/* $OpenBSD: bn_exp2.c,v 1.10 2015/02/09 15:49:22 jsing Exp $ */ /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) * All rights reserved. * * This package is an SSL implementation written * by Eric Young (eay@cryptsoft.com). * The implementation was written so as to conform with Netscapes SSL. * * This library is free for commercial and non-commercial use as long as * the following conditions are aheared to. The following conditions * apply to all code found in this distribution, be it the RC4, RSA, * lhash, DES, etc., code; not just the SSL code. The SSL documentation * included with this distribution is covered by the same copyright terms * except that the holder is Tim Hudson (tjh@cryptsoft.com). * * Copyright remains Eric Young's, and as such any Copyright notices in * the code are not to be removed. * If this package is used in a product, Eric Young should be given attribution * as the author of the parts of the library used. * This can be in the form of a textual message at program startup or * in documentation (online or textual) provided with the package. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. All advertising materials mentioning features or use of this software * must display the following acknowledgement: * "This product includes cryptographic software written by * Eric Young (eay@cryptsoft.com)" * The word 'cryptographic' can be left out if the rouines from the library * being used are not cryptographic related :-). * 4. If you include any Windows specific code (or a derivative thereof) from * the apps directory (application code) you must include an acknowledgement: * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" * * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * * The licence and distribution terms for any publically available version or * derivative of this code cannot be changed. i.e. this code cannot simply be * copied and put under another distribution licence * [including the GNU Public Licence.] */ /* ==================================================================== * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * * 3. All advertising materials mentioning features or use of this * software must display the following acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ #include #include #include "bn_lcl.h" #define TABLE_SIZE 32 int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1, const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) { int i, j, bits, b, bits1, bits2, ret = 0, wpos1, wpos2, window1, window2, wvalue1, wvalue2; int r_is_one = 1; BIGNUM *d, *r; const BIGNUM *a_mod_m; /* Tables of variables obtained from 'ctx' */ BIGNUM *val1[TABLE_SIZE], *val2[TABLE_SIZE]; BN_MONT_CTX *mont = NULL; bn_check_top(a1); bn_check_top(p1); bn_check_top(a2); bn_check_top(p2); bn_check_top(m); if (!(m->d[0] & 1)) { BNerr(BN_F_BN_MOD_EXP2_MONT, BN_R_CALLED_WITH_EVEN_MODULUS); return (0); } bits1 = BN_num_bits(p1); bits2 = BN_num_bits(p2); if ((bits1 == 0) && (bits2 == 0)) { ret = BN_one(rr); return ret; } bits = (bits1 > bits2) ? bits1 : bits2; BN_CTX_start(ctx); if ((d = BN_CTX_get(ctx)) == NULL) goto err; if ((r = BN_CTX_get(ctx)) == NULL) goto err; if ((val1[0] = BN_CTX_get(ctx)) == NULL) goto err; if ((val2[0] = BN_CTX_get(ctx)) == NULL) goto err; if (in_mont != NULL) mont = in_mont; else { if ((mont = BN_MONT_CTX_new()) == NULL) goto err; if (!BN_MONT_CTX_set(mont, m, ctx)) goto err; } window1 = BN_window_bits_for_exponent_size(bits1); window2 = BN_window_bits_for_exponent_size(bits2); /* * Build table for a1: val1[i] := a1^(2*i + 1) mod m for i = 0 .. 2^(window1-1) */ if (a1->neg || BN_ucmp(a1, m) >= 0) { if (!BN_mod(val1[0], a1, m, ctx)) goto err; a_mod_m = val1[0]; } else a_mod_m = a1; if (BN_is_zero(a_mod_m)) { BN_zero(rr); ret = 1; goto err; } if (!BN_to_montgomery(val1[0], a_mod_m, mont, ctx)) goto err; if (window1 > 1) { if (!BN_mod_mul_montgomery(d, val1[0], val1[0], mont, ctx)) goto err; j = 1 << (window1 - 1); for (i = 1; i < j; i++) { if (((val1[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul_montgomery(val1[i], val1[i - 1], d, mont, ctx)) goto err; } } /* * Build table for a2: val2[i] := a2^(2*i + 1) mod m for i = 0 .. 2^(window2-1) */ if (a2->neg || BN_ucmp(a2, m) >= 0) { if (!BN_mod(val2[0], a2, m, ctx)) goto err; a_mod_m = val2[0]; } else a_mod_m = a2; if (BN_is_zero(a_mod_m)) { BN_zero(rr); ret = 1; goto err; } if (!BN_to_montgomery(val2[0], a_mod_m, mont, ctx)) goto err; if (window2 > 1) { if (!BN_mod_mul_montgomery(d, val2[0], val2[0], mont, ctx)) goto err; j = 1 << (window2 - 1); for (i = 1; i < j; i++) { if (((val2[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul_montgomery(val2[i], val2[i - 1], d, mont, ctx)) goto err; } } /* Now compute the power product, using independent windows. */ r_is_one = 1; wvalue1 = 0; /* The 'value' of the first window */ wvalue2 = 0; /* The 'value' of the second window */ wpos1 = 0; /* If wvalue1 > 0, the bottom bit of the first window */ wpos2 = 0; /* If wvalue2 > 0, the bottom bit of the second window */ if (!BN_to_montgomery(r, BN_value_one(), mont, ctx)) goto err; for (b = bits - 1; b >= 0; b--) { if (!r_is_one) { if (!BN_mod_mul_montgomery(r, r,r, mont, ctx)) goto err; } if (!wvalue1) if (BN_is_bit_set(p1, b)) { /* consider bits b-window1+1 .. b for this window */ i = b - window1 + 1; while (!BN_is_bit_set(p1, i)) /* works for i<0 */ i++; wpos1 = i; wvalue1 = 1; for (i = b - 1; i >= wpos1; i--) { wvalue1 <<= 1; if (BN_is_bit_set(p1, i)) wvalue1++; } } if (!wvalue2) if (BN_is_bit_set(p2, b)) { /* consider bits b-window2+1 .. b for this window */ i = b - window2 + 1; while (!BN_is_bit_set(p2, i)) i++; wpos2 = i; wvalue2 = 1; for (i = b - 1; i >= wpos2; i--) { wvalue2 <<= 1; if (BN_is_bit_set(p2, i)) wvalue2++; } } if (wvalue1 && b == wpos1) { /* wvalue1 is odd and < 2^window1 */ if (!BN_mod_mul_montgomery(r, r, val1[wvalue1 >> 1], mont, ctx)) goto err; wvalue1 = 0; r_is_one = 0; } if (wvalue2 && b == wpos2) { /* wvalue2 is odd and < 2^window2 */ if (!BN_mod_mul_montgomery(r, r, val2[wvalue2 >> 1], mont, ctx)) goto err; wvalue2 = 0; r_is_one = 0; } } if (!BN_from_montgomery(rr, r,mont, ctx)) goto err; ret = 1; err: if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); BN_CTX_end(ctx); bn_check_top(rr); return (ret); }