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BN_MOD_MUL_MONTGOMERY(3)	    OpenSSL	      BN_MOD_MUL_MONTGOMERY(3)

NAME
       BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_free,
       BN_MONT_CTX_set,	BN_MONT_CTX_copy, BN_from_montgomery, BN_to_montgomery
       - Montgomery multiplication

SYNOPSIS
	#include <openssl/bn.h>

	BN_MONT_CTX *BN_MONT_CTX_new(void);
	void BN_MONT_CTX_free(BN_MONT_CTX *mont);

	int BN_MONT_CTX_set(BN_MONT_CTX	*mont, const BIGNUM *m,	BN_CTX *ctx);
	BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);

	int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a,	BIGNUM *b,
				  BN_MONT_CTX *mont, BN_CTX *ctx);

	int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
			       BN_CTX *ctx);

	int BN_to_montgomery(BIGNUM *r,	BIGNUM *a, BN_MONT_CTX *mont,
			     BN_CTX *ctx);

DESCRIPTION
       These functions implement Montgomery multiplication. They are used
       automatically when BN_mod_exp(3)	is called with suitable	input, but
       they may	be useful when several operations are to be performed using
       the same	modulus.

       BN_MONT_CTX_new() allocates and initializes a BN_MONT_CTX structure.

       BN_MONT_CTX_set() sets up the mont structure from the modulus m by
       precomputing its	inverse	and a value R.

       BN_MONT_CTX_copy() copies the BN_MONT_CTX from to to.

       BN_MONT_CTX_free() frees	the components of the BN_MONT_CTX, and,	if it
       was created by BN_MONT_CTX_new(), also the structure itself.  If	mont
       is NULL,	nothing	is done.

       BN_mod_mul_montgomery() computes	Mont(a,b):=a*b*R^-1 and	places the
       result in r.

       BN_from_montgomery() performs the Montgomery reduction r	= a*R^-1.

       BN_to_montgomery() computes Mont(a,R^2),	i.e. a*R.  Note	that a must be
       non-negative and	smaller	than the modulus.

       For all functions, ctx is a previously allocated	BN_CTX used for
       temporary variables.

RETURN VALUES
       BN_MONT_CTX_new() returns the newly allocated BN_MONT_CTX, and NULL on
       error.

       BN_MONT_CTX_free() has no return	value.

       For the other functions,	1 is returned for success, 0 on	error.	The
       error codes can be obtained by ERR_get_error(3).

WARNING
       The inputs must be reduced modulo m, otherwise the result will be
       outside the expected range.

SEE ALSO
       ERR_get_error(3), BN_add(3), BN_CTX_new(3)

HISTORY
       BN_MONT_CTX_init() was removed in OpenSSL 1.1.0

COPYRIGHT
       Copyright 2000-2017 The OpenSSL Project Authors.	All Rights Reserved.

       Licensed	under the OpenSSL license (the "License").  You	may not	use
       this file except	in compliance with the License.	 You can obtain	a copy
       in the file LICENSE in the source distribution or at
       <https://www.openssl.org/source/license.html>.

1.1.1a				  2018-11-20	      BN_MOD_MUL_MONTGOMERY(3)

NAME | SYNOPSIS | DESCRIPTION | RETURN VALUES | WARNING | SEE ALSO | HISTORY | COPYRIGHT

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