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Title "BN_add 3" For nroff, turn off justification. Always turn off hyphenation; it makes
way too many mistakes in technical documents.
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 Header "SYNOPSIS" .Vb 1 #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); .Ve Header "DESCRIPTION" \fIBN_add() adds a and b and places the result in r (\*(C`r=a+b\*(C'). \fIr may be the same \s-1BIGNUM\s0 as a or b.

\fIBN_sub() subtracts b from a and places the result in r (\*(C`r=a-b\*(C').

\fIBN_mul() multiplies a and b and places the result in r (\*(C`r=a*b\*(C'). \fIr may be the same \s-1BIGNUM\s0 as a or b. For multiplication by powers of 2, use BN_lshift\|(3).

\fIBN_sqr() takes the square of a and places the result in r (\*(C`r=a^2\*(C'). r and a may be the same \s-1BIGNUM\s0. This function is faster than BN_mul(r,a,a).

\fIBN_div() divides a by d and places the result in dv and the remainder in rem (\*(C`dv=a/d, rem=a%d\*(C'). Either of dv and rem may be \s-1NULL\s0, 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).

\fIBN_mod() corresponds to BN_div() with dv set to \s-1NULL\s0.

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

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

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

\fIBN_mod_mul() multiplies a by b and finds the non-negative remainder respective to modulus m (\*(C`r=(a*b) mod m\*(C'). r may be the same \s-1BIGNUM\s0 as a or b. For more efficient algorithms for repeated computations using the same modulus, see \fIBN_mod_mul_montgomery\|(3) and \fIBN_mod_mul_reciprocal\|(3).

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

\fIBN_exp() raises a to the p-th power and places the result in r (\*(C`r=a^p\*(C'). This function is faster than repeated applications of \fIBN_mul().

\fIBN_mod_exp() computes a to the p-th power modulo m (\*(C`r=a^p % m\*(C'). This function uses less time and space than BN_exp().

\fIBN_gcd() computes the greatest common divisor of a and b and places the result in r. r may be the same \s-1BIGNUM\s0 as a or \fIb.

For all functions, ctx is a previously allocated \s-1BN_CTX\s0 used for temporary variables; see BN_CTX_new\|(3).

Unless noted otherwise, the result \s-1BIGNUM\s0 must be different from the arguments.

Header "RETURN VALUES" For all functions, 1 is returned for success, 0 on error. The return value should always be checked (e.g., \*(C`if (!BN_add(r,a,b)) goto err;\*(C'). The error codes can be obtained by ERR_get_error\|(3). Header "SEE ALSO" \fIbn\|(3), ERR_get_error\|(3), BN_CTX_new\|(3), \fIBN_add_word\|(3), BN_set_bit\|(3) Header "HISTORY" \fIBN_add(), BN_sub(), BN_sqr(), BN_div(), BN_mod(), BN_mod_mul(), \fIBN_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. \fIBN_nnmod(), BN_mod_add(), BN_mod_sub(), and BN_mod_sqr() were added in OpenSSL 0.9.7.