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:
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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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, BN_ULONG *a, int top, int max)
312 BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
315 OPENSSL_assert(top <= max);
317 for (i = (top); i != 0; i--)
319 for (i = (max) - (top); i != 0; i--)
320 *_tmp1++ = (BN_ULONG) 0;
323 static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
326 BN_ULONG *_tmp1 = (buf), *_tmp2 = (a);
327 for (i = (top); i != 0; i--)
332 #define bn_cp_64(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
333 #define bn_64_set_0(to, n) (to)[n] = (BN_ULONG)0;
335 * two following macros are implemented under assumption that they
336 * are called in a sequence with *ascending* n, i.e. as they are...
338 #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))\
339 :(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
340 #define bn_32_set_0(to, n) (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
341 #define bn_cp_32(to,n,from,m) ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
342 # if defined(L_ENDIAN)
343 # if defined(__arch64__)
344 # define NIST_INT64 long
346 # define NIST_INT64 long long
350 #define bn_cp_64(to, n, from, m) \
352 bn_cp_32(to, (n)*2, from, (m)*2); \
353 bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
355 #define bn_64_set_0(to, n) \
357 bn_32_set_0(to, (n)*2); \
358 bn_32_set_0(to, (n)*2+1); \
360 #define bn_cp_32(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
361 #define bn_32_set_0(to, n) (to)[n] = (BN_ULONG)0;
362 # if defined(_WIN32) && !defined(__GNUC__)
363 # define NIST_INT64 __int64
365 # define NIST_INT64 long long
367 #endif /* BN_BITS2 != 64 */
370 #define nist_set_192(to, from, a1, a2, a3) \
372 bn_cp_64(to, 0, from, (a3) - 3) \
373 bn_cp_64(to, 1, from, (a2) - 3) \
374 bn_cp_64(to, 2, from, (a1) - 3) \
377 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
382 register BN_ULONG *r_d, *a_d = a->d;
383 BN_ULONG buf[BN_NIST_192_TOP],
384 c_d[BN_NIST_192_TOP],
387 static const BIGNUM _bignum_nist_p_192_sqr = {
388 (BN_ULONG *)_nist_p_192_sqr,
389 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
390 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
391 0,BN_FLG_STATIC_DATA };
393 field = &_bignum_nist_p_192; /* just to make sure */
395 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_192_sqr)>=0)
396 return BN_nnmod(r, a, field, ctx);
398 i = BN_ucmp(field, a);
405 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
409 if (!bn_wexpand(r, BN_NIST_192_TOP))
412 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
417 nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
419 #if defined(NIST_INT64)
421 NIST_INT64 acc; /* accumulator */
422 unsigned int *rp=(unsigned int *)r_d;
423 const unsigned int *bp=(const unsigned int *)buf;
425 acc = rp[0]; acc += bp[3*2-6];
426 acc += bp[5*2-6]; rp[0] = (unsigned int)acc; acc >>= 32;
428 acc += rp[1]; acc += bp[3*2-5];
429 acc += bp[5*2-5]; rp[1] = (unsigned int)acc; acc >>= 32;
431 acc += rp[2]; acc += bp[3*2-6];
433 acc += bp[5*2-6]; rp[2] = (unsigned int)acc; acc >>= 32;
435 acc += rp[3]; acc += bp[3*2-5];
437 acc += bp[5*2-5]; rp[3] = (unsigned int)acc; acc >>= 32;
439 acc += rp[4]; acc += bp[4*2-6];
440 acc += bp[5*2-6]; rp[4] = (unsigned int)acc; acc >>= 32;
442 acc += rp[5]; acc += bp[4*2-5];
443 acc += bp[5*2-5]; rp[5] = (unsigned int)acc;
445 carry = (int)(acc>>32);
449 BN_ULONG t_d[BN_NIST_192_TOP];
451 nist_set_192(t_d, buf, 0, 3, 3);
452 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
453 nist_set_192(t_d, buf, 4, 4, 0);
454 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
455 nist_set_192(t_d, buf, 5, 5, 5)
456 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
460 carry = (int)bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
465 * we need 'if (carry==0 || result>=modulus) result-=modulus;'
466 * as comparison implies subtraction, we can write
467 * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
468 * this is what happens below, but without explicit if:-) a.
470 mask = 0-(PTR_SIZE_INT)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
471 mask &= 0-(PTR_SIZE_INT)carry;
473 (((PTR_SIZE_INT)c_d&~mask) | ((PTR_SIZE_INT)r_d&mask));
474 nist_cp_bn(r_d, res, BN_NIST_192_TOP);
475 r->top = BN_NIST_192_TOP;
481 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
483 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
485 bn_cp_32(to, 0, from, (a7) - 7) \
486 bn_cp_32(to, 1, from, (a6) - 7) \
487 bn_cp_32(to, 2, from, (a5) - 7) \
488 bn_cp_32(to, 3, from, (a4) - 7) \
489 bn_cp_32(to, 4, from, (a3) - 7) \
490 bn_cp_32(to, 5, from, (a2) - 7) \
491 bn_cp_32(to, 6, from, (a1) - 7) \
494 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
499 BN_ULONG *r_d, *a_d = a->d;
500 BN_ULONG buf[BN_NIST_224_TOP],
501 c_d[BN_NIST_224_TOP],
504 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
505 static const BIGNUM _bignum_nist_p_224_sqr = {
506 (BN_ULONG *)_nist_p_224_sqr,
507 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
508 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
509 0,BN_FLG_STATIC_DATA };
512 field = &_bignum_nist_p_224; /* just to make sure */
514 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_224_sqr)>=0)
515 return BN_nnmod(r, a, field, ctx);
517 i = BN_ucmp(field, a);
524 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
528 if (!bn_wexpand(r, BN_NIST_224_TOP))
531 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
537 /* copy upper 256 bits of 448 bit number ... */
538 nist_cp_bn_0(c_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
539 /* ... and right shift by 32 to obtain upper 224 bits */
540 nist_set_224(buf, c_d, 14, 13, 12, 11, 10, 9, 8);
541 /* truncate lower part to 224 bits too */
542 r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
544 nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
547 #if defined(NIST_INT64) && BN_BITS2!=64
549 NIST_INT64 acc; /* accumulator */
550 unsigned int *rp=(unsigned int *)r_d;
551 const unsigned int *bp=(const unsigned int *)buf;
553 acc = rp[0]; acc -= bp[7-7];
554 acc -= bp[11-7]; rp[0] = (unsigned int)acc; acc >>= 32;
556 acc += rp[1]; acc -= bp[8-7];
557 acc -= bp[12-7]; rp[1] = (unsigned int)acc; acc >>= 32;
559 acc += rp[2]; acc -= bp[9-7];
560 acc -= bp[13-7]; rp[2] = (unsigned int)acc; acc >>= 32;
562 acc += rp[3]; acc += bp[7-7];
564 acc -= bp[10-7]; rp[3] = (unsigned int)acc; acc>>= 32;
566 acc += rp[4]; acc += bp[8-7];
568 acc -= bp[11-7]; rp[4] = (unsigned int)acc; acc >>= 32;
570 acc += rp[5]; acc += bp[9-7];
572 acc -= bp[12-7]; rp[5] = (unsigned int)acc; acc >>= 32;
574 acc += rp[6]; acc += bp[10-7];
575 acc -= bp[13-7]; rp[6] = (unsigned int)acc;
577 carry = (int)(acc>>32);
584 BN_ULONG t_d[BN_NIST_224_TOP];
586 nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
587 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
588 nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
589 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
590 nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
591 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
592 nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
593 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
596 carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
603 carry = (int)bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
605 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
610 /* it's a bit more comlicated logic in this case.
611 * if bn_add_words yields no carry, then result
612 * has to be adjusted by unconditionally *adding*
613 * the modulus. but if it does, then result has
614 * to be compared to the modulus and conditionally
615 * adjusted by *subtracting* the latter. */
616 carry = (int)bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
617 mask = 0-(PTR_SIZE_INT)carry;
618 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
619 ((PTR_SIZE_INT)bn_add_words&~mask);
624 /* otherwise it's effectively same as in BN_nist_mod_192... */
625 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
626 mask &= 0-(PTR_SIZE_INT)carry;
627 res = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
628 ((PTR_SIZE_INT)r_d&mask));
629 nist_cp_bn(r_d, res, BN_NIST_224_TOP);
630 r->top = BN_NIST_224_TOP;
636 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
638 bn_cp_32(to, 0, from, (a8) - 8) \
639 bn_cp_32(to, 1, from, (a7) - 8) \
640 bn_cp_32(to, 2, from, (a6) - 8) \
641 bn_cp_32(to, 3, from, (a5) - 8) \
642 bn_cp_32(to, 4, from, (a4) - 8) \
643 bn_cp_32(to, 5, from, (a3) - 8) \
644 bn_cp_32(to, 6, from, (a2) - 8) \
645 bn_cp_32(to, 7, from, (a1) - 8) \
648 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
653 register BN_ULONG *a_d = a->d, *r_d;
654 BN_ULONG buf[BN_NIST_256_TOP],
655 c_d[BN_NIST_256_TOP],
658 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
659 static const BIGNUM _bignum_nist_p_256_sqr = {
660 (BN_ULONG *)_nist_p_256_sqr,
661 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
662 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
663 0,BN_FLG_STATIC_DATA };
665 field = &_bignum_nist_p_256; /* just to make sure */
667 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_256_sqr)>=0)
668 return BN_nnmod(r, a, field, ctx);
670 i = BN_ucmp(field, a);
677 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
681 if (!bn_wexpand(r, BN_NIST_256_TOP))
684 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
689 nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
691 #if defined(NIST_INT64)
693 NIST_INT64 acc; /* accumulator */
694 unsigned int *rp=(unsigned int *)r_d;
695 const unsigned int *bp=(const unsigned int *)buf;
697 acc = rp[0]; acc += bp[8-8];
702 acc -= bp[14-8]; rp[0] = (unsigned int)acc; acc >>= 32;
704 acc += rp[1]; acc += bp[9-8];
709 acc -= bp[15-8]; rp[1] = (unsigned int)acc; acc >>= 32;
711 acc += rp[2]; acc += bp[10-8];
715 acc -= bp[15-8]; rp[2] = (unsigned int)acc; acc >>= 32;
717 acc += rp[3]; acc += bp[11-8];
724 acc -= bp[9-8]; rp[3] = (unsigned int)acc; acc >>= 32;
726 acc += rp[4]; acc += bp[12-8];
732 acc -= bp[10-8]; rp[4] = (unsigned int)acc; acc >>= 32;
734 acc += rp[5]; acc += bp[13-8];
740 acc -= bp[11-8]; rp[5] = (unsigned int)acc; acc >>= 32;
742 acc += rp[6]; acc += bp[14-8];
749 acc -= bp[9-8]; rp[6] = (unsigned int)acc; acc >>= 32;
751 acc += rp[7]; acc += bp[15-8];
758 acc -= bp[13-8]; rp[7] = (unsigned int)acc;
760 carry = (int)(acc>>32);
764 BN_ULONG t_d[BN_NIST_256_TOP];
767 nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
769 nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
770 carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
773 register BN_ULONG *ap,t,c;
776 for (i = BN_NIST_256_TOP; i != 0; --i)
779 *(ap++)=((t<<1)|c)&BN_MASK2;
785 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
787 nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
788 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
790 nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
791 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
793 nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
794 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
796 nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
797 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
799 nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
800 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
802 nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
803 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
807 /* see BN_nist_mod_224 for explanation */
810 carry = (int)bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
813 carry = (int)bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
814 mask = 0-(PTR_SIZE_INT)carry;
815 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
816 ((PTR_SIZE_INT)bn_add_words&~mask);
821 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
822 mask &= 0-(PTR_SIZE_INT)carry;
823 res = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
824 ((PTR_SIZE_INT)r_d&mask));
825 nist_cp_bn(r_d, res, BN_NIST_256_TOP);
826 r->top = BN_NIST_256_TOP;
832 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
834 bn_cp_32(to, 0, from, (a12) - 12) \
835 bn_cp_32(to, 1, from, (a11) - 12) \
836 bn_cp_32(to, 2, from, (a10) - 12) \
837 bn_cp_32(to, 3, from, (a9) - 12) \
838 bn_cp_32(to, 4, from, (a8) - 12) \
839 bn_cp_32(to, 5, from, (a7) - 12) \
840 bn_cp_32(to, 6, from, (a6) - 12) \
841 bn_cp_32(to, 7, from, (a5) - 12) \
842 bn_cp_32(to, 8, from, (a4) - 12) \
843 bn_cp_32(to, 9, from, (a3) - 12) \
844 bn_cp_32(to, 10, from, (a2) - 12) \
845 bn_cp_32(to, 11, from, (a1) - 12) \
848 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
853 register BN_ULONG *r_d, *a_d = a->d;
854 BN_ULONG buf[BN_NIST_384_TOP],
855 c_d[BN_NIST_384_TOP],
858 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
859 static const BIGNUM _bignum_nist_p_384_sqr = {
860 (BN_ULONG *)_nist_p_384_sqr,
861 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
862 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
863 0,BN_FLG_STATIC_DATA };
866 field = &_bignum_nist_p_384; /* just to make sure */
868 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_384_sqr)>=0)
869 return BN_nnmod(r, a, field, ctx);
871 i = BN_ucmp(field, a);
878 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
882 if (!bn_wexpand(r, BN_NIST_384_TOP))
885 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
890 nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
892 #if defined(NIST_INT64)
894 NIST_INT64 acc; /* accumulator */
895 unsigned int *rp=(unsigned int *)r_d;
896 const unsigned int *bp=(const unsigned int *)buf;
898 acc = rp[0]; acc += bp[12-12];
901 acc -= bp[23-12]; rp[0] = (unsigned int)acc; acc >>= 32;
903 acc += rp[1]; acc += bp[13-12];
907 acc -= bp[20-12]; rp[1] = (unsigned int)acc; acc >>= 32;
909 acc += rp[2]; acc += bp[14-12];
912 acc -= bp[21-12]; rp[2] = (unsigned int)acc; acc >>= 32;
914 acc += rp[3]; acc += bp[15-12];
920 acc -= bp[23-12]; rp[3] = (unsigned int)acc; acc >>= 32;
922 acc += rp[4]; acc += bp[21-12];
931 acc -= bp[23-12]; rp[4] = (unsigned int)acc; acc >>= 32;
933 acc += rp[5]; acc += bp[22-12];
940 acc -= bp[16-12]; rp[5] = (unsigned int)acc; acc >>= 32;
942 acc += rp[6]; acc += bp[23-12];
948 acc -= bp[17-12]; rp[6] = (unsigned int)acc; acc >>= 32;
950 acc += rp[7]; acc += bp[19-12];
954 acc -= bp[18-12]; rp[7] = (unsigned int)acc; acc >>= 32;
956 acc += rp[8]; acc += bp[20-12];
959 acc -= bp[19-12]; rp[8] = (unsigned int)acc; acc >>= 32;
961 acc += rp[9]; acc += bp[21-12];
964 acc -= bp[20-12]; rp[9] = (unsigned int)acc; acc >>= 32;
966 acc += rp[10]; acc += bp[22-12];
969 acc -= bp[21-12]; rp[10] = (unsigned int)acc; acc >>= 32;
971 acc += rp[11]; acc += bp[23-12];
974 acc -= bp[22-12]; rp[11] = (unsigned int)acc;
976 carry = (int)(acc>>32);
980 BN_ULONG t_d[BN_NIST_384_TOP];
983 nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
986 register BN_ULONG *ap,t,c;
989 for (i = 3; i != 0; --i)
992 *(ap++)=((t<<1)|c)&BN_MASK2;
997 carry = (int)bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
998 t_d, BN_NIST_256_TOP);
1000 carry += (int)bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
1002 nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
1003 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1005 nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
1006 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1008 nist_set_384(t_d, buf,0,0,0,0,23,22,21,20,0,0,0,0);
1009 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1011 nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
1012 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1014 nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
1015 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1017 nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
1018 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1020 nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
1021 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1025 /* see BN_nist_mod_224 for explanation */
1028 carry = (int)bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
1031 carry = (int)bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
1032 mask = 0-(PTR_SIZE_INT)carry;
1033 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
1034 ((PTR_SIZE_INT)bn_add_words&~mask);
1039 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
1040 mask &= 0-(PTR_SIZE_INT)carry;
1041 res = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
1042 ((PTR_SIZE_INT)r_d&mask));
1043 nist_cp_bn(r_d, res, BN_NIST_384_TOP);
1044 r->top = BN_NIST_384_TOP;
1050 #define BN_NIST_521_RSHIFT (521%BN_BITS2)
1051 #define BN_NIST_521_LSHIFT (BN_BITS2-BN_NIST_521_RSHIFT)
1052 #define BN_NIST_521_TOP_MASK ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
1054 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
1057 int top = a->top, i;
1058 BN_ULONG *r_d, *a_d = a->d,
1059 t_d[BN_NIST_521_TOP],
1062 static const BIGNUM _bignum_nist_p_521_sqr = {
1063 (BN_ULONG *)_nist_p_521_sqr,
1064 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
1065 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
1066 0,BN_FLG_STATIC_DATA };
1068 field = &_bignum_nist_p_521; /* just to make sure */
1070 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_521_sqr)>=0)
1071 return BN_nnmod(r, a, field, ctx);
1073 i = BN_ucmp(field, a);
1080 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
1084 if (!bn_wexpand(r,BN_NIST_521_TOP))
1087 nist_cp_bn(r_d,a_d, BN_NIST_521_TOP);
1092 /* upper 521 bits, copy ... */
1093 nist_cp_bn_0(t_d,a_d + (BN_NIST_521_TOP-1), top - (BN_NIST_521_TOP-1),BN_NIST_521_TOP);
1094 /* ... and right shift */
1095 for (val=t_d[0],i=0; i<BN_NIST_521_TOP-1; i++)
1097 tmp = val>>BN_NIST_521_RSHIFT;
1099 t_d[i] = (tmp | val<<BN_NIST_521_LSHIFT) & BN_MASK2;
1101 t_d[i] = val>>BN_NIST_521_RSHIFT;
1102 /* lower 521 bits */
1103 r_d[i] &= BN_NIST_521_TOP_MASK;
1105 bn_add_words(r_d,r_d,t_d,BN_NIST_521_TOP);
1106 mask = 0-(PTR_SIZE_INT)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
1107 res = (BN_ULONG *)(((PTR_SIZE_INT)t_d&~mask) |
1108 ((PTR_SIZE_INT)r_d&mask));
1109 nist_cp_bn(r_d,res,BN_NIST_521_TOP);
1110 r->top = BN_NIST_521_TOP;
1116 int (*BN_nist_mod_func(const BIGNUM *p))(BIGNUM *r, const BIGNUM *a, const BIGNUM *field, BN_CTX *ctx)
1118 if (BN_ucmp(&_bignum_nist_p_192, p) == 0)
1119 return BN_nist_mod_192;
1120 if (BN_ucmp(&_bignum_nist_p_224, p) == 0)
1121 return BN_nist_mod_224;
1122 if (BN_ucmp(&_bignum_nist_p_256, p) == 0)
1123 return BN_nist_mod_256;
1124 if (BN_ucmp(&_bignum_nist_p_384, p) == 0)
1125 return BN_nist_mod_384;
1126 if (BN_ucmp(&_bignum_nist_p_521, p) == 0)
1127 return BN_nist_mod_521;