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 multipli-
cation
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 opera-
tions 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 unini-
tialized 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 struc-
ture 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.
MirOS BSD #10-current 2005-02-05 1
BN_MOD_MUL_MONTGOMERY(3) OpenSSL BN_MOD_MUL_MONTGOMERY(3)
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 VALUESBN_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 ALSObn(3), ERR_get_error(3), BN_add(3), BN_CTX_new(3)HISTORYBN_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.
MirOS BSD #10-current 2005-02-05 2
