BN_mod_mul_montgomery(3) — Subroutines

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() is called with suitable input, but they may be useful when several operations are performed using the same modulus.

The BN_MONT_CTX_new() function allocates and initializes a BN_MONT_CTX structure. The BN_MONT_CTX_init() function initializes an existing uninitialized BN_MONT_CTX.

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

The BN_MONT_CTX_copy() function copies the BN_MONT_CTX from to to.

The BN_MONT_CTX_free() function frees the components of the BN_MONT_CTX, and, if it was created by BN_MONT_CTX_new(), also the structure itself.

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

The BN_from_montgomery() function performs the Montgomery reduction r = a∗R^-1.

The BN_to_montgomery() function computes Mont(a,R^2), i.e. a∗R.

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

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

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

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

HISTORY

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

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

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