1656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project/* crypto/bn/bn_kron.c */ 2656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project/* ==================================================================== 3656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved. 4656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 5656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * Redistribution and use in source and binary forms, with or without 6656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * modification, are permitted provided that the following conditions 7656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * are met: 8656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 9656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 1. Redistributions of source code must retain the above copyright 10656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * notice, this list of conditions and the following disclaimer. 11656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 12656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 2. Redistributions in binary form must reproduce the above copyright 13656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * notice, this list of conditions and the following disclaimer in 14656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * the documentation and/or other materials provided with the 15656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * distribution. 16656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 17656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 3. All advertising materials mentioning features or use of this 18656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * software must display the following acknowledgment: 19656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * "This product includes software developed by the OpenSSL Project 20656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 21656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 22656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 23656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * endorse or promote products derived from this software without 24656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * prior written permission. For written permission, please contact 25656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * openssl-core@openssl.org. 26656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 27656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 5. Products derived from this software may not be called "OpenSSL" 28656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * nor may "OpenSSL" appear in their names without prior written 29656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * permission of the OpenSSL Project. 30656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 31656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 6. Redistributions of any form whatsoever must retain the following 32656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * acknowledgment: 33656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * "This product includes software developed by the OpenSSL Project 34656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 35656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 36656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 37656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 38656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 39656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 40656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 41656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 42656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 43656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 44656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 45656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 46656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 47656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * OF THE POSSIBILITY OF SUCH DAMAGE. 48656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * ==================================================================== 49656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 50656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * This product includes cryptographic software written by Eric Young 51656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * (eay@cryptsoft.com). This product includes software written by Tim 52656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * Hudson (tjh@cryptsoft.com). 53656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * 54656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project */ 55656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 56656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project#include "cryptlib.h" 57656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project#include "bn_lcl.h" 58656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 59656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project/* least significant word */ 60656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project#define BN_lsw(n) (((n)->top == 0) ? (BN_ULONG) 0 : (n)->d[0]) 61656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 62656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project/* Returns -2 for errors because both -1 and 0 are valid results. */ 63656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Projectint BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) 64656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project { 65656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project int i; 66656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project int ret = -2; /* avoid 'uninitialized' warning */ 67656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project int err = 0; 68656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project BIGNUM *A, *B, *tmp; 69656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* In 'tab', only odd-indexed entries are relevant: 70656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * For any odd BIGNUM n, 71656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * tab[BN_lsw(n) & 7] 72656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * is $(-1)^{(n^2-1)/8}$ (using TeX notation). 73656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * Note that the sign of n does not matter. 74656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project */ 75656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project static const int tab[8] = {0, 1, 0, -1, 0, -1, 0, 1}; 76656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 77656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project bn_check_top(a); 78656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project bn_check_top(b); 79656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 80656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project BN_CTX_start(ctx); 81656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project A = BN_CTX_get(ctx); 82656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project B = BN_CTX_get(ctx); 83656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (B == NULL) goto end; 84656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 85656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project err = !BN_copy(A, a); 86656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (err) goto end; 87656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project err = !BN_copy(B, b); 88656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (err) goto end; 89656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 90656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* 91656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * Kronecker symbol, imlemented according to Henri Cohen, 92656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * "A Course in Computational Algebraic Number Theory" 93656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * (algorithm 1.4.10). 94656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project */ 95656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 96656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* Cohen's step 1: */ 97656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 98656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (BN_is_zero(B)) 99656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project { 100656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project ret = BN_abs_is_word(A, 1); 101656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project goto end; 102656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project } 103656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 104656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* Cohen's step 2: */ 105656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 106656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (!BN_is_odd(A) && !BN_is_odd(B)) 107656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project { 108656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project ret = 0; 109656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project goto end; 110656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project } 111656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 112656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* now B is non-zero */ 113656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project i = 0; 114656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project while (!BN_is_bit_set(B, i)) 115656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project i++; 116656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project err = !BN_rshift(B, B, i); 117656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (err) goto end; 118656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (i & 1) 119656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project { 120656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* i is odd */ 121656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* (thus B was even, thus A must be odd!) */ 122656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 123656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* set 'ret' to $(-1)^{(A^2-1)/8}$ */ 124656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project ret = tab[BN_lsw(A) & 7]; 125656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project } 126656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project else 127656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project { 128656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* i is even */ 129656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project ret = 1; 130656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project } 131656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 132656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (B->neg) 133656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project { 134656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project B->neg = 0; 135656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (A->neg) 136656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project ret = -ret; 137656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project } 138656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 139656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* now B is positive and odd, so what remains to be done is 140656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project * to compute the Jacobi symbol (A/B) and multiply it by 'ret' */ 141656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 142656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project while (1) 143656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project { 144656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* Cohen's step 3: */ 145656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 146656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* B is positive and odd */ 147656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 148656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (BN_is_zero(A)) 149656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project { 150656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project ret = BN_is_one(B) ? ret : 0; 151656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project goto end; 152656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project } 153656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 154656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* now A is non-zero */ 155656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project i = 0; 156656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project while (!BN_is_bit_set(A, i)) 157656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project i++; 158656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project err = !BN_rshift(A, A, i); 159656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (err) goto end; 160656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (i & 1) 161656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project { 162656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* i is odd */ 163656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* multiply 'ret' by $(-1)^{(B^2-1)/8}$ */ 164656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project ret = ret * tab[BN_lsw(B) & 7]; 165656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project } 166656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 167656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* Cohen's step 4: */ 168656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* multiply 'ret' by $(-1)^{(A-1)(B-1)/4}$ */ 169656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2) 170656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project ret = -ret; 171656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project 172656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project /* (A, B) := (B mod |A|, |A|) */ 173656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project err = !BN_nnmod(B, B, A, ctx); 174656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (err) goto end; 175656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project tmp = A; A = B; B = tmp; 176656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project tmp->neg = 0; 177656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project } 178656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Projectend: 179656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project BN_CTX_end(ctx); 180656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project if (err) 181656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project return -2; 182656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project else 183656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project return ret; 184656d9c7f52f88b3a3daccafa7655dec086c4756eThe Android Open Source Project } 185