1BN_MOD_MUL_MONTGOMERY(3)            OpenSSL           BN_MOD_MUL_MONTGOMERY(3)
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NAME

6       BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_free,
7       BN_MONT_CTX_set, BN_MONT_CTX_copy, BN_from_montgomery, BN_to_montgomery
8       - Montgomery multiplication
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SYNOPSIS

11        #include <openssl/bn.h>
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13        BN_MONT_CTX *BN_MONT_CTX_new(void);
14        void BN_MONT_CTX_free(BN_MONT_CTX *mont);
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16        int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
17        BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
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19        int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
20                                  BN_MONT_CTX *mont, BN_CTX *ctx);
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22        int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
23                               BN_CTX *ctx);
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25        int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
26                             BN_CTX *ctx);
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DESCRIPTION

29       These functions implement Montgomery multiplication. They are used
30       automatically when BN_mod_exp(3) is called with suitable input, but
31       they may be useful when several operations are to be performed using
32       the same modulus.
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34       BN_MONT_CTX_new() allocates and initializes a BN_MONT_CTX structure.
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36       BN_MONT_CTX_set() sets up the mont structure from the modulus m by
37       precomputing its inverse and a value R.
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39       BN_MONT_CTX_copy() copies the BN_MONT_CTX from to to.
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41       BN_MONT_CTX_free() frees the components of the BN_MONT_CTX, and, if it
42       was created by BN_MONT_CTX_new(), also the structure itself.  If mont
43       is NULL, nothing is done.
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45       BN_mod_mul_montgomery() computes Mont(a,b):=a*b*R^-1 and places the
46       result in r.
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48       BN_from_montgomery() performs the Montgomery reduction r = a*R^-1.
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50       BN_to_montgomery() computes Mont(a,R^2), i.e. a*R.  Note that a must be
51       nonnegative and smaller than the modulus.
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53       For all functions, ctx is a previously allocated BN_CTX used for
54       temporary variables.
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RETURN VALUES

57       BN_MONT_CTX_new() returns the newly allocated BN_MONT_CTX, and NULL on
58       error.
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60       BN_MONT_CTX_free() has no return value.
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62       For the other functions, 1 is returned for success, 0 on error.  The
63       error codes can be obtained by ERR_get_error(3).
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WARNINGS

66       The inputs must be reduced modulo m, otherwise the result will be
67       outside the expected range.
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SEE ALSO

70       ERR_get_error(3), BN_add(3), BN_CTX_new(3)
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HISTORY

73       BN_MONT_CTX_init() was removed in OpenSSL 1.1.0
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76       Copyright 2000-2020 The OpenSSL Project Authors. All Rights Reserved.
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78       Licensed under the OpenSSL license (the "License").  You may not use
79       this file except in compliance with the License.  You can obtain a copy
80       in the file LICENSE in the source distribution or at
81       <https://www.openssl.org/source/license.html>.
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851.1.1l                            2021-09-15          BN_MOD_MUL_MONTGOMERY(3)
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