New manpage.

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=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 BN_mod_exp(3) is called with suitable input,

but they may be useful when several operations are to be perfomed

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 B<mont> structure from the modulus B<m>

by precomputing its inverse and a value R.

BN_MONT_CTX_copy() copies the B<N_MONT_CTX> B<from> to B<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_mont() computes Mont(B<a>,B<b>):=B<a>*B<b>*R^-1 and places

the result in B<r>.

BN_from_montgomery() performs the Montgomery reduction B<r> = B<a>*R^-1.

BN_to_montgomery() computes Mont(B<a>,R^2).

For all functions, B<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 use_word;   /* 0 for word form, 1 for bignum form */

        int ri;         /* number of bits in R */

        BIGNUM RR;      /* R^2 (used to convert to Montgomery form) */

        BIGNUM N;       /* The modulus */

        BIGNUM Ni;      /* The inverse of N (bignum form) */

        BN_ULONG n0;    /* The inverse of N in word form */

        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 ERR_get_error(3).

=head1 SEE ALSO

bn(3), err(3), BN_add(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.

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