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), 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.
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¶
BN_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 ALSO¶
bn(3),
ERR_get_error(3),
BN_add(3),
BN_CTX_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.