BN_MOD_MUL_MONTGOMERY(3)

NAME
BN_MONT_CTX_new, BN_MONT_CTX_init, BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy, BN_mod_mul_montgomery, 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. It is deprecated and dangerous: see CAVEATS.

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 a NULL pointer, no action occurs.

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 or NULL on error.

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

SEE ALSO
BN_add(3), BN_CTX_new(3), BN_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.

CAVEATS
BN_MONT_CTX_init() must not be called on a context that was used previously, or memory used by the embedded BIGNUM structures is leaked immediately. Besides, it must not be called on a context created with BN_MONT_CTX_new(), or the context itself will likely be leaked later. It can only be used on a static BN_MONT_CTX structure, on one located on the stack, or on one malloc(3)'ed manually, but all these options are discouraged because they will no longer work once BN_MONT_CTX is made opaque.