BNmodmulmontgomery(3) OpenSSL BNmodmulmontgomery(3)

NAME
       BNmodmulmontgomery, BNMONTCTXnew, BNMONTCTXinit,
       BNMONTCTXfree, BNMONTCTXset, BNMONTCTXcopy,
       BNfrommontgomery, BNtomontgomery - Montgomery multiplication

SYNOPSIS
        #include 

        BNMONTCTX *BNMONTCTXnew(void);
        void BNMONTCTXinit(BNMONTCTX *ctx);
        void BNMONTCTXfree(BNMONTCTX *mont);

        int BNMONTCTXset(BNMONTCTX *mont, const BIGNUM *m, BNCTX *ctx);
        BNMONTCTX *BNMONTCTXcopy(BNMONTCTX *to, BNMONTCTX *from);

        int BNmodmulmontgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
                BNMONTCTX *mont, BNCTX *ctx);

        int BNfrommontgomery(BIGNUM *r, BIGNUM *a, BNMONTCTX *mont,
                BNCTX *ctx);

        int BNtomontgomery(BIGNUM *r, BIGNUM *a, BNMONTCTX *mont,
                BNCTX *ctx);

DESCRIPTION
       These functions implement Montgomery multiplication. They are used
       automatically when BNmodexp(3) is called with suitable input, but
       they may be useful when several operations are to be performed using
       the same modulus.

       BNMONTCTXnew() allocates and initializes a BBNNMMOONNTTCCTTXX structure.
       BNMONTCTXinit() initializes an existing uninitialized BBNNMMOONNTTCCTTXX.

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

       BNMONTCTXcopy() copies the BBNNMMOONNTTCCTTXX from to to.

       BNMONTCTXfree() frees the components of the BBNNMMOONNTTCCTTXX, and, if it
       was created by BNMONTCTXnew(), also the structure itself.

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

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

       BNtomontgomery() 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 BBNNCCTTXX used for
       temporary variables.

       The BBNNMMOONNTTCCTTXX structure is defined as follows:

        typedef struct bnmontctxst
               {
               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) */
               BNULONG n0;    /* least significant word of Ni */
               int flags;
               } BNMONTCTX;

       BNtomontgomery() is a macro.

RETURN VALUES
       BNMONTCTXnew() returns the newly allocated BBNNMMOONNTTCCTTXX, and NULL on
       error.

       BNMONTCTXinit() and BNMONTCTXfree() have no return values.

       For the other functions, 1 is returned for success, 0 on error.  The
       error codes can be obtained by ERRgeterror(3).

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

SEE ALSO
       bn(3), ERRgeterror(3), BNadd(3), BNCTXnew(3)

HISTORY       BNMONTCTXnew(), BNMONTCTXfree(), BNMONTCTXset(),
       BNmodmulmontgomery(), BNfrommontgomery() and BNtomontgomery()
       are available in all versions of SSLeay and OpenSSL.

       BNMONTCTXinit() and BNMONTCTXcopy() were added in SSLeay 0.9.1b.



0.9.7l                            2002-09-25          BNmodmulmontgomery(3)