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) = 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. Warning: The inputs must be reduced modulo m, otherwise the result will be outside the expected range.

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() return no values. For the other functions, 1 is returned for success, 0 on error. The error codes can be obtained by ERR_get_error(3).

SEE ALSO

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