BN_mod_mul_montgomery(3)					      OpenSSL						  BN_mod_mul_montgomery(3)

NAME

       BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init, 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_init(BN_MONT_CTX *ctx);
	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_init() initializes an existing uninitialized BN_MONT_CTX.

       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.

       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.

       The BN_MONT_CTX structure is defined as follows:

	typedef struct bn_mont_ctx_st
	       {
	       int ri;	       /* number of bits in R */
	       BIGNUM RR;      /* R^2 (used to convert to Montgomery form) */
	       BIGNUM N;       /* The modulus */
	       BIGNUM Ni;      /* R*(1/R mod N) - N*Ni = 1
				* (Ni is only stored for bignum algorithm) */
	       BN_ULONG n0;    /* least significant word of Ni */
	       int flags;
	       } BN_MONT_CTX;

       BN_to_montgomery() is a macro.

RETURN VALUES

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

       BN_MONT_CTX_init() and BN_MONT_CTX_free() have no return values.

       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

       bn(3), ERR_get_error(3), BN_add(3), BN_CTX_new(3)

HISTORY

       BN_MONT_CTX_new(), BN_MONT_CTX_free(), BN_MONT_CTX_set(), BN_mod_mul_montgomery(), BN_from_montgomery() and BN_to_montgomery() are
       available in all versions of SSLeay and OpenSSL.

       BN_MONT_CTX_init() and BN_MONT_CTX_copy() were added in SSLeay 0.9.1b.

1.0.1e								    2013-02-11						  BN_mod_mul_montgomery(3)