BN_mod_exp(3)

     BN_add(3)              0.9.6h (2002-09-25)              BN_add(3)

     NAME
          BN_add, BN_sub, BN_mul, BN_div, BN_sqr, BN_mod, BN_mod_mul,
          BN_exp, BN_mod_exp, BN_gcd - arithmetic operations on
          BIGNUMs

     SYNOPSIS
           #include <openssl/bn.h>

           int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);

           int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);

           int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);

           int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
                   BN_CTX *ctx);

           int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);

           int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);

           int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
                   BN_CTX *ctx);

           int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);

           int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
                   const BIGNUM *m, BN_CTX *ctx);

           int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);

     DESCRIPTION
          BN_add() adds a and b and places the result in r ("r=a+b").
          r may be the same BIGNUM as a or b.

          BN_sub() subtracts b from a and places the result in r
          ("r=a-b").

          BN_mul() multiplies a and b and places the result in r
          ("r=a*b").  r may be the same BIGNUM as a or b.  For
          multiplication by powers of 2, use BN_lshift(3).

          BN_div() divides a by d and places the result in dv and the
          remainder in rem ("dv=a/d, rem=a%d"). Either of dv and rem
          may be NULL, in which case the respective value is not
          returned.  For division by powers of 2, use BN_rshift(3).

          BN_sqr() takes the square of a and places the result in r
          ("r=a^2"). r and a may be the same BIGNUM.  This function is
          faster than BN_mul(r,a,a).

          BN_mod() find the remainder of a divided by m and places it

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     BN_add(3)              0.9.6h (2002-09-25)              BN_add(3)

          in rem ("rem=a%m").

          BN_mod_mul() multiplies a by b and finds the remainder when
          divided by m ("r=(a*b)%m"). r may be the same BIGNUM as a or
          b. For a more efficient algorithm, see
          BN_mod_mul_montgomery(3); for repeated computations using
          the same modulus, see BN_mod_mul_reciprocal(3).

          BN_exp() raises a to the p-th power and places the result in
          r ("r=a^p"). This function is faster than repeated
          applications of BN_mul().

          BN_mod_exp() computes a to the p-th power modulo m ("r=a^p %
          m"). This function uses less time and space than BN_exp().

          BN_gcd() computes the greatest common divisor of a and b and
          places the result in r. r may be the same BIGNUM as a or b.

          For all functions, ctx is a previously allocated BN_CTX used
          for temporary variables; see BN_CTX_new(3).

          Unless noted otherwise, the result BIGNUM must be different
          from the arguments.

     RETURN VALUES
          For all functions, 1 is returned for success, 0 on error.
          The return value should always be checked (e.g., "if
          (!BN_add(r,a,b)) goto err;").  The error codes can be
          obtained by ERR_get_error(3).

     SEE ALSO
          bn(3), ERR_get_error(3), BN_CTX_new(3), BN_add_word(3),
          BN_set_bit(3)

     HISTORY
          BN_add(), BN_sub(), BN_div(), BN_sqr(), BN_mod(),
          BN_mod_mul(), BN_mod_exp() and BN_gcd() are available in all
          versions of SSLeay and OpenSSL. The ctx argument to BN_mul()
          was added in SSLeay 0.9.1b. BN_exp() appeared in SSLeay
          0.9.0.

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