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      1 /* crypto/bn/bn_exp2.c */
      2 /* Copyright (C) 1995-1998 Eric Young (eay (at) cryptsoft.com)
      3  * All rights reserved.
      4  *
      5  * This package is an SSL implementation written
      6  * by Eric Young (eay (at) cryptsoft.com).
      7  * The implementation was written so as to conform with Netscapes SSL.
      8  *
      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 (at) cryptsoft.com).
     15  *
     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.
     22  *
     23  * Redistribution and use in source and binary forms, with or without
     24  * modification, are permitted provided that the following conditions
     25  * are met:
     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 (at) 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 (at) cryptsoft.com)"
     40  *
     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
     51  * SUCH DAMAGE.
     52  *
     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.]
     57  */
     58 /* ====================================================================
     59  * Copyright (c) 1998-2000 The OpenSSL Project.  All rights reserved.
     60  *
     61  * Redistribution and use in source and binary forms, with or without
     62  * modification, are permitted provided that the following conditions
     63  * are met:
     64  *
     65  * 1. Redistributions of source code must retain the above copyright
     66  *    notice, this list of conditions and the following disclaimer.
     67  *
     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
     71  *    distribution.
     72  *
     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/)"
     77  *
     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 (at) openssl.org.
     82  *
     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.
     86  *
     87  * 6. Redistributions of any form whatsoever must retain the following
     88  *    acknowledgment:
     89  *    "This product includes software developed by the OpenSSL Project
     90  *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
     91  *
     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  * ====================================================================
    105  *
    106  * This product includes cryptographic software written by Eric Young
    107  * (eay (at) cryptsoft.com).  This product includes software written by Tim
    108  * Hudson (tjh (at) cryptsoft.com).
    109  *
    110  */
    111 
    112 #include <stdio.h>
    113 #include "cryptlib.h"
    114 #include "bn_lcl.h"
    115 
    116 #define TABLE_SIZE	32
    117 
    118 int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1,
    119 	const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
    120 	BN_CTX *ctx, BN_MONT_CTX *in_mont)
    121 	{
    122 	int i,j,bits,b,bits1,bits2,ret=0,wpos1,wpos2,window1,window2,wvalue1,wvalue2;
    123 	int r_is_one=1;
    124 	BIGNUM *d,*r;
    125 	const BIGNUM *a_mod_m;
    126 	/* Tables of variables obtained from 'ctx' */
    127 	BIGNUM *val1[TABLE_SIZE], *val2[TABLE_SIZE];
    128 	BN_MONT_CTX *mont=NULL;
    129 
    130 	bn_check_top(a1);
    131 	bn_check_top(p1);
    132 	bn_check_top(a2);
    133 	bn_check_top(p2);
    134 	bn_check_top(m);
    135 
    136 	if (!(m->d[0] & 1))
    137 		{
    138 		BNerr(BN_F_BN_MOD_EXP2_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
    139 		return(0);
    140 		}
    141 	bits1=BN_num_bits(p1);
    142 	bits2=BN_num_bits(p2);
    143 	if ((bits1 == 0) && (bits2 == 0))
    144 		{
    145 		ret = BN_one(rr);
    146 		return ret;
    147 		}
    148 
    149 	bits=(bits1 > bits2)?bits1:bits2;
    150 
    151 	BN_CTX_start(ctx);
    152 	d = BN_CTX_get(ctx);
    153 	r = BN_CTX_get(ctx);
    154 	val1[0] = BN_CTX_get(ctx);
    155 	val2[0] = BN_CTX_get(ctx);
    156 	if(!d || !r || !val1[0] || !val2[0]) goto err;
    157 
    158 	if (in_mont != NULL)
    159 		mont=in_mont;
    160 	else
    161 		{
    162 		if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
    163 		if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
    164 		}
    165 
    166 	window1 = BN_window_bits_for_exponent_size(bits1);
    167 	window2 = BN_window_bits_for_exponent_size(bits2);
    168 
    169 	/*
    170 	 * Build table for a1:   val1[i] := a1^(2*i + 1) mod m  for i = 0 .. 2^(window1-1)
    171 	 */
    172 	if (a1->neg || BN_ucmp(a1,m) >= 0)
    173 		{
    174 		if (!BN_mod(val1[0],a1,m,ctx))
    175 			goto err;
    176 		a_mod_m = val1[0];
    177 		}
    178 	else
    179 		a_mod_m = a1;
    180 	if (BN_is_zero(a_mod_m))
    181 		{
    182 		BN_zero(rr);
    183 		ret = 1;
    184 		goto err;
    185 		}
    186 
    187 	if (!BN_to_montgomery(val1[0],a_mod_m,mont,ctx)) goto err;
    188 	if (window1 > 1)
    189 		{
    190 		if (!BN_mod_mul_montgomery(d,val1[0],val1[0],mont,ctx)) goto err;
    191 
    192 		j=1<<(window1-1);
    193 		for (i=1; i<j; i++)
    194 			{
    195 			if(((val1[i] = BN_CTX_get(ctx)) == NULL) ||
    196 					!BN_mod_mul_montgomery(val1[i],val1[i-1],
    197 						d,mont,ctx))
    198 				goto err;
    199 			}
    200 		}
    201 
    202 
    203 	/*
    204 	 * Build table for a2:   val2[i] := a2^(2*i + 1) mod m  for i = 0 .. 2^(window2-1)
    205 	 */
    206 	if (a2->neg || BN_ucmp(a2,m) >= 0)
    207 		{
    208 		if (!BN_mod(val2[0],a2,m,ctx))
    209 			goto err;
    210 		a_mod_m = val2[0];
    211 		}
    212 	else
    213 		a_mod_m = a2;
    214 	if (BN_is_zero(a_mod_m))
    215 		{
    216 		BN_zero(rr);
    217 		ret = 1;
    218 		goto err;
    219 		}
    220 	if (!BN_to_montgomery(val2[0],a_mod_m,mont,ctx)) goto err;
    221 	if (window2 > 1)
    222 		{
    223 		if (!BN_mod_mul_montgomery(d,val2[0],val2[0],mont,ctx)) goto err;
    224 
    225 		j=1<<(window2-1);
    226 		for (i=1; i<j; i++)
    227 			{
    228 			if(((val2[i] = BN_CTX_get(ctx)) == NULL) ||
    229 					!BN_mod_mul_montgomery(val2[i],val2[i-1],
    230 						d,mont,ctx))
    231 				goto err;
    232 			}
    233 		}
    234 
    235 
    236 	/* Now compute the power product, using independent windows. */
    237 	r_is_one=1;
    238 	wvalue1=0;  /* The 'value' of the first window */
    239 	wvalue2=0;  /* The 'value' of the second window */
    240 	wpos1=0;    /* If wvalue1 > 0, the bottom bit of the first window */
    241 	wpos2=0;    /* If wvalue2 > 0, the bottom bit of the second window */
    242 
    243 	if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
    244 	for (b=bits-1; b>=0; b--)
    245 		{
    246 		if (!r_is_one)
    247 			{
    248 			if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
    249 				goto err;
    250 			}
    251 
    252 		if (!wvalue1)
    253 			if (BN_is_bit_set(p1, b))
    254 				{
    255 				/* consider bits b-window1+1 .. b for this window */
    256 				i = b-window1+1;
    257 				while (!BN_is_bit_set(p1, i)) /* works for i<0 */
    258 					i++;
    259 				wpos1 = i;
    260 				wvalue1 = 1;
    261 				for (i = b-1; i >= wpos1; i--)
    262 					{
    263 					wvalue1 <<= 1;
    264 					if (BN_is_bit_set(p1, i))
    265 						wvalue1++;
    266 					}
    267 				}
    268 
    269 		if (!wvalue2)
    270 			if (BN_is_bit_set(p2, b))
    271 				{
    272 				/* consider bits b-window2+1 .. b for this window */
    273 				i = b-window2+1;
    274 				while (!BN_is_bit_set(p2, i))
    275 					i++;
    276 				wpos2 = i;
    277 				wvalue2 = 1;
    278 				for (i = b-1; i >= wpos2; i--)
    279 					{
    280 					wvalue2 <<= 1;
    281 					if (BN_is_bit_set(p2, i))
    282 						wvalue2++;
    283 					}
    284 				}
    285 
    286 		if (wvalue1 && b == wpos1)
    287 			{
    288 			/* wvalue1 is odd and < 2^window1 */
    289 			if (!BN_mod_mul_montgomery(r,r,val1[wvalue1>>1],mont,ctx))
    290 				goto err;
    291 			wvalue1 = 0;
    292 			r_is_one = 0;
    293 			}
    294 
    295 		if (wvalue2 && b == wpos2)
    296 			{
    297 			/* wvalue2 is odd and < 2^window2 */
    298 			if (!BN_mod_mul_montgomery(r,r,val2[wvalue2>>1],mont,ctx))
    299 				goto err;
    300 			wvalue2 = 0;
    301 			r_is_one = 0;
    302 			}
    303 		}
    304 	BN_from_montgomery(rr,r,mont,ctx);
    305 	ret=1;
    306 err:
    307 	if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
    308 	BN_CTX_end(ctx);
    309 	bn_check_top(rr);
    310 	return(ret);
    311 	}
    312