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    /* $OpenBSD: bn_mod.c,v 1.12 2017/01/29 17:49:22 beck Exp $ */  | 
    
    
    2  | 
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    /* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>  | 
    
    
    3  | 
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     * for the OpenSSL project. */  | 
    
    
    4  | 
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    /* ====================================================================  | 
    
    
    5  | 
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     * Copyright (c) 1998-2000 The OpenSSL Project.  All rights reserved.  | 
    
    
    6  | 
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     *  | 
    
    
    7  | 
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     * Redistribution and use in source and binary forms, with or without  | 
    
    
    8  | 
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     * modification, are permitted provided that the following conditions  | 
    
    
    9  | 
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     * are met:  | 
    
    
    10  | 
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     *  | 
    
    
    11  | 
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     * 1. Redistributions of source code must retain the above copyright  | 
    
    
    12  | 
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     *    notice, this list of conditions and the following disclaimer.  | 
    
    
    13  | 
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     *  | 
    
    
    14  | 
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     * 2. Redistributions in binary form must reproduce the above copyright  | 
    
    
    15  | 
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     *    notice, this list of conditions and the following disclaimer in  | 
    
    
    16  | 
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     *    the documentation and/or other materials provided with the  | 
    
    
    17  | 
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     *    distribution.  | 
    
    
    18  | 
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     *  | 
    
    
    19  | 
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     * 3. All advertising materials mentioning features or use of this  | 
    
    
    20  | 
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     *    software must display the following acknowledgment:  | 
    
    
    21  | 
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     *    "This product includes software developed by the OpenSSL Project  | 
    
    
    22  | 
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     *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"  | 
    
    
    23  | 
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     *  | 
    
    
    24  | 
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     * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to  | 
    
    
    25  | 
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     *    endorse or promote products derived from this software without  | 
    
    
    26  | 
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     *    prior written permission. For written permission, please contact  | 
    
    
    27  | 
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     *    openssl-core@openssl.org.  | 
    
    
    28  | 
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     *  | 
    
    
    29  | 
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     * 5. Products derived from this software may not be called "OpenSSL"  | 
    
    
    30  | 
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     *    nor may "OpenSSL" appear in their names without prior written  | 
    
    
    31  | 
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     *    permission of the OpenSSL Project.  | 
    
    
    32  | 
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     *  | 
    
    
    33  | 
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     * 6. Redistributions of any form whatsoever must retain the following  | 
    
    
    34  | 
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     *    acknowledgment:  | 
    
    
    35  | 
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     *    "This product includes software developed by the OpenSSL Project  | 
    
    
    36  | 
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     *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"  | 
    
    
    37  | 
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     *  | 
    
    
    38  | 
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     * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY  | 
    
    
    39  | 
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     * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE  | 
    
    
    40  | 
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     * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR  | 
    
    
    41  | 
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     * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR  | 
    
    
    42  | 
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     * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,  | 
    
    
    43  | 
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     * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT  | 
    
    
    44  | 
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     * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;  | 
    
    
    45  | 
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     * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)  | 
    
    
    46  | 
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     * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,  | 
    
    
    47  | 
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     * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)  | 
    
    
    48  | 
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     * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED  | 
    
    
    49  | 
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     * OF THE POSSIBILITY OF SUCH DAMAGE.  | 
    
    
    50  | 
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     * ====================================================================  | 
    
    
    51  | 
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     *  | 
    
    
    52  | 
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     * This product includes cryptographic software written by Eric Young  | 
    
    
    53  | 
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     * (eay@cryptsoft.com).  This product includes software written by Tim  | 
    
    
    54  | 
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     * Hudson (tjh@cryptsoft.com).  | 
    
    
    55  | 
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     *  | 
    
    
    56  | 
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     */  | 
    
    
    57  | 
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    /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)  | 
    
    
    58  | 
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     * All rights reserved.  | 
    
    
    59  | 
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     *  | 
    
    
    60  | 
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     * This package is an SSL implementation written  | 
    
    
    61  | 
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     * by Eric Young (eay@cryptsoft.com).  | 
    
    
    62  | 
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     * The implementation was written so as to conform with Netscapes SSL.  | 
    
    
    63  | 
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     *  | 
    
    
    64  | 
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     * This library is free for commercial and non-commercial use as long as  | 
    
    
    65  | 
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     * the following conditions are aheared to.  The following conditions  | 
    
    
    66  | 
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     * apply to all code found in this distribution, be it the RC4, RSA,  | 
    
    
    67  | 
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     * lhash, DES, etc., code; not just the SSL code.  The SSL documentation  | 
    
    
    68  | 
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     * included with this distribution is covered by the same copyright terms  | 
    
    
    69  | 
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     * except that the holder is Tim Hudson (tjh@cryptsoft.com).  | 
    
    
    70  | 
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     *  | 
    
    
    71  | 
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     * Copyright remains Eric Young's, and as such any Copyright notices in  | 
    
    
    72  | 
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     * the code are not to be removed.  | 
    
    
    73  | 
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     * If this package is used in a product, Eric Young should be given attribution  | 
    
    
    74  | 
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     * as the author of the parts of the library used.  | 
    
    
    75  | 
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     * This can be in the form of a textual message at program startup or  | 
    
    
    76  | 
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     * in documentation (online or textual) provided with the package.  | 
    
    
    77  | 
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     *  | 
    
    
    78  | 
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     * Redistribution and use in source and binary forms, with or without  | 
    
    
    79  | 
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     * modification, are permitted provided that the following conditions  | 
    
    
    80  | 
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     * are met:  | 
    
    
    81  | 
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     * 1. Redistributions of source code must retain the copyright  | 
    
    
    82  | 
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     *    notice, this list of conditions and the following disclaimer.  | 
    
    
    83  | 
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     * 2. Redistributions in binary form must reproduce the above copyright  | 
    
    
    84  | 
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     *    notice, this list of conditions and the following disclaimer in the  | 
    
    
    85  | 
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     *    documentation and/or other materials provided with the distribution.  | 
    
    
    86  | 
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     * 3. All advertising materials mentioning features or use of this software  | 
    
    
    87  | 
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     *    must display the following acknowledgement:  | 
    
    
    88  | 
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     *    "This product includes cryptographic software written by  | 
    
    
    89  | 
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     *     Eric Young (eay@cryptsoft.com)"  | 
    
    
    90  | 
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     *    The word 'cryptographic' can be left out if the rouines from the library  | 
    
    
    91  | 
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     *    being used are not cryptographic related :-).  | 
    
    
    92  | 
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     * 4. If you include any Windows specific code (or a derivative thereof) from  | 
    
    
    93  | 
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     *    the apps directory (application code) you must include an acknowledgement:  | 
    
    
    94  | 
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     *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"  | 
    
    
    95  | 
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     *  | 
    
    
    96  | 
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     * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND  | 
    
    
    97  | 
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     * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE  | 
    
    
    98  | 
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     * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE  | 
    
    
    99  | 
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     * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE  | 
    
    
    100  | 
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     * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL  | 
    
    
    101  | 
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     * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS  | 
    
    
    102  | 
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     * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)  | 
    
    
    103  | 
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     * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT  | 
    
    
    104  | 
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     * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY  | 
    
    
    105  | 
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     * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF  | 
    
    
    106  | 
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     * SUCH DAMAGE.  | 
    
    
    107  | 
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     *  | 
    
    
    108  | 
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     * The licence and distribution terms for any publically available version or  | 
    
    
    109  | 
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     * derivative of this code cannot be changed.  i.e. this code cannot simply be  | 
    
    
    110  | 
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     * copied and put under another distribution licence  | 
    
    
    111  | 
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     * [including the GNU Public Licence.]  | 
    
    
    112  | 
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     */  | 
    
    
    113  | 
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    114  | 
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    #include <openssl/err.h>  | 
    
    
    115  | 
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    116  | 
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    #include "bn_lcl.h"  | 
    
    
    117  | 
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    118  | 
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    int  | 
    
    
    119  | 
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    BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)  | 
    
    
    120  | 
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    { | 
    
    
    121  | 
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    	/* like BN_mod, but returns non-negative remainder  | 
    
    
    122  | 
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    	 * (i.e.,  0 <= r < |d|  always holds) */  | 
    
    
    123  | 
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    124  | 
    ✓✓ | 
    956746  | 
    	if (!(BN_mod_ct(r, m,d, ctx)))  | 
    
    
    125  | 
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    15  | 
    		return 0;  | 
    
    
    126  | 
    ✓✓ | 
    478358  | 
    	if (!r->neg)  | 
    
    
    127  | 
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    477741  | 
    		return 1;  | 
    
    
    128  | 
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    	/* now -|d| < r < 0,  so we have to set  r := r + |d| */  | 
    
    
    129  | 
    ✗✓ | 
    617  | 
    	if (d->neg)  | 
    
    
    130  | 
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    		return BN_sub(r, r, d);  | 
    
    
    131  | 
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    	else  | 
    
    
    132  | 
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    617  | 
    		return BN_add(r, r, d);  | 
    
    
    133  | 
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    478373  | 
    }  | 
    
    
    134  | 
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    135  | 
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    int  | 
    
    
    136  | 
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    BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,  | 
    
    
    137  | 
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        BN_CTX *ctx)  | 
    
    
    138  | 
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    { | 
    
    
    139  | 
    ✗✓ | 
    252  | 
    	if (!BN_add(r, a, b))  | 
    
    
    140  | 
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    		return 0;  | 
    
    
    141  | 
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    126  | 
    	return BN_nnmod(r, r, m, ctx);  | 
    
    
    142  | 
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    126  | 
    }  | 
    
    
    143  | 
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    144  | 
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    /* BN_mod_add variant that may be used if both  a  and  b  are non-negative  | 
    
    
    145  | 
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     * and less than  m */  | 
    
    
    146  | 
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    int  | 
    
    
    147  | 
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    BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m)  | 
    
    
    148  | 
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    { | 
    
    
    149  | 
    ✗✓ | 
    5922760  | 
    	if (!BN_uadd(r, a, b))  | 
    
    
    150  | 
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    		return 0;  | 
    
    
    151  | 
    ✓✓ | 
    2961380  | 
    	if (BN_ucmp(r, m) >= 0)  | 
    
    
    152  | 
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    1467215  | 
    		return BN_usub(r, r, m);  | 
    
    
    153  | 
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    1494165  | 
    	return 1;  | 
    
    
    154  | 
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    2961380  | 
    }  | 
    
    
    155  | 
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    156  | 
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    int  | 
    
    
    157  | 
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    BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,  | 
    
    
    158  | 
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        BN_CTX *ctx)  | 
    
    
    159  | 
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    { | 
    
    
    160  | 
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    	if (!BN_sub(r, a, b))  | 
    
    
    161  | 
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    		return 0;  | 
    
    
    162  | 
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    	return BN_nnmod(r, r, m, ctx);  | 
    
    
    163  | 
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    }  | 
    
    
    164  | 
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    165  | 
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    /* BN_mod_sub variant that may be used if both  a  and  b  are non-negative  | 
    
    
    166  | 
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     * and less than  m */  | 
    
    
    167  | 
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    int  | 
    
    
    168  | 
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    BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m)  | 
    
    
    169  | 
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    { | 
    
    
    170  | 
    ✗✓ | 
    12003210  | 
    	if (!BN_sub(r, a, b))  | 
    
    
    171  | 
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    		return 0;  | 
    
    
    172  | 
    ✓✓ | 
    6001605  | 
    	if (r->neg)  | 
    
    
    173  | 
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    3002405  | 
    		return BN_add(r, r, m);  | 
    
    
    174  | 
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    2999200  | 
    	return 1;  | 
    
    
    175  | 
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    6001605  | 
    }  | 
    
    
    176  | 
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    177  | 
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    /* slow but works */  | 
    
    
    178  | 
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    int  | 
    
    
    179  | 
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    BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,  | 
    
    
    180  | 
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        BN_CTX *ctx)  | 
    
    
    181  | 
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    { | 
    
    
    182  | 
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    	BIGNUM *t;  | 
    
    
    183  | 
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    	int ret = 0;  | 
    
    
    184  | 
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    185  | 
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    	bn_check_top(a);  | 
    
    
    186  | 
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    	bn_check_top(b);  | 
    
    
    187  | 
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    	bn_check_top(m);  | 
    
    
    188  | 
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    189  | 
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    740342  | 
    	BN_CTX_start(ctx);  | 
    
    
    190  | 
    ✓✗ | 
    370171  | 
    	if ((t = BN_CTX_get(ctx)) == NULL)  | 
    
    
    191  | 
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    		goto err;  | 
    
    
    192  | 
    ✓✓ | 
    370171  | 
    	if (a == b) { | 
    
    
    193  | 
    ✓✗ | 
    272288  | 
    		if (!BN_sqr(t, a, ctx))  | 
    
    
    194  | 
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    			goto err;  | 
    
    
    195  | 
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    	} else { | 
    
    
    196  | 
    ✓✗ | 
    97883  | 
    		if (!BN_mul(t, a,b, ctx))  | 
    
    
    197  | 
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    			goto err;  | 
    
    
    198  | 
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    	}  | 
    
    
    199  | 
    ✓✓ | 
    370171  | 
    	if (!BN_nnmod(r, t,m, ctx))  | 
    
    
    200  | 
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    		goto err;  | 
    
    
    201  | 
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    	bn_check_top(r);  | 
    
    
    202  | 
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    370168  | 
    	ret = 1;  | 
    
    
    203  | 
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    204  | 
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    err:  | 
    
    
    205  | 
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    370171  | 
    	BN_CTX_end(ctx);  | 
    
    
    206  | 
     | 
    370171  | 
    	return (ret);  | 
    
    
    207  | 
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    }  | 
    
    
    208  | 
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    209  | 
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    int  | 
    
    
    210  | 
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    BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)  | 
    
    
    211  | 
     | 
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    { | 
    
    
    212  | 
    ✗✓ | 
    11928  | 
    	if (!BN_sqr(r, a, ctx))  | 
    
    
    213  | 
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    		return 0;  | 
    
    
    214  | 
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    	/* r->neg == 0,  thus we don't need BN_nnmod */  | 
    
    
    215  | 
     | 
    5964  | 
    	return BN_mod_ct(r, r, m, ctx);  | 
    
    
    216  | 
     | 
    5964  | 
    }  | 
    
    
    217  | 
     | 
     | 
     | 
    
    
    218  | 
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    int  | 
    
    
    219  | 
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    BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)  | 
    
    
    220  | 
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    { | 
    
    
    221  | 
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    	if (!BN_lshift1(r, a))  | 
    
    
    222  | 
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    		return 0;  | 
    
    
    223  | 
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    	bn_check_top(r);  | 
    
    
    224  | 
     | 
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    	return BN_nnmod(r, r, m, ctx);  | 
    
    
    225  | 
     | 
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    }  | 
    
    
    226  | 
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    227  | 
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    /* BN_mod_lshift1 variant that may be used if  a  is non-negative  | 
    
    
    228  | 
     | 
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     * and less than  m */  | 
    
    
    229  | 
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    int  | 
    
    
    230  | 
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    BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m)  | 
    
    
    231  | 
     | 
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    { | 
    
    
    232  | 
    ✗✓ | 
    7756430  | 
    	if (!BN_lshift1(r, a))  | 
    
    
    233  | 
     | 
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    		return 0;  | 
    
    
    234  | 
     | 
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    	bn_check_top(r);  | 
    
    
    235  | 
    ✓✓ | 
    3878215  | 
    	if (BN_cmp(r, m) >= 0)  | 
    
    
    236  | 
     | 
    1938426  | 
    		return BN_sub(r, r, m);  | 
    
    
    237  | 
     | 
    1939789  | 
    	return 1;  | 
    
    
    238  | 
     | 
    3878215  | 
    }  | 
    
    
    239  | 
     | 
     | 
     | 
    
    
    240  | 
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    int  | 
    
    
    241  | 
     | 
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    BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx)  | 
    
    
    242  | 
     | 
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    { | 
    
    
    243  | 
     | 
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    	BIGNUM *abs_m = NULL;  | 
    
    
    244  | 
     | 
     | 
    	int ret;  | 
    
    
    245  | 
     | 
     | 
     | 
    
    
    246  | 
     | 
     | 
    	if (!BN_nnmod(r, a, m, ctx))  | 
    
    
    247  | 
     | 
     | 
    		return 0;  | 
    
    
    248  | 
     | 
     | 
     | 
    
    
    249  | 
     | 
     | 
    	if (m->neg) { | 
    
    
    250  | 
     | 
     | 
    		abs_m = BN_dup(m);  | 
    
    
    251  | 
     | 
     | 
    		if (abs_m == NULL)  | 
    
    
    252  | 
     | 
     | 
    			return 0;  | 
    
    
    253  | 
     | 
     | 
    		abs_m->neg = 0;  | 
    
    
    254  | 
     | 
     | 
    	}  | 
    
    
    255  | 
     | 
     | 
     | 
    
    
    256  | 
     | 
     | 
    	ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));  | 
    
    
    257  | 
     | 
     | 
    	bn_check_top(r);  | 
    
    
    258  | 
     | 
     | 
     | 
    
    
    259  | 
     | 
     | 
    	BN_free(abs_m);  | 
    
    
    260  | 
     | 
     | 
    	return ret;  | 
    
    
    261  | 
     | 
     | 
    }  | 
    
    
    262  | 
     | 
     | 
     | 
    
    
    263  | 
     | 
     | 
    /* BN_mod_lshift variant that may be used if  a  is non-negative  | 
    
    
    264  | 
     | 
     | 
     * and less than  m */  | 
    
    
    265  | 
     | 
     | 
    int  | 
    
    
    266  | 
     | 
     | 
    BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m)  | 
    
    
    267  | 
     | 
     | 
    { | 
    
    
    268  | 
    ✓✓ | 
    4798764  | 
    	if (r != a) { | 
    
    
    269  | 
    ✗✓ | 
    1199691  | 
    		if (BN_copy(r, a) == NULL)  | 
    
    
    270  | 
     | 
     | 
    			return 0;  | 
    
    
    271  | 
     | 
     | 
    	}  | 
    
    
    272  | 
     | 
     | 
     | 
    
    
    273  | 
    ✓✓ | 
    14782506  | 
    	while (n > 0) { | 
    
    
    274  | 
     | 
     | 
    		int max_shift;  | 
    
    
    275  | 
     | 
     | 
     | 
    
    
    276  | 
     | 
     | 
    		/* 0 < r < m */  | 
    
    
    277  | 
     | 
    4991871  | 
    		max_shift = BN_num_bits(m) - BN_num_bits(r);  | 
    
    
    278  | 
     | 
     | 
    		/* max_shift >= 0 */  | 
    
    
    279  | 
     | 
     | 
     | 
    
    
    280  | 
    ✗✓ | 
    4991871  | 
    		if (max_shift < 0) { | 
    
    
    281  | 
     | 
     | 
    			BNerror(BN_R_INPUT_NOT_REDUCED);  | 
    
    
    282  | 
     | 
     | 
    			return 0;  | 
    
    
    283  | 
     | 
     | 
    		}  | 
    
    
    284  | 
     | 
     | 
     | 
    
    
    285  | 
    ✓✓ | 
    4991871  | 
    		if (max_shift > n)  | 
    
    
    286  | 
     | 
    675561  | 
    			max_shift = n;  | 
    
    
    287  | 
     | 
     | 
     | 
    
    
    288  | 
    ✓✓ | 
    4991871  | 
    		if (max_shift) { | 
    
    
    289  | 
    ✗✓ | 
    2359642  | 
    			if (!BN_lshift(r, r, max_shift))  | 
    
    
    290  | 
     | 
     | 
    				return 0;  | 
    
    
    291  | 
     | 
    2359642  | 
    			n -= max_shift;  | 
    
    
    292  | 
     | 
    2359642  | 
    		} else { | 
    
    
    293  | 
    ✗✓ | 
    2632229  | 
    			if (!BN_lshift1(r, r))  | 
    
    
    294  | 
     | 
     | 
    				return 0;  | 
    
    
    295  | 
     | 
    2632229  | 
    			--n;  | 
    
    
    296  | 
     | 
     | 
    		}  | 
    
    
    297  | 
     | 
     | 
     | 
    
    
    298  | 
     | 
     | 
    		/* BN_num_bits(r) <= BN_num_bits(m) */  | 
    
    
    299  | 
     | 
     | 
     | 
    
    
    300  | 
    ✓✓ | 
    4991871  | 
    		if (BN_cmp(r, m) >= 0) { | 
    
    
    301  | 
    ✗✓ | 
    3001323  | 
    			if (!BN_sub(r, r, m))  | 
    
    
    302  | 
     | 
     | 
    				return 0;  | 
    
    
    303  | 
     | 
     | 
    		}  | 
    
    
    304  | 
    ✓✗ | 
    4991871  | 
    	}  | 
    
    
    305  | 
     | 
     | 
    	bn_check_top(r);  | 
    
    
    306  | 
     | 
     | 
     | 
    
    
    307  | 
     | 
    2399382  | 
    	return 1;  | 
    
    
    308  | 
     | 
    2399382  | 
    }  |