BN_mod_mul_montgomery(3)

     BN_mod_mul_montgomery(30.9.6h (2002-09-25BN_mod_mul_montgomery(3)

     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.

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     BN_mod_mul_montgomery(30.9.6h (2002-09-25BN_mod_mul_montgomery(3)

          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).

     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.

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