1 /* crypto/bn/bn_exp.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
58 /* ====================================================================
59 * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
87 * 6. Redistributions of any form whatsoever must retain the following
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
116 #define TABLE_SIZE 32
119 int BN_mod_mul(BIGNUM
*ret
, BIGNUM
*a
, BIGNUM
*b
, const BIGNUM
*m
, BN_CTX
*ctx
)
129 if ((t
= BN_CTX_get(ctx
)) == NULL
) goto err
;
131 { if (!BN_sqr(t
,a
,ctx
)) goto err
; }
133 { if (!BN_mul(t
,a
,b
,ctx
)) goto err
; }
134 if (!BN_mod(ret
,t
,m
,ctx
)) goto err
;
141 int BN_mod_exp(BIGNUM
*r
, BIGNUM
*a
, const BIGNUM
*p
, const BIGNUM
*m
,
151 /* I have finally been able to take out this pre-condition of
152 * the top bit being set. It was caused by an error in BN_div
153 * with negatives. There was also another problem when for a^b%m
154 * a >= m. eay 07-May-97 */
155 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
161 BN_ULONG A
= a
->d
[0];
162 ret
=BN_mod_exp_mont_word(r
,A
,p
,m
,ctx
,NULL
);
165 ret
=BN_mod_exp_mont(r
,a
,p
,m
,ctx
,NULL
);
170 { ret
=BN_mod_exp_recp(r
,a
,p
,m
,ctx
); }
172 { ret
=BN_mod_exp_simple(r
,a
,p
,m
,ctx
); }
180 int BN_mod_exp_recp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
181 const BIGNUM
*m
, BN_CTX
*ctx
)
183 int i
,j
,bits
,ret
=0,wstart
,wend
,window
,wvalue
;
186 BIGNUM val
[TABLE_SIZE
];
198 if ((aa
= BN_CTX_get(ctx
)) == NULL
) goto err
;
200 BN_RECP_CTX_init(&recp
);
201 if (BN_RECP_CTX_set(&recp
,m
,ctx
) <= 0) goto err
;
206 if (!BN_mod(&(val
[0]),a
,m
,ctx
)) goto err
; /* 1 */
208 window
= BN_window_bits_for_exponent_size(bits
);
211 if (!BN_mod_mul_reciprocal(aa
,&(val
[0]),&(val
[0]),&recp
,ctx
))
217 if (!BN_mod_mul_reciprocal(&(val
[i
]),&(val
[i
-1]),aa
,&recp
,ctx
))
223 start
=1; /* This is used to avoid multiplication etc
224 * when there is only the value '1' in the
226 wvalue
=0; /* The 'value' of the window */
227 wstart
=bits
-1; /* The top bit of the window */
228 wend
=0; /* The bottom bit of the window */
230 if (!BN_one(r
)) goto err
;
234 if (BN_is_bit_set(p
,wstart
) == 0)
237 if (!BN_mod_mul_reciprocal(r
,r
,r
,&recp
,ctx
))
239 if (wstart
== 0) break;
243 /* We now have wstart on a 'set' bit, we now need to work out
244 * how bit a window to do. To do this we need to scan
245 * forward until the last set bit before the end of the
250 for (i
=1; i
<window
; i
++)
252 if (wstart
-i
< 0) break;
253 if (BN_is_bit_set(p
,wstart
-i
))
261 /* wend is the size of the current window */
263 /* add the 'bytes above' */
267 if (!BN_mod_mul_reciprocal(r
,r
,r
,&recp
,ctx
))
271 /* wvalue will be an odd number < 2^window */
272 if (!BN_mod_mul_reciprocal(r
,r
,&(val
[wvalue
>>1]),&recp
,ctx
))
275 /* move the 'window' down further */
279 if (wstart
< 0) break;
285 BN_clear_free(&(val
[i
]));
286 BN_RECP_CTX_free(&recp
);
291 /* The old fallback, simple version :-) */
292 int BN_mod_exp_simple(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
293 const BIGNUM
*m
, BN_CTX
*ctx
)
295 int i
,j
,bits
,ret
=0,wstart
,wend
,window
,wvalue
,ts
=0;
298 BIGNUM val
[TABLE_SIZE
];
309 if ((d
= BN_CTX_get(ctx
)) == NULL
) goto err
;
313 if (!BN_mod(&(val
[0]),a
,m
,ctx
)) goto err
; /* 1 */
315 window
= BN_window_bits_for_exponent_size(bits
);
318 if (!BN_mod_mul(d
,&(val
[0]),&(val
[0]),m
,ctx
))
324 if (!BN_mod_mul(&(val
[i
]),&(val
[i
-1]),d
,m
,ctx
))
330 start
=1; /* This is used to avoid multiplication etc
331 * when there is only the value '1' in the
333 wvalue
=0; /* The 'value' of the window */
334 wstart
=bits
-1; /* The top bit of the window */
335 wend
=0; /* The bottom bit of the window */
337 if (!BN_one(r
)) goto err
;
341 if (BN_is_bit_set(p
,wstart
) == 0)
344 if (!BN_mod_mul(r
,r
,r
,m
,ctx
))
346 if (wstart
== 0) break;
350 /* We now have wstart on a 'set' bit, we now need to work out
351 * how bit a window to do. To do this we need to scan
352 * forward until the last set bit before the end of the
357 for (i
=1; i
<window
; i
++)
359 if (wstart
-i
< 0) break;
360 if (BN_is_bit_set(p
,wstart
-i
))
368 /* wend is the size of the current window */
370 /* add the 'bytes above' */
374 if (!BN_mod_mul(r
,r
,r
,m
,ctx
))
378 /* wvalue will be an odd number < 2^window */
379 if (!BN_mod_mul(r
,r
,&(val
[wvalue
>>1]),m
,ctx
))
382 /* move the 'window' down further */
386 if (wstart
< 0) break;
392 BN_clear_free(&(val
[i
]));
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