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=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