| 1 | =pod
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| 2 |
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| 3 | =head1 NAME
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| 4 |
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| 5 | BN_mod_mul_montgomery, BN_MONT_CTX_new,
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| 6 | BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
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| 7 | BN_from_montgomery, BN_to_montgomery - Montgomery multiplication
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| 8 |
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| 9 | =head1 SYNOPSIS
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| 10 |
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| 11 | #include <openssl/bn.h>
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| 12 |
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| 13 | BN_MONT_CTX *BN_MONT_CTX_new(void);
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| 14 | void BN_MONT_CTX_free(BN_MONT_CTX *mont);
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| 15 |
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| 16 | int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
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| 17 | BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
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| 18 |
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| 19 | int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
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| 20 | BN_MONT_CTX *mont, BN_CTX *ctx);
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| 21 |
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| 22 | int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
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| 23 | BN_CTX *ctx);
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| 24 |
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| 25 | int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
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| 26 | BN_CTX *ctx);
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| 27 |
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| 28 | =head1 DESCRIPTION
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| 29 |
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| 30 | These functions implement Montgomery multiplication. They are used
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| 31 | automatically when L<BN_mod_exp(3)> is called with suitable input,
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| 32 | but they may be useful when several operations are to be performed
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| 33 | using the same modulus.
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| 34 |
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| 35 | BN_MONT_CTX_new() allocates and initializes a B<BN_MONT_CTX> structure.
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| 36 |
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| 37 | BN_MONT_CTX_set() sets up the I<mont> structure from the modulus I<m>
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| 38 | by precomputing its inverse and a value R.
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| 39 |
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| 40 | BN_MONT_CTX_copy() copies the B<BN_MONT_CTX> I<from> to I<to>.
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| 41 |
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| 42 | BN_MONT_CTX_free() frees the components of the B<BN_MONT_CTX>, and, if
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| 43 | it was created by BN_MONT_CTX_new(), also the structure itself.
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| 44 | If B<mont> is NULL, nothing is done.
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| 45 |
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| 46 | BN_mod_mul_montgomery() computes Mont(I<a>,I<b>):=I<a>*I<b>*R^-1 and places
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| 47 | the result in I<r>.
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| 48 |
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| 49 | BN_from_montgomery() performs the Montgomery reduction I<r> = I<a>*R^-1.
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| 50 |
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| 51 | BN_to_montgomery() computes Mont(I<a>,R^2), i.e. I<a>*R.
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| 52 | Note that I<a> must be nonnegative and smaller than the modulus.
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| 53 |
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| 54 | For all functions, I<ctx> is a previously allocated B<BN_CTX> used for
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| 55 | temporary variables.
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| 56 |
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| 57 | =head1 RETURN VALUES
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| 58 |
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| 59 | BN_MONT_CTX_new() returns the newly allocated B<BN_MONT_CTX>, and NULL
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| 60 | on error.
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| 61 |
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| 62 | BN_MONT_CTX_free() has no return value.
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| 63 |
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| 64 | For the other functions, 1 is returned for success, 0 on error.
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| 65 | The error codes can be obtained by L<ERR_get_error(3)>.
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| 66 |
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| 67 | =head1 WARNINGS
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| 68 |
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| 69 | The inputs must be reduced modulo B<m>, otherwise the result will be
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| 70 | outside the expected range.
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| 71 |
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| 72 | =head1 SEE ALSO
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| 73 |
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| 74 | L<ERR_get_error(3)>, L<BN_add(3)>,
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| 75 | L<BN_CTX_new(3)>
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| 76 |
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| 77 | =head1 HISTORY
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| 78 |
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| 79 | BN_MONT_CTX_init() was removed in OpenSSL 1.1.0
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| 80 |
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| 81 | =head1 COPYRIGHT
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| 82 |
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| 83 | Copyright 2000-2020 The OpenSSL Project Authors. All Rights Reserved.
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| 84 |
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| 85 | Licensed under the OpenSSL license (the "License"). You may not use
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| 86 | this file except in compliance with the License. You can obtain a copy
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| 87 | in the file LICENSE in the source distribution or at
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| 88 | L<https://www.openssl.org/source/license.html>.
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| 89 |
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| 90 | =cut
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