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) */
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 *dst, const BN_ULONG *src, int top, int max)
314 OPENSSL_assert(top <= max);
316 for (i = 0; i < top; i++)
322 static void nist_cp_bn(BN_ULONG *dst, const BN_ULONG *src, int top)
326 for (i = 0; i < top; i++)
331 #define bn_cp_64(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
332 #define bn_64_set_0(to, n) (to)[n] = (BN_ULONG)0;
334 * two following macros are implemented under assumption that they
335 * are called in a sequence with *ascending* n, i.e. as they are...
337 #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))\
338 :(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
339 #define bn_32_set_0(to, n) (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
340 #define bn_cp_32(to,n,from,m) ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
341 # if defined(L_ENDIAN)
342 # if defined(__arch64__)
343 # define NIST_INT64 long
345 # define NIST_INT64 long long
349 #define bn_cp_64(to, n, from, m) \
351 bn_cp_32(to, (n)*2, from, (m)*2); \
352 bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
354 #define bn_64_set_0(to, n) \
356 bn_32_set_0(to, (n)*2); \
357 bn_32_set_0(to, (n)*2+1); \
359 #define bn_cp_32(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
360 #define bn_32_set_0(to, n) (to)[n] = (BN_ULONG)0;
361 # if defined(_WIN32) && !defined(__GNUC__)
362 # define NIST_INT64 __int64
363 # elif defined(BN_LLONG)
364 # define NIST_INT64 long long
366 #endif /* BN_BITS2 != 64 */
368 #define nist_set_192(to, from, a1, a2, a3) \
370 bn_cp_64(to, 0, from, (a3) - 3) \
371 bn_cp_64(to, 1, from, (a2) - 3) \
372 bn_cp_64(to, 2, from, (a1) - 3) \
375 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
380 register BN_ULONG *r_d, *a_d = a->d;
382 BN_ULONG bn[BN_NIST_192_TOP];
383 unsigned int ui[BN_NIST_192_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
385 BN_ULONG c_d[BN_NIST_192_TOP],
388 static const BIGNUM _bignum_nist_p_192_sqr = {
389 (BN_ULONG *)_nist_p_192_sqr,
390 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
391 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
392 0,BN_FLG_STATIC_DATA };
394 field = &_bignum_nist_p_192; /* just to make sure */
396 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_192_sqr)>=0)
397 return BN_nnmod(r, a, field, ctx);
399 i = BN_ucmp(field, a);
406 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
410 if (!bn_wexpand(r, BN_NIST_192_TOP))
413 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
418 nist_cp_bn_0(buf.bn, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
420 #if defined(NIST_INT64)
422 NIST_INT64 acc; /* accumulator */
423 unsigned int *rp=(unsigned int *)r_d;
424 const unsigned int *bp=(const unsigned int *)buf.ui;
426 acc = rp[0]; acc += bp[3*2-6];
427 acc += bp[5*2-6]; rp[0] = (unsigned int)acc; acc >>= 32;
429 acc += rp[1]; acc += bp[3*2-5];
430 acc += bp[5*2-5]; rp[1] = (unsigned int)acc; acc >>= 32;
432 acc += rp[2]; acc += bp[3*2-6];
434 acc += bp[5*2-6]; rp[2] = (unsigned int)acc; acc >>= 32;
436 acc += rp[3]; acc += bp[3*2-5];
438 acc += bp[5*2-5]; rp[3] = (unsigned int)acc; acc >>= 32;
440 acc += rp[4]; acc += bp[4*2-6];
441 acc += bp[5*2-6]; rp[4] = (unsigned int)acc; acc >>= 32;
443 acc += rp[5]; acc += bp[4*2-5];
444 acc += bp[5*2-5]; rp[5] = (unsigned int)acc;
446 carry = (int)(acc>>32);
450 BN_ULONG t_d[BN_NIST_192_TOP];
452 nist_set_192(t_d, buf.bn, 0, 3, 3);
453 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
454 nist_set_192(t_d, buf.bn, 4, 4, 0);
455 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
456 nist_set_192(t_d, buf.bn, 5, 5, 5)
457 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
461 carry = (int)bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
466 * we need 'if (carry==0 || result>=modulus) result-=modulus;'
467 * as comparison implies subtraction, we can write
468 * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
469 * this is what happens below, but without explicit if:-) a.
471 mask = 0-(PTR_SIZE_INT)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
472 mask &= 0-(PTR_SIZE_INT)carry;
475 (((PTR_SIZE_INT)res&~mask) | ((PTR_SIZE_INT)r_d&mask));
476 nist_cp_bn(r_d, res, BN_NIST_192_TOP);
477 r->top = BN_NIST_192_TOP;
483 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
485 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
487 bn_cp_32(to, 0, from, (a7) - 7) \
488 bn_cp_32(to, 1, from, (a6) - 7) \
489 bn_cp_32(to, 2, from, (a5) - 7) \
490 bn_cp_32(to, 3, from, (a4) - 7) \
491 bn_cp_32(to, 4, from, (a3) - 7) \
492 bn_cp_32(to, 5, from, (a2) - 7) \
493 bn_cp_32(to, 6, from, (a1) - 7) \
496 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
501 BN_ULONG *r_d, *a_d = a->d;
503 BN_ULONG bn[BN_NIST_224_TOP];
504 unsigned int ui[BN_NIST_224_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
506 BN_ULONG c_d[BN_NIST_224_TOP],
509 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
510 static const BIGNUM _bignum_nist_p_224_sqr = {
511 (BN_ULONG *)_nist_p_224_sqr,
512 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
513 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
514 0,BN_FLG_STATIC_DATA };
517 field = &_bignum_nist_p_224; /* just to make sure */
519 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_224_sqr)>=0)
520 return BN_nnmod(r, a, field, ctx);
522 i = BN_ucmp(field, a);
529 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
533 if (!bn_wexpand(r, BN_NIST_224_TOP))
536 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
542 /* copy upper 256 bits of 448 bit number ... */
543 nist_cp_bn_0(c_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
544 /* ... and right shift by 32 to obtain upper 224 bits */
545 nist_set_224(buf.bn, c_d, 14, 13, 12, 11, 10, 9, 8);
546 /* truncate lower part to 224 bits too */
547 r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
549 nist_cp_bn_0(buf.bn, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
552 #if defined(NIST_INT64) && BN_BITS2!=64
554 NIST_INT64 acc; /* accumulator */
555 unsigned int *rp=(unsigned int *)r_d;
556 const unsigned int *bp=(const unsigned int *)buf.ui;
558 acc = rp[0]; acc -= bp[7-7];
559 acc -= bp[11-7]; rp[0] = (unsigned int)acc; acc >>= 32;
561 acc += rp[1]; acc -= bp[8-7];
562 acc -= bp[12-7]; rp[1] = (unsigned int)acc; acc >>= 32;
564 acc += rp[2]; acc -= bp[9-7];
565 acc -= bp[13-7]; rp[2] = (unsigned int)acc; acc >>= 32;
567 acc += rp[3]; acc += bp[7-7];
569 acc -= bp[10-7]; rp[3] = (unsigned int)acc; acc>>= 32;
571 acc += rp[4]; acc += bp[8-7];
573 acc -= bp[11-7]; rp[4] = (unsigned int)acc; acc >>= 32;
575 acc += rp[5]; acc += bp[9-7];
577 acc -= bp[12-7]; rp[5] = (unsigned int)acc; acc >>= 32;
579 acc += rp[6]; acc += bp[10-7];
580 acc -= bp[13-7]; rp[6] = (unsigned int)acc;
582 carry = (int)(acc>>32);
589 BN_ULONG t_d[BN_NIST_224_TOP];
591 nist_set_224(t_d, buf.bn, 10, 9, 8, 7, 0, 0, 0);
592 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
593 nist_set_224(t_d, buf.bn, 0, 13, 12, 11, 0, 0, 0);
594 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
595 nist_set_224(t_d, buf.bn, 13, 12, 11, 10, 9, 8, 7);
596 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
597 nist_set_224(t_d, buf.bn, 0, 0, 0, 0, 13, 12, 11);
598 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
601 carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
608 carry = (int)bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
610 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
615 /* it's a bit more comlicated logic in this case.
616 * if bn_add_words yields no carry, then result
617 * has to be adjusted by unconditionally *adding*
618 * the modulus. but if it does, then result has
619 * to be compared to the modulus and conditionally
620 * adjusted by *subtracting* the latter. */
621 carry = (int)bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
622 mask = 0-(PTR_SIZE_INT)carry;
623 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
624 ((PTR_SIZE_INT)bn_add_words&~mask);
629 /* otherwise it's effectively same as in BN_nist_mod_192... */
630 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
631 mask &= 0-(PTR_SIZE_INT)carry;
633 res = (BN_ULONG *)(((PTR_SIZE_INT)res&~mask) |
634 ((PTR_SIZE_INT)r_d&mask));
635 nist_cp_bn(r_d, res, BN_NIST_224_TOP);
636 r->top = BN_NIST_224_TOP;
642 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
644 bn_cp_32(to, 0, from, (a8) - 8) \
645 bn_cp_32(to, 1, from, (a7) - 8) \
646 bn_cp_32(to, 2, from, (a6) - 8) \
647 bn_cp_32(to, 3, from, (a5) - 8) \
648 bn_cp_32(to, 4, from, (a4) - 8) \
649 bn_cp_32(to, 5, from, (a3) - 8) \
650 bn_cp_32(to, 6, from, (a2) - 8) \
651 bn_cp_32(to, 7, from, (a1) - 8) \
654 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
659 register BN_ULONG *a_d = a->d, *r_d;
661 BN_ULONG bn[BN_NIST_256_TOP];
662 unsigned int ui[BN_NIST_256_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
664 BN_ULONG c_d[BN_NIST_256_TOP],
667 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
668 static const BIGNUM _bignum_nist_p_256_sqr = {
669 (BN_ULONG *)_nist_p_256_sqr,
670 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
671 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
672 0,BN_FLG_STATIC_DATA };
674 field = &_bignum_nist_p_256; /* just to make sure */
676 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_256_sqr)>=0)
677 return BN_nnmod(r, a, field, ctx);
679 i = BN_ucmp(field, a);
686 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
690 if (!bn_wexpand(r, BN_NIST_256_TOP))
693 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
698 nist_cp_bn_0(buf.bn, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
700 #if defined(NIST_INT64)
702 NIST_INT64 acc; /* accumulator */
703 unsigned int *rp=(unsigned int *)r_d;
704 const unsigned int *bp=(const unsigned int *)buf.ui;
706 acc = rp[0]; acc += bp[8-8];
711 acc -= bp[14-8]; rp[0] = (unsigned int)acc; acc >>= 32;
713 acc += rp[1]; acc += bp[9-8];
718 acc -= bp[15-8]; rp[1] = (unsigned int)acc; acc >>= 32;
720 acc += rp[2]; acc += bp[10-8];
724 acc -= bp[15-8]; rp[2] = (unsigned int)acc; acc >>= 32;
726 acc += rp[3]; acc += bp[11-8];
733 acc -= bp[9-8]; rp[3] = (unsigned int)acc; acc >>= 32;
735 acc += rp[4]; acc += bp[12-8];
741 acc -= bp[10-8]; rp[4] = (unsigned int)acc; acc >>= 32;
743 acc += rp[5]; acc += bp[13-8];
749 acc -= bp[11-8]; rp[5] = (unsigned int)acc; acc >>= 32;
751 acc += rp[6]; acc += bp[14-8];
758 acc -= bp[9-8]; rp[6] = (unsigned int)acc; acc >>= 32;
760 acc += rp[7]; acc += bp[15-8];
767 acc -= bp[13-8]; rp[7] = (unsigned int)acc;
769 carry = (int)(acc>>32);
773 BN_ULONG t_d[BN_NIST_256_TOP];
776 nist_set_256(t_d, buf.bn, 15, 14, 13, 12, 11, 0, 0, 0);
778 nist_set_256(c_d, buf.bn, 0, 15, 14, 13, 12, 0, 0, 0);
779 carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
782 register BN_ULONG *ap,t,c;
785 for (i = BN_NIST_256_TOP; i != 0; --i)
788 *(ap++)=((t<<1)|c)&BN_MASK2;
794 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
796 nist_set_256(t_d, buf.bn, 15, 14, 0, 0, 0, 10, 9, 8);
797 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
799 nist_set_256(t_d, buf.bn, 8, 13, 15, 14, 13, 11, 10, 9);
800 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
802 nist_set_256(t_d, buf.bn, 10, 8, 0, 0, 0, 13, 12, 11);
803 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
805 nist_set_256(t_d, buf.bn, 11, 9, 0, 0, 15, 14, 13, 12);
806 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
808 nist_set_256(t_d, buf.bn, 12, 0, 10, 9, 8, 15, 14, 13);
809 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
811 nist_set_256(t_d, buf.bn, 13, 0, 11, 10, 9, 0, 15, 14);
812 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
816 /* see BN_nist_mod_224 for explanation */
819 carry = (int)bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
822 carry = (int)bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
823 mask = 0-(PTR_SIZE_INT)carry;
824 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
825 ((PTR_SIZE_INT)bn_add_words&~mask);
830 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
831 mask &= 0-(PTR_SIZE_INT)carry;
833 res = (BN_ULONG *)(((PTR_SIZE_INT)res&~mask) |
834 ((PTR_SIZE_INT)r_d&mask));
835 nist_cp_bn(r_d, res, BN_NIST_256_TOP);
836 r->top = BN_NIST_256_TOP;
842 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
844 bn_cp_32(to, 0, from, (a12) - 12) \
845 bn_cp_32(to, 1, from, (a11) - 12) \
846 bn_cp_32(to, 2, from, (a10) - 12) \
847 bn_cp_32(to, 3, from, (a9) - 12) \
848 bn_cp_32(to, 4, from, (a8) - 12) \
849 bn_cp_32(to, 5, from, (a7) - 12) \
850 bn_cp_32(to, 6, from, (a6) - 12) \
851 bn_cp_32(to, 7, from, (a5) - 12) \
852 bn_cp_32(to, 8, from, (a4) - 12) \
853 bn_cp_32(to, 9, from, (a3) - 12) \
854 bn_cp_32(to, 10, from, (a2) - 12) \
855 bn_cp_32(to, 11, from, (a1) - 12) \
858 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
863 register BN_ULONG *r_d, *a_d = a->d;
865 BN_ULONG bn[BN_NIST_384_TOP];
866 unsigned int ui[BN_NIST_384_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
868 BN_ULONG c_d[BN_NIST_384_TOP],
871 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
872 static const BIGNUM _bignum_nist_p_384_sqr = {
873 (BN_ULONG *)_nist_p_384_sqr,
874 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
875 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
876 0,BN_FLG_STATIC_DATA };
879 field = &_bignum_nist_p_384; /* just to make sure */
881 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_384_sqr)>=0)
882 return BN_nnmod(r, a, field, ctx);
884 i = BN_ucmp(field, a);
891 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
895 if (!bn_wexpand(r, BN_NIST_384_TOP))
898 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
903 nist_cp_bn_0(buf.bn, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
905 #if defined(NIST_INT64)
907 NIST_INT64 acc; /* accumulator */
908 unsigned int *rp=(unsigned int *)r_d;
909 const unsigned int *bp=(const unsigned int *)buf.ui;
911 acc = rp[0]; acc += bp[12-12];
914 acc -= bp[23-12]; rp[0] = (unsigned int)acc; acc >>= 32;
916 acc += rp[1]; acc += bp[13-12];
920 acc -= bp[20-12]; rp[1] = (unsigned int)acc; acc >>= 32;
922 acc += rp[2]; acc += bp[14-12];
925 acc -= bp[21-12]; rp[2] = (unsigned int)acc; acc >>= 32;
927 acc += rp[3]; acc += bp[15-12];
933 acc -= bp[23-12]; rp[3] = (unsigned int)acc; acc >>= 32;
935 acc += rp[4]; acc += bp[21-12];
944 acc -= bp[23-12]; rp[4] = (unsigned int)acc; acc >>= 32;
946 acc += rp[5]; acc += bp[22-12];
953 acc -= bp[16-12]; rp[5] = (unsigned int)acc; acc >>= 32;
955 acc += rp[6]; acc += bp[23-12];
961 acc -= bp[17-12]; rp[6] = (unsigned int)acc; acc >>= 32;
963 acc += rp[7]; acc += bp[19-12];
967 acc -= bp[18-12]; rp[7] = (unsigned int)acc; acc >>= 32;
969 acc += rp[8]; acc += bp[20-12];
972 acc -= bp[19-12]; rp[8] = (unsigned int)acc; acc >>= 32;
974 acc += rp[9]; acc += bp[21-12];
977 acc -= bp[20-12]; rp[9] = (unsigned int)acc; acc >>= 32;
979 acc += rp[10]; acc += bp[22-12];
982 acc -= bp[21-12]; rp[10] = (unsigned int)acc; acc >>= 32;
984 acc += rp[11]; acc += bp[23-12];
987 acc -= bp[22-12]; rp[11] = (unsigned int)acc;
989 carry = (int)(acc>>32);
993 BN_ULONG t_d[BN_NIST_384_TOP];
996 nist_set_256(t_d, buf.bn, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
999 register BN_ULONG *ap,t,c;
1002 for (i = 3; i != 0; --i)
1005 *(ap++)=((t<<1)|c)&BN_MASK2;
1006 c=(t & BN_TBIT)?1:0;
1010 carry = (int)bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
1011 t_d, BN_NIST_256_TOP);
1013 carry += (int)bn_add_words(r_d, r_d, buf.bn, BN_NIST_384_TOP);
1015 nist_set_384(t_d,buf.bn,20,19,18,17,16,15,14,13,12,23,22,21);
1016 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1018 nist_set_384(t_d,buf.bn,19,18,17,16,15,14,13,12,20,0,23,0);
1019 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1021 nist_set_384(t_d, buf.bn,0,0,0,0,23,22,21,20,0,0,0,0);
1022 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1024 nist_set_384(t_d,buf.bn,0,0,0,0,0,0,23,22,21,0,0,20);
1025 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1027 nist_set_384(t_d,buf.bn,22,21,20,19,18,17,16,15,14,13,12,23);
1028 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1030 nist_set_384(t_d,buf.bn,0,0,0,0,0,0,0,23,22,21,20,0);
1031 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1033 nist_set_384(t_d,buf.bn,0,0,0,0,0,0,0,23,23,0,0,0);
1034 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1038 /* see BN_nist_mod_224 for explanation */
1041 carry = (int)bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
1044 carry = (int)bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
1045 mask = 0-(PTR_SIZE_INT)carry;
1046 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
1047 ((PTR_SIZE_INT)bn_add_words&~mask);
1052 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
1053 mask &= 0-(PTR_SIZE_INT)carry;
1055 res = (BN_ULONG *)(((PTR_SIZE_INT)res&~mask) |
1056 ((PTR_SIZE_INT)r_d&mask));
1057 nist_cp_bn(r_d, res, BN_NIST_384_TOP);
1058 r->top = BN_NIST_384_TOP;
1064 #define BN_NIST_521_RSHIFT (521%BN_BITS2)
1065 #define BN_NIST_521_LSHIFT (BN_BITS2-BN_NIST_521_RSHIFT)
1066 #define BN_NIST_521_TOP_MASK ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
1068 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
1071 int top = a->top, i;
1072 BN_ULONG *r_d, *a_d = a->d,
1073 t_d[BN_NIST_521_TOP],
1076 static const BIGNUM _bignum_nist_p_521_sqr = {
1077 (BN_ULONG *)_nist_p_521_sqr,
1078 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
1079 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
1080 0,BN_FLG_STATIC_DATA };
1082 field = &_bignum_nist_p_521; /* just to make sure */
1084 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_521_sqr)>=0)
1085 return BN_nnmod(r, a, field, ctx);
1087 i = BN_ucmp(field, a);
1094 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
1098 if (!bn_wexpand(r,BN_NIST_521_TOP))
1101 nist_cp_bn(r_d,a_d, BN_NIST_521_TOP);
1106 /* upper 521 bits, copy ... */
1107 nist_cp_bn_0(t_d,a_d + (BN_NIST_521_TOP-1), top - (BN_NIST_521_TOP-1),BN_NIST_521_TOP);
1108 /* ... and right shift */
1109 for (val=t_d[0],i=0; i<BN_NIST_521_TOP-1; i++)
1111 tmp = val>>BN_NIST_521_RSHIFT;
1113 t_d[i] = (tmp | val<<BN_NIST_521_LSHIFT) & BN_MASK2;
1115 t_d[i] = val>>BN_NIST_521_RSHIFT;
1116 /* lower 521 bits */
1117 r_d[i] &= BN_NIST_521_TOP_MASK;
1119 bn_add_words(r_d,r_d,t_d,BN_NIST_521_TOP);
1120 mask = 0-(PTR_SIZE_INT)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
1122 res = (BN_ULONG *)(((PTR_SIZE_INT)res&~mask) |
1123 ((PTR_SIZE_INT)r_d&mask));
1124 nist_cp_bn(r_d,res,BN_NIST_521_TOP);
1125 r->top = BN_NIST_521_TOP;
1131 int (*BN_nist_mod_func(const BIGNUM *p))(BIGNUM *r, const BIGNUM *a, const BIGNUM *field, BN_CTX *ctx)
1133 if (BN_ucmp(&_bignum_nist_p_192, p) == 0)
1134 return BN_nist_mod_192;
1135 if (BN_ucmp(&_bignum_nist_p_224, p) == 0)
1136 return BN_nist_mod_224;
1137 if (BN_ucmp(&_bignum_nist_p_256, p) == 0)
1138 return BN_nist_mod_256;
1139 if (BN_ucmp(&_bignum_nist_p_384, p) == 0)
1140 return BN_nist_mod_384;
1141 if (BN_ucmp(&_bignum_nist_p_521, p) == 0)
1142 return BN_nist_mod_521;