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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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) */
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, const BN_ULONG *a, int top, int max)
292 BN_ULONG *_tmp1 = (buf);
293 const BN_ULONG *_tmp2 = (a);
296 OPENSSL_assert(top <= max);
298 for (i = (top); i != 0; i--)
300 for (i = (max) - (top); i != 0; i--)
301 *_tmp1++ = (BN_ULONG) 0;
304 static void nist_cp_bn(BN_ULONG *buf, const BN_ULONG *a, int top)
307 BN_ULONG *_tmp1 = (buf);
308 const BN_ULONG *_tmp2 = (a);
310 for (i = (top); i != 0; i--)
315 #define bn_cp_64(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
316 #define bn_64_set_0(to, n) (to)[n] = (BN_ULONG)0;
318 * two following macros are implemented under assumption that they
319 * are called in a sequence with *ascending* n, i.e. as they are...
321 #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))\
322 :(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
323 #define bn_32_set_0(to, n) (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
324 #define bn_cp_32(to,n,from,m) ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
325 # if defined(L_ENDIAN)
326 # if defined(__arch64__)
327 # define NIST_INT64 long
329 # define NIST_INT64 long long
333 #define bn_cp_64(to, n, from, m) \
335 bn_cp_32(to, (n)*2, from, (m)*2); \
336 bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
338 #define bn_64_set_0(to, n) \
340 bn_32_set_0(to, (n)*2); \
341 bn_32_set_0(to, (n)*2+1); \
343 #define bn_cp_32(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
344 #define bn_32_set_0(to, n) (to)[n] = (BN_ULONG)0;
345 # if defined(_WIN32) && !defined(__GNUC__)
346 # define NIST_INT64 __int64
347 # elif defined(BN_LLONG)
348 # define NIST_INT64 long long
350 #endif /* BN_BITS2 != 64 */
352 #define nist_set_192(to, from, a1, a2, a3) \
354 bn_cp_64(to, 0, from, (a3) - 3) \
355 bn_cp_64(to, 1, from, (a2) - 3) \
356 bn_cp_64(to, 2, from, (a1) - 3) \
359 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
364 register BN_ULONG *r_d, *a_d = a->d;
366 BN_ULONG bn[BN_NIST_192_TOP];
367 unsigned int ui[BN_NIST_192_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
369 BN_ULONG c_d[BN_NIST_192_TOP],
372 static const BIGNUM _bignum_nist_p_192_sqr = {
373 (BN_ULONG *)_nist_p_192_sqr,
374 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
375 sizeof(_nist_p_192_sqr)/sizeof(_nist_p_192_sqr[0]),
376 0,BN_FLG_STATIC_DATA };
378 field = &_bignum_nist_p_192; /* just to make sure */
380 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_192_sqr)>=0)
381 return BN_nnmod(r, a, field, ctx);
383 i = BN_ucmp(field, a);
390 return (r == a) ? 1 : (BN_copy(r ,a) != NULL);
394 if (!bn_wexpand(r, BN_NIST_192_TOP))
397 nist_cp_bn(r_d, a_d, BN_NIST_192_TOP);
402 nist_cp_bn_0(buf.bn, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
404 #if defined(NIST_INT64)
406 NIST_INT64 acc; /* accumulator */
407 unsigned int *rp=(unsigned int *)r_d;
408 const unsigned int *bp=(const unsigned int *)buf.ui;
410 acc = rp[0]; acc += bp[3*2-6];
411 acc += bp[5*2-6]; rp[0] = (unsigned int)acc; acc >>= 32;
413 acc += rp[1]; acc += bp[3*2-5];
414 acc += bp[5*2-5]; rp[1] = (unsigned int)acc; acc >>= 32;
416 acc += rp[2]; acc += bp[3*2-6];
418 acc += bp[5*2-6]; rp[2] = (unsigned int)acc; acc >>= 32;
420 acc += rp[3]; acc += bp[3*2-5];
422 acc += bp[5*2-5]; rp[3] = (unsigned int)acc; acc >>= 32;
424 acc += rp[4]; acc += bp[4*2-6];
425 acc += bp[5*2-6]; rp[4] = (unsigned int)acc; acc >>= 32;
427 acc += rp[5]; acc += bp[4*2-5];
428 acc += bp[5*2-5]; rp[5] = (unsigned int)acc;
430 carry = (int)(acc>>32);
434 BN_ULONG t_d[BN_NIST_192_TOP];
436 nist_set_192(t_d, buf.bn, 0, 3, 3);
437 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
438 nist_set_192(t_d, buf.bn, 4, 4, 0);
439 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
440 nist_set_192(t_d, buf.bn, 5, 5, 5)
441 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
445 carry = (int)bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
450 * we need 'if (carry==0 || result>=modulus) result-=modulus;'
451 * as comparison implies subtraction, we can write
452 * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
453 * this is what happens below, but without explicit if:-) a.
455 mask = 0-(PTR_SIZE_INT)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
456 mask &= 0-(PTR_SIZE_INT)carry;
459 (((PTR_SIZE_INT)res&~mask) | ((PTR_SIZE_INT)r_d&mask));
460 nist_cp_bn(r_d, res, BN_NIST_192_TOP);
461 r->top = BN_NIST_192_TOP;
467 typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
469 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
471 bn_cp_32(to, 0, from, (a7) - 7) \
472 bn_cp_32(to, 1, from, (a6) - 7) \
473 bn_cp_32(to, 2, from, (a5) - 7) \
474 bn_cp_32(to, 3, from, (a4) - 7) \
475 bn_cp_32(to, 4, from, (a3) - 7) \
476 bn_cp_32(to, 5, from, (a2) - 7) \
477 bn_cp_32(to, 6, from, (a1) - 7) \
480 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
485 BN_ULONG *r_d, *a_d = a->d;
487 BN_ULONG bn[BN_NIST_224_TOP];
488 unsigned int ui[BN_NIST_224_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
490 BN_ULONG c_d[BN_NIST_224_TOP],
493 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
494 static const BIGNUM _bignum_nist_p_224_sqr = {
495 (BN_ULONG *)_nist_p_224_sqr,
496 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
497 sizeof(_nist_p_224_sqr)/sizeof(_nist_p_224_sqr[0]),
498 0,BN_FLG_STATIC_DATA };
501 field = &_bignum_nist_p_224; /* just to make sure */
503 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_224_sqr)>=0)
504 return BN_nnmod(r, a, field, ctx);
506 i = BN_ucmp(field, a);
513 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
517 if (!bn_wexpand(r, BN_NIST_224_TOP))
520 nist_cp_bn(r_d, a_d, BN_NIST_224_TOP);
526 /* copy upper 256 bits of 448 bit number ... */
527 nist_cp_bn_0(c_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
528 /* ... and right shift by 32 to obtain upper 224 bits */
529 nist_set_224(buf.bn, c_d, 14, 13, 12, 11, 10, 9, 8);
530 /* truncate lower part to 224 bits too */
531 r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
533 nist_cp_bn_0(buf.bn, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
536 #if defined(NIST_INT64) && BN_BITS2!=64
538 NIST_INT64 acc; /* accumulator */
539 unsigned int *rp=(unsigned int *)r_d;
540 const unsigned int *bp=(const unsigned int *)buf.ui;
542 acc = rp[0]; acc -= bp[7-7];
543 acc -= bp[11-7]; rp[0] = (unsigned int)acc; acc >>= 32;
545 acc += rp[1]; acc -= bp[8-7];
546 acc -= bp[12-7]; rp[1] = (unsigned int)acc; acc >>= 32;
548 acc += rp[2]; acc -= bp[9-7];
549 acc -= bp[13-7]; rp[2] = (unsigned int)acc; acc >>= 32;
551 acc += rp[3]; acc += bp[7-7];
553 acc -= bp[10-7]; rp[3] = (unsigned int)acc; acc>>= 32;
555 acc += rp[4]; acc += bp[8-7];
557 acc -= bp[11-7]; rp[4] = (unsigned int)acc; acc >>= 32;
559 acc += rp[5]; acc += bp[9-7];
561 acc -= bp[12-7]; rp[5] = (unsigned int)acc; acc >>= 32;
563 acc += rp[6]; acc += bp[10-7];
564 acc -= bp[13-7]; rp[6] = (unsigned int)acc;
566 carry = (int)(acc>>32);
573 BN_ULONG t_d[BN_NIST_224_TOP];
575 nist_set_224(t_d, buf.bn, 10, 9, 8, 7, 0, 0, 0);
576 carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
577 nist_set_224(t_d, buf.bn, 0, 13, 12, 11, 0, 0, 0);
578 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
579 nist_set_224(t_d, buf.bn, 13, 12, 11, 10, 9, 8, 7);
580 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
581 nist_set_224(t_d, buf.bn, 0, 0, 0, 0, 13, 12, 11);
582 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
585 carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
592 carry = (int)bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
594 carry=(int)(~(r_d[BN_NIST_224_TOP-1]>>32))&1;
599 /* it's a bit more comlicated logic in this case.
600 * if bn_add_words yields no carry, then result
601 * has to be adjusted by unconditionally *adding*
602 * the modulus. but if it does, then result has
603 * to be compared to the modulus and conditionally
604 * adjusted by *subtracting* the latter. */
605 carry = (int)bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
606 mask = 0-(PTR_SIZE_INT)carry;
607 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
608 ((PTR_SIZE_INT)bn_add_words&~mask);
613 /* otherwise it's effectively same as in BN_nist_mod_192... */
614 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
615 mask &= 0-(PTR_SIZE_INT)carry;
617 res = (BN_ULONG *)(((PTR_SIZE_INT)res&~mask) |
618 ((PTR_SIZE_INT)r_d&mask));
619 nist_cp_bn(r_d, res, BN_NIST_224_TOP);
620 r->top = BN_NIST_224_TOP;
626 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
628 bn_cp_32(to, 0, from, (a8) - 8) \
629 bn_cp_32(to, 1, from, (a7) - 8) \
630 bn_cp_32(to, 2, from, (a6) - 8) \
631 bn_cp_32(to, 3, from, (a5) - 8) \
632 bn_cp_32(to, 4, from, (a4) - 8) \
633 bn_cp_32(to, 5, from, (a3) - 8) \
634 bn_cp_32(to, 6, from, (a2) - 8) \
635 bn_cp_32(to, 7, from, (a1) - 8) \
638 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
643 register BN_ULONG *a_d = a->d, *r_d;
645 BN_ULONG bn[BN_NIST_256_TOP];
646 unsigned int ui[BN_NIST_256_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
648 BN_ULONG c_d[BN_NIST_256_TOP],
651 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
652 static const BIGNUM _bignum_nist_p_256_sqr = {
653 (BN_ULONG *)_nist_p_256_sqr,
654 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
655 sizeof(_nist_p_256_sqr)/sizeof(_nist_p_256_sqr[0]),
656 0,BN_FLG_STATIC_DATA };
658 field = &_bignum_nist_p_256; /* just to make sure */
660 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_256_sqr)>=0)
661 return BN_nnmod(r, a, field, ctx);
663 i = BN_ucmp(field, a);
670 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
674 if (!bn_wexpand(r, BN_NIST_256_TOP))
677 nist_cp_bn(r_d, a_d, BN_NIST_256_TOP);
682 nist_cp_bn_0(buf.bn, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
684 #if defined(NIST_INT64)
686 NIST_INT64 acc; /* accumulator */
687 unsigned int *rp=(unsigned int *)r_d;
688 const unsigned int *bp=(const unsigned int *)buf.ui;
690 acc = rp[0]; acc += bp[8-8];
695 acc -= bp[14-8]; rp[0] = (unsigned int)acc; acc >>= 32;
697 acc += rp[1]; acc += bp[9-8];
702 acc -= bp[15-8]; rp[1] = (unsigned int)acc; acc >>= 32;
704 acc += rp[2]; acc += bp[10-8];
708 acc -= bp[15-8]; rp[2] = (unsigned int)acc; acc >>= 32;
710 acc += rp[3]; acc += bp[11-8];
717 acc -= bp[9-8]; rp[3] = (unsigned int)acc; acc >>= 32;
719 acc += rp[4]; acc += bp[12-8];
725 acc -= bp[10-8]; rp[4] = (unsigned int)acc; acc >>= 32;
727 acc += rp[5]; acc += bp[13-8];
733 acc -= bp[11-8]; rp[5] = (unsigned int)acc; acc >>= 32;
735 acc += rp[6]; acc += bp[14-8];
742 acc -= bp[9-8]; rp[6] = (unsigned int)acc; acc >>= 32;
744 acc += rp[7]; acc += bp[15-8];
751 acc -= bp[13-8]; rp[7] = (unsigned int)acc;
753 carry = (int)(acc>>32);
757 BN_ULONG t_d[BN_NIST_256_TOP];
760 nist_set_256(t_d, buf.bn, 15, 14, 13, 12, 11, 0, 0, 0);
762 nist_set_256(c_d, buf.bn, 0, 15, 14, 13, 12, 0, 0, 0);
763 carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
766 register BN_ULONG *ap,t,c;
769 for (i = BN_NIST_256_TOP; i != 0; --i)
772 *(ap++)=((t<<1)|c)&BN_MASK2;
778 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
780 nist_set_256(t_d, buf.bn, 15, 14, 0, 0, 0, 10, 9, 8);
781 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
783 nist_set_256(t_d, buf.bn, 8, 13, 15, 14, 13, 11, 10, 9);
784 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
786 nist_set_256(t_d, buf.bn, 10, 8, 0, 0, 0, 13, 12, 11);
787 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
789 nist_set_256(t_d, buf.bn, 11, 9, 0, 0, 15, 14, 13, 12);
790 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
792 nist_set_256(t_d, buf.bn, 12, 0, 10, 9, 8, 15, 14, 13);
793 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
795 nist_set_256(t_d, buf.bn, 13, 0, 11, 10, 9, 0, 15, 14);
796 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
800 /* see BN_nist_mod_224 for explanation */
803 carry = (int)bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
806 carry = (int)bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
807 mask = 0-(PTR_SIZE_INT)carry;
808 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
809 ((PTR_SIZE_INT)bn_add_words&~mask);
814 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
815 mask &= 0-(PTR_SIZE_INT)carry;
817 res = (BN_ULONG *)(((PTR_SIZE_INT)res&~mask) |
818 ((PTR_SIZE_INT)r_d&mask));
819 nist_cp_bn(r_d, res, BN_NIST_256_TOP);
820 r->top = BN_NIST_256_TOP;
826 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
828 bn_cp_32(to, 0, from, (a12) - 12) \
829 bn_cp_32(to, 1, from, (a11) - 12) \
830 bn_cp_32(to, 2, from, (a10) - 12) \
831 bn_cp_32(to, 3, from, (a9) - 12) \
832 bn_cp_32(to, 4, from, (a8) - 12) \
833 bn_cp_32(to, 5, from, (a7) - 12) \
834 bn_cp_32(to, 6, from, (a6) - 12) \
835 bn_cp_32(to, 7, from, (a5) - 12) \
836 bn_cp_32(to, 8, from, (a4) - 12) \
837 bn_cp_32(to, 9, from, (a3) - 12) \
838 bn_cp_32(to, 10, from, (a2) - 12) \
839 bn_cp_32(to, 11, from, (a1) - 12) \
842 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
847 register BN_ULONG *r_d, *a_d = a->d;
849 BN_ULONG bn[BN_NIST_384_TOP];
850 unsigned int ui[BN_NIST_384_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
852 BN_ULONG c_d[BN_NIST_384_TOP],
855 union { bn_addsub_f f; PTR_SIZE_INT p; } u;
856 static const BIGNUM _bignum_nist_p_384_sqr = {
857 (BN_ULONG *)_nist_p_384_sqr,
858 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
859 sizeof(_nist_p_384_sqr)/sizeof(_nist_p_384_sqr[0]),
860 0,BN_FLG_STATIC_DATA };
863 field = &_bignum_nist_p_384; /* just to make sure */
865 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_384_sqr)>=0)
866 return BN_nnmod(r, a, field, ctx);
868 i = BN_ucmp(field, a);
875 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
879 if (!bn_wexpand(r, BN_NIST_384_TOP))
882 nist_cp_bn(r_d, a_d, BN_NIST_384_TOP);
887 nist_cp_bn_0(buf.bn, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
889 #if defined(NIST_INT64)
891 NIST_INT64 acc; /* accumulator */
892 unsigned int *rp=(unsigned int *)r_d;
893 const unsigned int *bp=(const unsigned int *)buf.ui;
895 acc = rp[0]; acc += bp[12-12];
898 acc -= bp[23-12]; rp[0] = (unsigned int)acc; acc >>= 32;
900 acc += rp[1]; acc += bp[13-12];
904 acc -= bp[20-12]; rp[1] = (unsigned int)acc; acc >>= 32;
906 acc += rp[2]; acc += bp[14-12];
909 acc -= bp[21-12]; rp[2] = (unsigned int)acc; acc >>= 32;
911 acc += rp[3]; acc += bp[15-12];
917 acc -= bp[23-12]; rp[3] = (unsigned int)acc; acc >>= 32;
919 acc += rp[4]; acc += bp[21-12];
928 acc -= bp[23-12]; rp[4] = (unsigned int)acc; acc >>= 32;
930 acc += rp[5]; acc += bp[22-12];
937 acc -= bp[16-12]; rp[5] = (unsigned int)acc; acc >>= 32;
939 acc += rp[6]; acc += bp[23-12];
945 acc -= bp[17-12]; rp[6] = (unsigned int)acc; acc >>= 32;
947 acc += rp[7]; acc += bp[19-12];
951 acc -= bp[18-12]; rp[7] = (unsigned int)acc; acc >>= 32;
953 acc += rp[8]; acc += bp[20-12];
956 acc -= bp[19-12]; rp[8] = (unsigned int)acc; acc >>= 32;
958 acc += rp[9]; acc += bp[21-12];
961 acc -= bp[20-12]; rp[9] = (unsigned int)acc; acc >>= 32;
963 acc += rp[10]; acc += bp[22-12];
966 acc -= bp[21-12]; rp[10] = (unsigned int)acc; acc >>= 32;
968 acc += rp[11]; acc += bp[23-12];
971 acc -= bp[22-12]; rp[11] = (unsigned int)acc;
973 carry = (int)(acc>>32);
977 BN_ULONG t_d[BN_NIST_384_TOP];
980 nist_set_256(t_d, buf.bn, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
983 register BN_ULONG *ap,t,c;
986 for (i = 3; i != 0; --i)
989 *(ap++)=((t<<1)|c)&BN_MASK2;
994 carry = (int)bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
995 t_d, BN_NIST_256_TOP);
997 carry += (int)bn_add_words(r_d, r_d, buf.bn, BN_NIST_384_TOP);
999 nist_set_384(t_d,buf.bn,20,19,18,17,16,15,14,13,12,23,22,21);
1000 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1002 nist_set_384(t_d,buf.bn,19,18,17,16,15,14,13,12,20,0,23,0);
1003 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1005 nist_set_384(t_d, buf.bn,0,0,0,0,23,22,21,20,0,0,0,0);
1006 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1008 nist_set_384(t_d,buf.bn,0,0,0,0,0,0,23,22,21,0,0,20);
1009 carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1011 nist_set_384(t_d,buf.bn,22,21,20,19,18,17,16,15,14,13,12,23);
1012 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1014 nist_set_384(t_d,buf.bn,0,0,0,0,0,0,0,23,22,21,20,0);
1015 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1017 nist_set_384(t_d,buf.bn,0,0,0,0,0,0,0,23,23,0,0,0);
1018 carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
1022 /* see BN_nist_mod_224 for explanation */
1025 carry = (int)bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
1028 carry = (int)bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
1029 mask = 0-(PTR_SIZE_INT)carry;
1030 u.p = ((PTR_SIZE_INT)bn_sub_words&mask) |
1031 ((PTR_SIZE_INT)bn_add_words&~mask);
1036 mask = 0-(PTR_SIZE_INT)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
1037 mask &= 0-(PTR_SIZE_INT)carry;
1039 res = (BN_ULONG *)(((PTR_SIZE_INT)res&~mask) |
1040 ((PTR_SIZE_INT)r_d&mask));
1041 nist_cp_bn(r_d, res, BN_NIST_384_TOP);
1042 r->top = BN_NIST_384_TOP;
1048 #define BN_NIST_521_RSHIFT (521%BN_BITS2)
1049 #define BN_NIST_521_LSHIFT (BN_BITS2-BN_NIST_521_RSHIFT)
1050 #define BN_NIST_521_TOP_MASK ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
1052 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
1055 int top = a->top, i;
1056 BN_ULONG *r_d, *a_d = a->d,
1057 t_d[BN_NIST_521_TOP],
1060 static const BIGNUM _bignum_nist_p_521_sqr = {
1061 (BN_ULONG *)_nist_p_521_sqr,
1062 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
1063 sizeof(_nist_p_521_sqr)/sizeof(_nist_p_521_sqr[0]),
1064 0,BN_FLG_STATIC_DATA };
1066 field = &_bignum_nist_p_521; /* just to make sure */
1068 if (BN_is_negative(a) || BN_ucmp(a,&_bignum_nist_p_521_sqr)>=0)
1069 return BN_nnmod(r, a, field, ctx);
1071 i = BN_ucmp(field, a);
1078 return (r == a)? 1 : (BN_copy(r ,a) != NULL);
1082 if (!bn_wexpand(r,BN_NIST_521_TOP))
1085 nist_cp_bn(r_d,a_d, BN_NIST_521_TOP);
1090 /* upper 521 bits, copy ... */
1091 nist_cp_bn_0(t_d,a_d + (BN_NIST_521_TOP-1), top - (BN_NIST_521_TOP-1),BN_NIST_521_TOP);
1092 /* ... and right shift */
1093 for (val=t_d[0],i=0; i<BN_NIST_521_TOP-1; i++)
1095 tmp = val>>BN_NIST_521_RSHIFT;
1097 t_d[i] = (tmp | val<<BN_NIST_521_LSHIFT) & BN_MASK2;
1099 t_d[i] = val>>BN_NIST_521_RSHIFT;
1100 /* lower 521 bits */
1101 r_d[i] &= BN_NIST_521_TOP_MASK;
1103 bn_add_words(r_d,r_d,t_d,BN_NIST_521_TOP);
1104 mask = 0-(PTR_SIZE_INT)bn_sub_words(t_d,r_d,_nist_p_521,BN_NIST_521_TOP);
1106 res = (BN_ULONG *)(((PTR_SIZE_INT)res&~mask) |
1107 ((PTR_SIZE_INT)r_d&mask));
1108 nist_cp_bn(r_d,res,BN_NIST_521_TOP);
1109 r->top = BN_NIST_521_TOP;