=pod =head1 NAME 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 =head1 SYNOPSIS #include 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); =head1 DESCRIPTION BN_add() adds I and I and places the result in I (C). I may be the same B as I or I. BN_sub() subtracts I from I and places the result in I (C). BN_mul() multiplies I and I and places the result in I (C). I may be the same B as I or I. For multiplication by powers of 2, use L. BN_sqr() takes the square of I and places the result in I (C). I and I may be the same B. This function is faster than BN_mul(r,a,a). BN_div() divides I by I and places the result in I and the remainder in I (C). Either of I and I may be B, in which case the respective value is not returned. The result is rounded towards zero; thus if I 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 I set to B. BN_nnmod() reduces I modulo I and places the non-negative remainder in I. BN_mod_add() adds I to I modulo I and places the non-negative result in I. BN_mod_sub() subtracts I from I modulo I and places the non-negative result in I. BN_mod_mul() multiplies I by I and finds the non-negative remainder respective to modulus I (C). I may be the same B as I or I. For more efficient algorithms for repeated computations using the same modulus, see L and L. BN_mod_sqr() takes the square of I modulo B and places the result in I. BN_exp() raises I to the I

-th power and places the result in I (C). This function is faster than repeated applications of BN_mul(). BN_mod_exp() computes I to the I

-th power modulo I (C). This function uses less time and space than BN_exp(). BN_gcd() computes the greatest common divisor of I and I and places the result in I. I may be the same B as I or I. For all functions, I is a previously allocated B used for temporary variables; see L. Unless noted otherwise, the result B must be different from the arguments. =head1 RETURN VALUES For all functions, 1 is returned for success, 0 on error. The return value should always be checked (e.g., C). The error codes can be obtained by L. =head1 SEE ALSO L, L, L, L, L =head1 HISTORY 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 I 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. =cut