MirBSD manpage: BN_from_montgomery(3), BN_mod_mul_montgomery(3), BN_MONT_CTX_copy(3), BN_MONT_CTX_free(3), BN_MONT_CTX_init(3), BN_MONT_CTX_new(3), BN_MONT_CTX_set(3), BN_to_montgomery(3)



     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 multipli-


      #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);


     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 opera-
     tions 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 unini-
     tialized 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 struc-
     ture 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 =

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

MirBSD #10-current         2005-02-05                           1


     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.


     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

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


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


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


     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.

MirBSD #10-current         2005-02-05                           2

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