You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
101 lines
3.2 KiB
101 lines
3.2 KiB
=pod
|
|
|
|
=head1 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
|
|
|
|
=head1 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);
|
|
|
|
=head1 DESCRIPTION
|
|
|
|
These functions implement Montgomery multiplication. They are used
|
|
automatically when L<BN_mod_exp(3)|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 B<BN_MONT_CTX> structure.
|
|
BN_MONT_CTX_init() initializes an existing uninitialized B<BN_MONT_CTX>.
|
|
|
|
BN_MONT_CTX_set() sets up the I<mont> structure from the modulus I<m>
|
|
by precomputing its inverse and a value R.
|
|
|
|
BN_MONT_CTX_copy() copies the B<BN_MONT_CTX> I<from> to I<to>.
|
|
|
|
BN_MONT_CTX_free() frees the components of the B<BN_MONT_CTX>, and, if
|
|
it was created by BN_MONT_CTX_new(), also the structure itself.
|
|
|
|
BN_mod_mul_montgomery() computes Mont(I<a>,I<b>):=I<a>*I<b>*R^-1 and places
|
|
the result in I<r>.
|
|
|
|
BN_from_montgomery() performs the Montgomery reduction I<r> = I<a>*R^-1.
|
|
|
|
BN_to_montgomery() computes Mont(I<a>,R^2), i.e. I<a>*R.
|
|
Note that I<a> must be non-negative and smaller than the modulus.
|
|
|
|
For all functions, I<ctx> is a previously allocated B<BN_CTX> used for
|
|
temporary variables.
|
|
|
|
The B<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.
|
|
|
|
=head1 RETURN VALUES
|
|
|
|
BN_MONT_CTX_new() returns the newly allocated B<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 L<ERR_get_error(3)|ERR_get_error(3)>.
|
|
|
|
=head1 WARNING
|
|
|
|
The inputs must be reduced modulo B<m>, otherwise the result will be
|
|
outside the expected range.
|
|
|
|
=head1 SEE ALSO
|
|
|
|
L<bn(3)|bn(3)>, L<ERR_get_error(3)|ERR_get_error(3)>, L<BN_add(3)|BN_add(3)>,
|
|
L<BN_CTX_new(3)|BN_CTX_new(3)>
|
|
|
|
=head1 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.
|
|
|
|
=cut
|
|
|