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

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);

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 performed using the same modulus.

       BN_MONT_CTX_new() allocates and initializes a BN_MONT_CTX structure.  BN_MONT_CTX_init()
       initializes an existing uninitialized BN_MONT_CTX.

       BN_MONT_CTX_set() sets up the mont structure from the modulus m by precomputing its
       inverse and a value R.

       BN_MONT_CTX_copy() copies the BN_MONT_CTX from to to.

       BN_MONT_CTX_free() frees the components of the BN_MONT_CTX, and, if it was created by
       BN_MONT_CTX_new(), also the structure itself.

       BN_mod_mul_montgomery() computes Mont(a,b):=a*b*R^-1 and places the result in r.

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

       BN_to_montgomery() computes Mont(a,R^2), i.e. a*R.  Note that a must be non-negative and
       smaller than the modulus.

       For all functions, ctx is a previously allocated BN_CTX used for temporary variables.

       The 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.

RETURN VALUES

       BN_MONT_CTX_new() returns the newly allocated 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).

WARNING

       The inputs must be reduced modulo m, otherwise the result will be outside the expected
       range.

SEE ALSO

       bn(3), ERR_get_error(3), BN_add(3), BN_CTX_new(3)

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.