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
#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);
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 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.
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.
The inputs must be reduced modulo m, otherwise the result will be outside the expected range.
void BN_MONT_CTX_init(BN_MONT_CTX *c);
BN_MONT_CTX_init() is no longer available as of OpenSSL 1.1.0. It was used to initialize an existing uninitialized BN_MONT_CTX. Typically this would be done as follows:
BN_MONT_CTX ctx; BN_MONT_CTX_init(&ctx);
Instead applications should create a BN_MONT_CTX structure using BN_MONT_CTX_new:
BN_MONT_CTX *ctx; ctx = BN_MONT_CTX_new(); if(!ctx) /* handle error */ ... BN_MONT_CTX_free(ctx);
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. BN_MONT_CTX_init was removed in OpenSSL 1.1.0