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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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 */
349 #define nist_set_192(to, from, a1, a2, a3) \
351 bn_cp_64(to, 0, from, (a3) - 3) \
352 bn_cp_64(to, 1, from, (a2) - 3) \
353 bn_cp_64(to, 2, from, (a1) - 3) \
356 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
361 register BN_ULONG *r_d, *a_d = a->d;
363 BN_ULONG bn[BN_NIST_192_TOP];
364 unsigned int ui[BN_NIST_192_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
366 BN_ULONG c_d[BN_NIST_192_TOP],
369 static const BIGNUM _bignum_nist_p_192_sqr = {
370 (BN_ULONG *)_nist_p_192_sqr,
371 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
372 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
373 0,BN_FLG_STATIC_DATA };
375 field = &_bignum_nist_p_192; /* just to make sure */
377 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_192_sqr)>=0)
378 return BN_nnmod(r, a, field, ctx);
380 i = BN_ucmp(field, a);
387 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
391 if (!bn_wexpand(r, BN_NIST_192_TOP))
394 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
399 nist_cp_bn_0(buf.bn, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
401 #if defined(NIST_INT64)
403 NIST_INT64 acc; /* accumulator */
404 unsigned int *rp=(unsigned int *)r_d;
405 const unsigned int *bp=(const unsigned int *)buf.ui;
407 acc = rp[0]; acc += bp[3*2-6];
408 acc += bp[5*2-6]; rp[0] = (unsigned int)acc; acc >>= 32;
410 acc += rp[1]; acc += bp[3*2-5];
411 acc += bp[5*2-5]; rp[1] = (unsigned int)acc; acc >>= 32;
413 acc += rp[2]; acc += bp[3*2-6];
415 acc += bp[5*2-6]; rp[2] = (unsigned int)acc; acc >>= 32;
417 acc += rp[3]; acc += bp[3*2-5];
419 acc += bp[5*2-5]; rp[3] = (unsigned int)acc; acc >>= 32;
421 acc += rp[4]; acc += bp[4*2-6];
422 acc += bp[5*2-6]; rp[4] = (unsigned int)acc; acc >>= 32;
424 acc += rp[5]; acc += bp[4*2-5];
425 acc += bp[5*2-5]; rp[5] = (unsigned int)acc;
427 carry = (int)(acc>>32);
431 BN_ULONG t_d[BN_NIST_192_TOP];
433 nist_set_192(t_d, buf.bn, 0, 3, 3);
434 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
435 nist_set_192(t_d, buf.bn, 4, 4, 0);
436 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
437 nist_set_192(t_d, buf.bn, 5, 5, 5)
438 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
442 carry = (int)bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
447 * we need 'if (carry==0 || result>=modulus) result-=modulus;'
448 * as comparison implies subtraction, we can write
449 * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
450 * this is what happens below, but without explicit if:-) a.
452 mask = 0-(PTR_SIZE_INT)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
453 mask &= 0-(PTR_SIZE_INT)carry;
455 (((PTR_SIZE_INT)c_d&~mask) | ((PTR_SIZE_INT)r_d&mask));
456 nist_cp_bn(r_d, res, BN_NIST_192_TOP);
457 r->top = BN_NIST_192_TOP;
463 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
465 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
467 bn_cp_32(to, 0, from, (a7) - 7) \
468 bn_cp_32(to, 1, from, (a6) - 7) \
469 bn_cp_32(to, 2, from, (a5) - 7) \
470 bn_cp_32(to, 3, from, (a4) - 7) \
471 bn_cp_32(to, 4, from, (a3) - 7) \
472 bn_cp_32(to, 5, from, (a2) - 7) \
473 bn_cp_32(to, 6, from, (a1) - 7) \
476 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
481 BN_ULONG *r_d, *a_d = a->d;
482 BN_ULONG buf[BN_NIST_224_TOP],
483 c_d[BN_NIST_224_TOP],
486 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
487 static const BIGNUM _bignum_nist_p_224_sqr = {
488 (BN_ULONG *)_nist_p_224_sqr,
489 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
490 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
491 0,BN_FLG_STATIC_DATA };
494 field = &_bignum_nist_p_224; /* just to make sure */
496 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_224_sqr)>=0)
497 return BN_nnmod(r, a, field, ctx);
499 i = BN_ucmp(field, a);
506 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
510 if (!bn_wexpand(r, BN_NIST_224_TOP))
513 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
519 /* copy upper 256 bits of 448 bit number ... */
520 nist_cp_bn_0(c_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
521 /* ... and right shift by 32 to obtain upper 224 bits */
522 nist_set_224(buf, c_d, 14, 13, 12, 11, 10, 9, 8);
523 /* truncate lower part to 224 bits too */
524 r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
526 nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
529 #if defined(NIST_INT64) && BN_BITS2!=64
531 NIST_INT64 acc; /* accumulator */
532 unsigned int *rp=(unsigned int *)r_d;
533 const unsigned int *bp=(const unsigned int *)buf;
535 acc = rp[0]; acc -= bp[7-7];
536 acc -= bp[11-7]; rp[0] = (unsigned int)acc; acc >>= 32;
538 acc += rp[1]; acc -= bp[8-7];
539 acc -= bp[12-7]; rp[1] = (unsigned int)acc; acc >>= 32;
541 acc += rp[2]; acc -= bp[9-7];
542 acc -= bp[13-7]; rp[2] = (unsigned int)acc; acc >>= 32;
544 acc += rp[3]; acc += bp[7-7];
546 acc -= bp[10-7]; rp[3] = (unsigned int)acc; acc>>= 32;
548 acc += rp[4]; acc += bp[8-7];
550 acc -= bp[11-7]; rp[4] = (unsigned int)acc; acc >>= 32;
552 acc += rp[5]; acc += bp[9-7];
554 acc -= bp[12-7]; rp[5] = (unsigned int)acc; acc >>= 32;
556 acc += rp[6]; acc += bp[10-7];
557 acc -= bp[13-7]; rp[6] = (unsigned int)acc;
559 carry = (int)(acc>>32);
566 BN_ULONG t_d[BN_NIST_224_TOP];
568 nist_set_224(t_d, buf, 10, 9, 8, 7, 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, 0, 13, 12, 11, 0, 0, 0);
571 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
572 nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
573 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
574 nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
575 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
578 carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
585 carry = (int)bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
587 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
592 /* it's a bit more comlicated logic in this case.
593 * if bn_add_words yields no carry, then result
594 * has to be adjusted by unconditionally *adding*
595 * the modulus. but if it does, then result has
596 * to be compared to the modulus and conditionally
597 * adjusted by *subtracting* the latter. */
598 carry = (int)bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
599 mask = 0-(PTR_SIZE_INT)carry;
600 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
601 ((PTR_SIZE_INT)bn_add_words&~mask);
606 /* otherwise it's effectively same as in BN_nist_mod_192... */
607 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
608 mask &= 0-(PTR_SIZE_INT)carry;
609 res = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
610 ((PTR_SIZE_INT)r_d&mask));
611 nist_cp_bn(r_d, res, BN_NIST_224_TOP);
612 r->top = BN_NIST_224_TOP;
618 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
620 bn_cp_32(to, 0, from, (a8) - 8) \
621 bn_cp_32(to, 1, from, (a7) - 8) \
622 bn_cp_32(to, 2, from, (a6) - 8) \
623 bn_cp_32(to, 3, from, (a5) - 8) \
624 bn_cp_32(to, 4, from, (a4) - 8) \
625 bn_cp_32(to, 5, from, (a3) - 8) \
626 bn_cp_32(to, 6, from, (a2) - 8) \
627 bn_cp_32(to, 7, from, (a1) - 8) \
630 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
635 register BN_ULONG *a_d = a->d, *r_d;
637 BN_ULONG bn[BN_NIST_256_TOP];
638 unsigned int ui[BN_NIST_256_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
640 BN_ULONG c_d[BN_NIST_256_TOP],
643 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
644 static const BIGNUM _bignum_nist_p_256_sqr = {
645 (BN_ULONG *)_nist_p_256_sqr,
646 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
647 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
648 0,BN_FLG_STATIC_DATA };
650 field = &_bignum_nist_p_256; /* just to make sure */
652 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_256_sqr)>=0)
653 return BN_nnmod(r, a, field, ctx);
655 i = BN_ucmp(field, a);
662 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
666 if (!bn_wexpand(r, BN_NIST_256_TOP))
669 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
674 nist_cp_bn_0(buf.bn, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
676 #if defined(NIST_INT64)
678 NIST_INT64 acc; /* accumulator */
679 unsigned int *rp=(unsigned int *)r_d;
680 const unsigned int *bp=(const unsigned int *)buf.ui;
682 acc = rp[0]; acc += bp[8-8];
687 acc -= bp[14-8]; rp[0] = (unsigned int)acc; acc >>= 32;
689 acc += rp[1]; acc += bp[9-8];
694 acc -= bp[15-8]; rp[1] = (unsigned int)acc; acc >>= 32;
696 acc += rp[2]; acc += bp[10-8];
700 acc -= bp[15-8]; rp[2] = (unsigned int)acc; acc >>= 32;
702 acc += rp[3]; acc += bp[11-8];
709 acc -= bp[9-8]; rp[3] = (unsigned int)acc; acc >>= 32;
711 acc += rp[4]; acc += bp[12-8];
717 acc -= bp[10-8]; rp[4] = (unsigned int)acc; acc >>= 32;
719 acc += rp[5]; acc += bp[13-8];
725 acc -= bp[11-8]; rp[5] = (unsigned int)acc; acc >>= 32;
727 acc += rp[6]; acc += bp[14-8];
734 acc -= bp[9-8]; rp[6] = (unsigned int)acc; acc >>= 32;
736 acc += rp[7]; acc += bp[15-8];
743 acc -= bp[13-8]; rp[7] = (unsigned int)acc;
745 carry = (int)(acc>>32);
749 BN_ULONG t_d[BN_NIST_256_TOP];
752 nist_set_256(t_d, buf.bn, 15, 14, 13, 12, 11, 0, 0, 0);
754 nist_set_256(c_d, buf.bn, 0, 15, 14, 13, 12, 0, 0, 0);
755 carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
758 register BN_ULONG *ap,t,c;
761 for (i = BN_NIST_256_TOP; i != 0; --i)
764 *(ap++)=((t<<1)|c)&BN_MASK2;
770 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
772 nist_set_256(t_d, buf.bn, 15, 14, 0, 0, 0, 10, 9, 8);
773 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
775 nist_set_256(t_d, buf.bn, 8, 13, 15, 14, 13, 11, 10, 9);
776 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
778 nist_set_256(t_d, buf.bn, 10, 8, 0, 0, 0, 13, 12, 11);
779 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
781 nist_set_256(t_d, buf.bn, 11, 9, 0, 0, 15, 14, 13, 12);
782 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
784 nist_set_256(t_d, buf.bn, 12, 0, 10, 9, 8, 15, 14, 13);
785 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
787 nist_set_256(t_d, buf.bn, 13, 0, 11, 10, 9, 0, 15, 14);
788 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
792 /* see BN_nist_mod_224 for explanation */
795 carry = (int)bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
798 carry = (int)bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
799 mask = 0-(PTR_SIZE_INT)carry;
800 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
801 ((PTR_SIZE_INT)bn_add_words&~mask);
806 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
807 mask &= 0-(PTR_SIZE_INT)carry;
808 res = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
809 ((PTR_SIZE_INT)r_d&mask));
810 nist_cp_bn(r_d, res, BN_NIST_256_TOP);
811 r->top = BN_NIST_256_TOP;
817 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
819 bn_cp_32(to, 0, from, (a12) - 12) \
820 bn_cp_32(to, 1, from, (a11) - 12) \
821 bn_cp_32(to, 2, from, (a10) - 12) \
822 bn_cp_32(to, 3, from, (a9) - 12) \
823 bn_cp_32(to, 4, from, (a8) - 12) \
824 bn_cp_32(to, 5, from, (a7) - 12) \
825 bn_cp_32(to, 6, from, (a6) - 12) \
826 bn_cp_32(to, 7, from, (a5) - 12) \
827 bn_cp_32(to, 8, from, (a4) - 12) \
828 bn_cp_32(to, 9, from, (a3) - 12) \
829 bn_cp_32(to, 10, from, (a2) - 12) \
830 bn_cp_32(to, 11, from, (a1) - 12) \
833 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
838 register BN_ULONG *r_d, *a_d = a->d;
840 BN_ULONG bn[BN_NIST_384_TOP];
841 unsigned int ui[BN_NIST_384_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
843 BN_ULONG c_d[BN_NIST_384_TOP],
846 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
847 static const BIGNUM _bignum_nist_p_384_sqr = {
848 (BN_ULONG *)_nist_p_384_sqr,
849 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
850 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
851 0,BN_FLG_STATIC_DATA };
854 field = &_bignum_nist_p_384; /* just to make sure */
856 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_384_sqr)>=0)
857 return BN_nnmod(r, a, field, ctx);
859 i = BN_ucmp(field, a);
866 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
870 if (!bn_wexpand(r, BN_NIST_384_TOP))
873 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
878 nist_cp_bn_0(buf.bn, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
880 #if defined(NIST_INT64)
882 NIST_INT64 acc; /* accumulator */
883 unsigned int *rp=(unsigned int *)r_d;
884 const unsigned int *bp=(const unsigned int *)buf.ui;
886 acc = rp[0]; acc += bp[12-12];
889 acc -= bp[23-12]; rp[0] = (unsigned int)acc; acc >>= 32;
891 acc += rp[1]; acc += bp[13-12];
895 acc -= bp[20-12]; rp[1] = (unsigned int)acc; acc >>= 32;
897 acc += rp[2]; acc += bp[14-12];
900 acc -= bp[21-12]; rp[2] = (unsigned int)acc; acc >>= 32;
902 acc += rp[3]; acc += bp[15-12];
908 acc -= bp[23-12]; rp[3] = (unsigned int)acc; acc >>= 32;
910 acc += rp[4]; acc += bp[21-12];
919 acc -= bp[23-12]; rp[4] = (unsigned int)acc; acc >>= 32;
921 acc += rp[5]; acc += bp[22-12];
928 acc -= bp[16-12]; rp[5] = (unsigned int)acc; acc >>= 32;
930 acc += rp[6]; acc += bp[23-12];
936 acc -= bp[17-12]; rp[6] = (unsigned int)acc; acc >>= 32;
938 acc += rp[7]; acc += bp[19-12];
942 acc -= bp[18-12]; rp[7] = (unsigned int)acc; acc >>= 32;
944 acc += rp[8]; acc += bp[20-12];
947 acc -= bp[19-12]; rp[8] = (unsigned int)acc; acc >>= 32;
949 acc += rp[9]; acc += bp[21-12];
952 acc -= bp[20-12]; rp[9] = (unsigned int)acc; acc >>= 32;
954 acc += rp[10]; acc += bp[22-12];
957 acc -= bp[21-12]; rp[10] = (unsigned int)acc; acc >>= 32;
959 acc += rp[11]; acc += bp[23-12];
962 acc -= bp[22-12]; rp[11] = (unsigned int)acc;
964 carry = (int)(acc>>32);
968 BN_ULONG t_d[BN_NIST_384_TOP];
971 nist_set_256(t_d, buf.bn, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
974 register BN_ULONG *ap,t,c;
977 for (i = 3; i != 0; --i)
980 *(ap++)=((t<<1)|c)&BN_MASK2;
985 carry = (int)bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
986 t_d, BN_NIST_256_TOP);
988 carry += (int)bn_add_words(r_d, r_d, buf.bn, BN_NIST_384_TOP);
990 nist_set_384(t_d,buf.bn,20,19,18,17,16,15,14,13,12,23,22,21);
991 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
993 nist_set_384(t_d,buf.bn,19,18,17,16,15,14,13,12,20,0,23,0);
994 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
996 nist_set_384(t_d, buf.bn,0,0,0,0,23,22,21,20,0,0,0,0);
997 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
999 nist_set_384(t_d,buf.bn,0,0,0,0,0,0,23,22,21,0,0,20);
1000 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1002 nist_set_384(t_d,buf.bn,22,21,20,19,18,17,16,15,14,13,12,23);
1003 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1005 nist_set_384(t_d,buf.bn,0,0,0,0,0,0,0,23,22,21,20,0);
1006 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1008 nist_set_384(t_d,buf.bn,0,0,0,0,0,0,0,23,23,0,0,0);
1009 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1013 /* see BN_nist_mod_224 for explanation */
1016 carry = (int)bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
1019 carry = (int)bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
1020 mask = 0-(PTR_SIZE_INT)carry;
1021 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
1022 ((PTR_SIZE_INT)bn_add_words&~mask);
1027 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
1028 mask &= 0-(PTR_SIZE_INT)carry;
1029 res = (BN_ULONG *)(((PTR_SIZE_INT)c_d&~mask) |
1030 ((PTR_SIZE_INT)r_d&mask));
1031 nist_cp_bn(r_d, res, BN_NIST_384_TOP);
1032 r->top = BN_NIST_384_TOP;
1038 #define BN_NIST_521_RSHIFT (521%BN_BITS2)
1039 #define BN_NIST_521_LSHIFT (BN_BITS2-BN_NIST_521_RSHIFT)
1040 #define BN_NIST_521_TOP_MASK ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
1042 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
1045 int top = a->top, i;
1046 BN_ULONG *r_d, *a_d = a->d,
1047 t_d[BN_NIST_521_TOP],
1050 static const BIGNUM _bignum_nist_p_521_sqr = {
1051 (BN_ULONG *)_nist_p_521_sqr,
1052 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
1053 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
1054 0,BN_FLG_STATIC_DATA };
1056 field = &_bignum_nist_p_521; /* just to make sure */
1058 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_521_sqr)>=0)
1059 return BN_nnmod(r, a, field, ctx);
1061 i = BN_ucmp(field, a);
1068 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
1072 if (!bn_wexpand(r,BN_NIST_521_TOP))
1075 nist_cp_bn(r_d,a_d, BN_NIST_521_TOP);
1080 /* upper 521 bits, copy ... */
1081 nist_cp_bn_0(t_d,a_d + (BN_NIST_521_TOP-1), top - (BN_NIST_521_TOP-1),BN_NIST_521_TOP);
1082 /* ... and right shift */
1083 for (val=t_d[0],i=0; i<BN_NIST_521_TOP-1; i++)
1085 tmp = val>>BN_NIST_521_RSHIFT;
1087 t_d[i] = (tmp | val<<BN_NIST_521_LSHIFT) & BN_MASK2;
1089 t_d[i] = val>>BN_NIST_521_RSHIFT;
1090 /* lower 521 bits */
1091 r_d[i] &= BN_NIST_521_TOP_MASK;
1093 bn_add_words(r_d,r_d,t_d,BN_NIST_521_TOP);
1094 mask = 0-(PTR_SIZE_INT)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
1095 res = (BN_ULONG *)(((PTR_SIZE_INT)t_d&~mask) |
1096 ((PTR_SIZE_INT)r_d&mask));
1097 nist_cp_bn(r_d,res,BN_NIST_521_TOP);
1098 r->top = BN_NIST_521_TOP;