bignum_nist_p_384, p) == 0)
1105 return BN_nist_mod_384;
1106 if (BN_ucmp(&_bignum_nist_p_521, p) == 0)
1107 return BN_nist_mod_521;