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.
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
12 * 1. Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in
17 * the documentation and/or other materials provided with the
20 * 3. All advertising materials mentioning features or use of this
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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26 * endorse or promote products derived from this software without
27 * prior written permission. For written permission, please contact
28 * openssl-core@openssl.org.
30 * 5. Products derived from this software may not be called "OpenSSL"
31 * nor may "OpenSSL" appear in their names without prior written
32 * permission of the OpenSSL Project.
34 * 6. Redistributions of any form whatsoever must retain the following
36 * "This product includes software developed by the OpenSSL Project
37 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
39 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
40 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
41 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
42 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
43 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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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)
323 #define bn_cp_64(to, n, from, m) \
325 bn_cp_32(to, (n)*2, from, (m)*2); \
326 bn_cp_32(to, (n)*2+1, from, (m)*2+1); \
328 #define bn_64_set_0(to, n) \
330 bn_32_set_0(to, (n)*2); \
331 bn_32_set_0(to, (n)*2+1); \
334 #define bn_cp_32(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0;
335 #define bn_32_set_0(to, n) (to)[n] = (BN_ULONG)0;
337 #endif /* BN_BITS2 != 64 */
340 #define nist_set_192(to, from, a1, a2, a3) \
342 bn_cp_64(to, 0, from, (a3) - 3) \
343 bn_cp_64(to, 1, from, (a2) - 3) \
344 bn_cp_64(to, 2, from, (a1) - 3) \
347 int BN_nist_mod_192(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*field
,
352 register BN_ULONG
*r_d
, *a_d
= a
->d
;
353 BN_ULONG t_d
[BN_NIST_192_TOP
],
354 buf
[BN_NIST_192_TOP
],
355 c_d
[BN_NIST_192_TOP
],
358 static const BIGNUM _bignum_nist_p_192_sqr
= {
359 (BN_ULONG
*)_nist_p_192_sqr
,
360 sizeof(_nist_p_192_sqr
)/sizeof(_nist_p_192_sqr
[0]),
361 sizeof(_nist_p_192_sqr
)/sizeof(_nist_p_192_sqr
[0]),
362 0,BN_FLG_STATIC_DATA
};
364 field
= &_bignum_nist_p_192
; /* just to make sure */
366 if (BN_is_negative(a
) || BN_ucmp(a
,&_bignum_nist_p_192_sqr
)>=0)
367 return BN_nnmod(r
, a
, field
, ctx
);
369 i
= BN_ucmp(field
, a
);
376 return (r
== a
) ? 1 : (BN_copy(r
,a
) != NULL
);
380 if (!bn_wexpand(r
, BN_NIST_192_TOP
))
383 nist_cp_bn(r_d
, a_d
, BN_NIST_192_TOP
);
388 nist_cp_bn_0(buf
, a_d
+ BN_NIST_192_TOP
, top
- BN_NIST_192_TOP
, BN_NIST_192_TOP
);
390 nist_set_192(t_d
, buf
, 0, 3, 3);
391 carry
= bn_add_words(r_d
, r_d
, t_d
, BN_NIST_192_TOP
);
392 nist_set_192(t_d
, buf
, 4, 4, 0);
393 carry
+= bn_add_words(r_d
, r_d
, t_d
, BN_NIST_192_TOP
);
394 nist_set_192(t_d
, buf
, 5, 5, 5)
395 carry
+= bn_add_words(r_d
, r_d
, t_d
, BN_NIST_192_TOP
);
398 carry
= bn_sub_words(r_d
,r_d
,_nist_p_192
[carry
-1],BN_NIST_192_TOP
);
403 * we need 'if (carry==0 || result>=modulus) result-=modulus;'
404 * as comparison implies subtraction, we can write
405 * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
406 * this is what happens below, but without explicit if:-) a.
408 mask
= 0-(size_t)bn_sub_words(c_d
,r_d
,_nist_p_192
[0],BN_NIST_192_TOP
);
409 mask
&= 0-(size_t)carry
;
410 res
= (BN_ULONG
*)(((size_t)c_d
&~mask
) | ((size_t)r_d
&mask
));
411 nist_cp_bn(r_d
, res
, BN_NIST_192_TOP
);
412 r
->top
= BN_NIST_192_TOP
;
418 typedef BN_ULONG (*bn_addsub_f
)(BN_ULONG
*,const BN_ULONG
*,const BN_ULONG
*,int);
420 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
422 bn_cp_32(to, 0, from, (a7) - 7) \
423 bn_cp_32(to, 1, from, (a6) - 7) \
424 bn_cp_32(to, 2, from, (a5) - 7) \
425 bn_cp_32(to, 3, from, (a4) - 7) \
426 bn_cp_32(to, 4, from, (a3) - 7) \
427 bn_cp_32(to, 5, from, (a2) - 7) \
428 bn_cp_32(to, 6, from, (a1) - 7) \
431 int BN_nist_mod_224(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*field
,
436 BN_ULONG
*r_d
, *a_d
= a
->d
;
437 BN_ULONG t_d
[BN_NIST_224_TOP
],
438 buf
[BN_NIST_224_TOP
],
439 c_d
[BN_NIST_224_TOP
],
442 union { bn_addsub_f f
; size_t p
; } u
;
443 static const BIGNUM _bignum_nist_p_224_sqr
= {
444 (BN_ULONG
*)_nist_p_224_sqr
,
445 sizeof(_nist_p_224_sqr
)/sizeof(_nist_p_224_sqr
[0]),
446 sizeof(_nist_p_224_sqr
)/sizeof(_nist_p_224_sqr
[0]),
447 0,BN_FLG_STATIC_DATA
};
450 field
= &_bignum_nist_p_224
; /* just to make sure */
452 if (BN_is_negative(a
) || BN_ucmp(a
,&_bignum_nist_p_224_sqr
)>=0)
453 return BN_nnmod(r
, a
, field
, ctx
);
455 i
= BN_ucmp(field
, a
);
462 return (r
== a
)? 1 : (BN_copy(r
,a
) != NULL
);
466 if (!bn_wexpand(r
, BN_NIST_224_TOP
))
469 nist_cp_bn(r_d
, a_d
, BN_NIST_224_TOP
);
475 /* copy upper 256 bits of 448 bit number ... */
476 nist_cp_bn_0(t_d
, a_d
+ (BN_NIST_224_TOP
-1), top
- (BN_NIST_224_TOP
-1), BN_NIST_224_TOP
);
477 /* ... and right shift by 32 to obtain upper 224 bits */
478 nist_set_224(buf
, t_d
, 14, 13, 12, 11, 10, 9, 8);
479 /* truncate lower part to 224 bits too */
480 r_d
[BN_NIST_224_TOP
-1] &= BN_MASK2l
;
482 nist_cp_bn_0(buf
, a_d
+ BN_NIST_224_TOP
, top
- BN_NIST_224_TOP
, BN_NIST_224_TOP
);
484 nist_set_224(t_d
, buf
, 10, 9, 8, 7, 0, 0, 0);
485 carry
= bn_add_words(r_d
, r_d
, t_d
, BN_NIST_224_TOP
);
486 nist_set_224(t_d
, buf
, 0, 13, 12, 11, 0, 0, 0);
487 carry
+= bn_add_words(r_d
, r_d
, t_d
, BN_NIST_224_TOP
);
488 nist_set_224(t_d
, buf
, 13, 12, 11, 10, 9, 8, 7);
489 carry
-= bn_sub_words(r_d
, r_d
, t_d
, BN_NIST_224_TOP
);
490 nist_set_224(t_d
, buf
, 0, 0, 0, 0, 13, 12, 11);
491 carry
-= bn_sub_words(r_d
, r_d
, t_d
, BN_NIST_224_TOP
);
494 carry
= (int)(r_d
[BN_NIST_224_TOP
-1]>>32);
499 carry
= bn_sub_words(r_d
,r_d
,_nist_p_224
[carry
-1],BN_NIST_224_TOP
);
501 carry
=(int)(~(r_d
[BN_NIST_224_TOP
-1]>>32))&1;
506 /* it's a bit more comlicated logic in this case.
507 * if bn_add_words yields no carry, then result
508 * has to be adjusted by unconditionally *adding*
509 * the modulus. but if it does, then result has
510 * to be compared to the modulus and conditionally
511 * adjusted by *subtracting* the latter. */
512 carry
= bn_add_words(r_d
,r_d
,_nist_p_224
[-carry
-1],BN_NIST_224_TOP
);
513 mask
= 0-(size_t)carry
;
514 u
.p
= ((size_t)bn_sub_words
&mask
) | ((size_t)bn_add_words
&~mask
);
519 /* otherwise it's effectively same as in BN_nist_mod_192... */
520 mask
= 0-(size_t)(*u
.f
)(c_d
,r_d
,_nist_p_224
[0],BN_NIST_224_TOP
);
521 mask
&= 0-(size_t)carry
;
522 res
= (BN_ULONG
*)(((size_t)c_d
&~mask
) | ((size_t)r_d
&mask
));
523 nist_cp_bn(r_d
, res
, BN_NIST_224_TOP
);
524 r
->top
= BN_NIST_224_TOP
;
530 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
532 bn_cp_32(to, 0, from, (a8) - 8) \
533 bn_cp_32(to, 1, from, (a7) - 8) \
534 bn_cp_32(to, 2, from, (a6) - 8) \
535 bn_cp_32(to, 3, from, (a5) - 8) \
536 bn_cp_32(to, 4, from, (a4) - 8) \
537 bn_cp_32(to, 5, from, (a3) - 8) \
538 bn_cp_32(to, 6, from, (a2) - 8) \
539 bn_cp_32(to, 7, from, (a1) - 8) \
542 int BN_nist_mod_256(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*field
,
547 register BN_ULONG
*a_d
= a
->d
, *r_d
;
548 BN_ULONG t_d
[BN_NIST_256_TOP
],
549 buf
[BN_NIST_256_TOP
],
550 c_d
[BN_NIST_256_TOP
],
553 union { bn_addsub_f f
; size_t p
; } u
;
554 static const BIGNUM _bignum_nist_p_256_sqr
= {
555 (BN_ULONG
*)_nist_p_256_sqr
,
556 sizeof(_nist_p_256_sqr
)/sizeof(_nist_p_256_sqr
[0]),
557 sizeof(_nist_p_256_sqr
)/sizeof(_nist_p_256_sqr
[0]),
558 0,BN_FLG_STATIC_DATA
};
560 field
= &_bignum_nist_p_256
; /* just to make sure */
562 if (BN_is_negative(a
) || BN_ucmp(a
,&_bignum_nist_p_256_sqr
)>=0)
563 return BN_nnmod(r
, a
, field
, ctx
);
565 i
= BN_ucmp(field
, a
);
572 return (r
== a
)? 1 : (BN_copy(r
,a
) != NULL
);
576 if (!bn_wexpand(r
, BN_NIST_256_TOP
))
579 nist_cp_bn(r_d
, a_d
, BN_NIST_256_TOP
);
584 nist_cp_bn_0(buf
, a_d
+ BN_NIST_256_TOP
, top
- BN_NIST_256_TOP
, BN_NIST_256_TOP
);
587 nist_set_256(t_d
, buf
, 15, 14, 13, 12, 11, 0, 0, 0);
589 nist_set_256(c_d
, buf
, 0, 15, 14, 13, 12, 0, 0, 0);
590 carry
= bn_add_words(t_d
, t_d
, c_d
, BN_NIST_256_TOP
);
593 register BN_ULONG
*ap
,t
,c
;
596 for (i
= BN_NIST_256_TOP
; i
!= 0; --i
)
599 *(ap
++)=((t
<<1)|c
)&BN_MASK2
;
605 carry
+= bn_add_words(r_d
, r_d
, t_d
, BN_NIST_256_TOP
);
607 nist_set_256(t_d
, buf
, 15, 14, 0, 0, 0, 10, 9, 8);
608 carry
+= bn_add_words(r_d
, r_d
, t_d
, BN_NIST_256_TOP
);
610 nist_set_256(t_d
, buf
, 8, 13, 15, 14, 13, 11, 10, 9);
611 carry
+= bn_add_words(r_d
, r_d
, t_d
, BN_NIST_256_TOP
);
613 nist_set_256(t_d
, buf
, 10, 8, 0, 0, 0, 13, 12, 11);
614 carry
-= bn_sub_words(r_d
, r_d
, t_d
, BN_NIST_256_TOP
);
616 nist_set_256(t_d
, buf
, 11, 9, 0, 0, 15, 14, 13, 12);
617 carry
-= bn_sub_words(r_d
, r_d
, t_d
, BN_NIST_256_TOP
);
619 nist_set_256(t_d
, buf
, 12, 0, 10, 9, 8, 15, 14, 13);
620 carry
-= bn_sub_words(r_d
, r_d
, t_d
, BN_NIST_256_TOP
);
622 nist_set_256(t_d
, buf
, 13, 0, 11, 10, 9, 0, 15, 14);
623 carry
-= bn_sub_words(r_d
, r_d
, t_d
, BN_NIST_256_TOP
);
625 /* see BN_nist_mod_224 for explanation */
628 carry
= bn_sub_words(r_d
,r_d
,_nist_p_256
[carry
-1],BN_NIST_256_TOP
);
631 carry
= bn_add_words(r_d
,r_d
,_nist_p_256
[-carry
-1],BN_NIST_256_TOP
);
632 mask
= 0-(size_t)carry
;
633 u
.p
= ((size_t)bn_sub_words
&mask
) | ((size_t)bn_add_words
&~mask
);
638 mask
= 0-(size_t)(*u
.f
)(c_d
,r_d
,_nist_p_256
[0],BN_NIST_256_TOP
);
639 mask
&= 0-(size_t)carry
;
640 res
= (BN_ULONG
*)(((size_t)c_d
&~mask
) | ((size_t)r_d
&mask
));
641 nist_cp_bn(r_d
, res
, BN_NIST_256_TOP
);
642 r
->top
= BN_NIST_256_TOP
;
648 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
650 bn_cp_32(to, 0, from, (a12) - 12) \
651 bn_cp_32(to, 1, from, (a11) - 12) \
652 bn_cp_32(to, 2, from, (a10) - 12) \
653 bn_cp_32(to, 3, from, (a9) - 12) \
654 bn_cp_32(to, 4, from, (a8) - 12) \
655 bn_cp_32(to, 5, from, (a7) - 12) \
656 bn_cp_32(to, 6, from, (a6) - 12) \
657 bn_cp_32(to, 7, from, (a5) - 12) \
658 bn_cp_32(to, 8, from, (a4) - 12) \
659 bn_cp_32(to, 9, from, (a3) - 12) \
660 bn_cp_32(to, 10, from, (a2) - 12) \
661 bn_cp_32(to, 11, from, (a1) - 12) \
664 int BN_nist_mod_384(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*field
,
669 register BN_ULONG
*r_d
, *a_d
= a
->d
;
670 BN_ULONG t_d
[BN_NIST_384_TOP
],
671 buf
[BN_NIST_384_TOP
],
672 c_d
[BN_NIST_384_TOP
],
675 union { bn_addsub_f f
; size_t p
; } u
;
676 static const BIGNUM _bignum_nist_p_384_sqr
= {
677 (BN_ULONG
*)_nist_p_384_sqr
,
678 sizeof(_nist_p_384_sqr
)/sizeof(_nist_p_384_sqr
[0]),
679 sizeof(_nist_p_384_sqr
)/sizeof(_nist_p_384_sqr
[0]),
680 0,BN_FLG_STATIC_DATA
};
683 field
= &_bignum_nist_p_384
; /* just to make sure */
685 if (BN_is_negative(a
) || BN_ucmp(a
,&_bignum_nist_p_384_sqr
)>=0)
686 return BN_nnmod(r
, a
, field
, ctx
);
688 i
= BN_ucmp(field
, a
);
695 return (r
== a
)? 1 : (BN_copy(r
,a
) != NULL
);
699 if (!bn_wexpand(r
, BN_NIST_384_TOP
))
702 nist_cp_bn(r_d
, a_d
, BN_NIST_384_TOP
);
707 nist_cp_bn_0(buf
, a_d
+ BN_NIST_384_TOP
, top
- BN_NIST_384_TOP
, BN_NIST_384_TOP
);
710 nist_set_256(t_d
, buf
, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
713 register BN_ULONG
*ap
,t
,c
;
716 for (i
= 3; i
!= 0; --i
)
719 *(ap
++)=((t
<<1)|c
)&BN_MASK2
;
724 carry
= bn_add_words(r_d
+(128/BN_BITS2
), r_d
+(128/BN_BITS2
),
725 t_d
, BN_NIST_256_TOP
);
727 carry
+= bn_add_words(r_d
, r_d
, buf
, BN_NIST_384_TOP
);
729 nist_set_384(t_d
,buf
,20,19,18,17,16,15,14,13,12,23,22,21);
730 carry
+= bn_add_words(r_d
, r_d
, t_d
, BN_NIST_384_TOP
);
732 nist_set_384(t_d
,buf
,19,18,17,16,15,14,13,12,20,0,23,0);
733 carry
+= bn_add_words(r_d
, r_d
, t_d
, BN_NIST_384_TOP
);
735 nist_set_384(t_d
, buf
,0,0,0,0,23,22,21,20,0,0,0,0);
736 carry
+= bn_add_words(r_d
, r_d
, t_d
, BN_NIST_384_TOP
);
738 nist_set_384(t_d
,buf
,0,0,0,0,0,0,23,22,21,0,0,20);
739 carry
+= bn_add_words(r_d
, r_d
, t_d
, BN_NIST_384_TOP
);
741 nist_set_384(t_d
,buf
,22,21,20,19,18,17,16,15,14,13,12,23);
742 carry
-= bn_sub_words(r_d
, r_d
, t_d
, BN_NIST_384_TOP
);
744 nist_set_384(t_d
,buf
,0,0,0,0,0,0,0,23,22,21,20,0);
745 carry
-= bn_sub_words(r_d
, r_d
, t_d
, BN_NIST_384_TOP
);
747 nist_set_384(t_d
,buf
,0,0,0,0,0,0,0,23,23,0,0,0);
748 carry
-= bn_sub_words(r_d
, r_d
, t_d
, BN_NIST_384_TOP
);
750 /* see BN_nist_mod_224 for explanation */
753 carry
= bn_sub_words(r_d
,r_d
,_nist_p_384
[carry
-1],BN_NIST_384_TOP
);
756 carry
= bn_add_words(r_d
,r_d
,_nist_p_384
[-carry
-1],BN_NIST_384_TOP
);
757 mask
= 0-(size_t)carry
;
758 u
.p
= ((size_t)bn_sub_words
&mask
) | ((size_t)bn_add_words
&~mask
);
763 mask
= 0-(size_t)(*u
.f
)(c_d
,r_d
,_nist_p_384
[0],BN_NIST_384_TOP
);
764 mask
&= 0-(size_t)carry
;
765 res
= (BN_ULONG
*)(((size_t)c_d
&~mask
) | ((size_t)r_d
&mask
));
766 nist_cp_bn(r_d
, res
, BN_NIST_384_TOP
);
767 r
->top
= BN_NIST_384_TOP
;
773 #define BN_NIST_521_RSHIFT (521%BN_BITS2)
774 #define BN_NIST_521_LSHIFT (BN_BITS2-BN_NIST_521_RSHIFT)
775 #define BN_NIST_521_TOP_MASK ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT)
777 int BN_nist_mod_521(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*field
,
781 BN_ULONG
*r_d
, *a_d
= a
->d
,
782 t_d
[BN_NIST_521_TOP
],
785 static const BIGNUM _bignum_nist_p_521_sqr
= {
786 (BN_ULONG
*)_nist_p_521_sqr
,
787 sizeof(_nist_p_521_sqr
)/sizeof(_nist_p_521_sqr
[0]),
788 sizeof(_nist_p_521_sqr
)/sizeof(_nist_p_521_sqr
[0]),
789 0,BN_FLG_STATIC_DATA
};
791 field
= &_bignum_nist_p_521
; /* just to make sure */
793 if (BN_is_negative(a
) || BN_ucmp(a
,&_bignum_nist_p_521_sqr
)>=0)
794 return BN_nnmod(r
, a
, field
, ctx
);
796 i
= BN_ucmp(field
, a
);
803 return (r
== a
)? 1 : (BN_copy(r
,a
) != NULL
);
807 if (!bn_wexpand(r
,BN_NIST_521_TOP
))
810 nist_cp_bn(r_d
,a_d
, BN_NIST_521_TOP
);
815 /* upper 521 bits, copy ... */
816 nist_cp_bn_0(t_d
,a_d
+ (BN_NIST_521_TOP
-1), top
- (BN_NIST_521_TOP
-1),BN_NIST_521_TOP
);
817 /* ... and right shift */
818 for (val
=t_d
[0],i
=0; i
<BN_NIST_521_TOP
-1; i
++)
820 tmp
= val
>>BN_NIST_521_RSHIFT
;
822 t_d
[i
] = (tmp
| val
<<BN_NIST_521_LSHIFT
) & BN_MASK2
;
824 t_d
[i
] = val
>>BN_NIST_521_RSHIFT
;
826 r_d
[i
] &= BN_NIST_521_TOP_MASK
;
828 bn_add_words(r_d
,r_d
,t_d
,BN_NIST_521_TOP
);
829 mask
= 0-(size_t)bn_sub_words(t_d
,r_d
,_nist_p_521
,BN_NIST_521_TOP
);
830 res
= (BN_ULONG
*)(((size_t)t_d
&~mask
) | ((size_t)r_d
&mask
));
831 nist_cp_bn(r_d
,res
,BN_NIST_521_TOP
);
832 r
->top
= BN_NIST_521_TOP
;