NAME    [Toc]    [Back]

       BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod,
       BN_mod_add, BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp,
       BN_mod_exp, BN_gcd - arithmetic operations on BIGNUMs

SYNOPSIS    [Toc]    [Back]

        #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_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);

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

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

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

        int BN_mod_add(BIGNUM *r, BIGNUM  *a,  BIGNUM  *b,  const
BIGNUM *m,
                BN_CTX *ctx);

        int  BN_mod_sub(BIGNUM  *r,  BIGNUM  *a, BIGNUM *b, const
BIGNUM *m,
                BN_CTX *ctx);

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

        int  BN_mod_sqr(BIGNUM  *r,  BIGNUM  *a, 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    [Toc]    [Back]

       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_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_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.  The result is rounded towards zero; thus if a
       is negative, the remainder will be zero or negative.  For
       division by powers of 2, use BN_rshift(3).

       BN_mod() corresponds to BN_div() with dv set to NULL.

       BN_nnmod() reduces a modulo m and places the non-negative
       remainder in r.

       BN_mod_add() adds a to b modulo m and places the non-negative
 result in r.

       BN_mod_sub() subtracts b from a modulo m and places the
       non-negative result in r.

       BN_mod_mul() multiplies a by b and finds the non-negative
       remainder respective to modulus m ("r=(a*b) mod m"). r may
       be the same BIGNUM as a or b. For more efficient algorithms
 for repeated computations using the same modulus,
       see BN_mod_mul_montgomery(3) and BN_mod_mul_reciprocal(3).

       BN_mod_sqr() takes the square of a modulo m and places the
       result in r.

       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    [Toc]    [Back]

       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    [Toc]    [Back]

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

HISTORY    [Toc]    [Back]

       BN_add(), BN_sub(), BN_sqr(), BN_div(), 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.  BN_nnmod(), BN_mod_add(), BN_mod_sub(), and
       BN_mod_sqr() were added in OpenSSL 0.9.7.


OpenBSD 3.6                 2002-05-14                          3