=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 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 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 structure. BN_MONT_CTX_init() initializes an existing uninitialized B. BN_MONT_CTX_set() sets up the I structure from the modulus I by precomputing its inverse and a value R. BN_MONT_CTX_copy() copies the B I to I. BN_MONT_CTX_free() frees the components of the B, and, if it was created by BN_MONT_CTX_new(), also the structure itself. BN_mod_mul_montgomery() computes Mont(I,I):=I*I*R^-1 and places the result in I. BN_from_montgomery() performs the Montgomery reduction I = I*R^-1. BN_to_montgomery() computes Mont(I,R^2), i.e. I*R. Note that I must be non-negative and smaller than the modulus. For all functions, I is a previously allocated B used for temporary variables. The B 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, 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. =head1 WARNING The inputs must be reduced modulo B, otherwise the result will be outside the expected range. =head1 SEE ALSO L, L, L, L =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