=pod=head1 NAMEBN_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 DESCRIPTIONThese functions implement Montgomery multiplication. They are usedautomatically 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 performedusing 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, ifit 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 placesthe 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 fortemporary 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 VALUESBN_MONT_CTX_new() returns the newly allocated B<BN_MONT_CTX>, and NULLon 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 WARNINGThe inputs must be reduced modulo B<m>, otherwise the result will beoutside the expected range.=head1 SEE ALSOL<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 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.=cut