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+.\" Automatically generated by Pod::Man version 1.15
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+.\" ======================================================================
+.\"
+.IX Title "BN_ADD 1"
+.TH BN_ADD 1 "perl v5.6.1" "2000-04-13" "User Contributed Perl Documentation"
+.UC
+.SH "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
+.SH "SYNOPSIS"
+.IX Header "SYNOPSIS"
+.Vb 1
+\& #include <openssl/bn.h>
+.Ve
+.Vb 1
+\& int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
+.Ve
+.Vb 1
+\& int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
+.Ve
+.Vb 1
+\& int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
+.Ve
+.Vb 2
+\& int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
+\& BN_CTX *ctx);
+.Ve
+.Vb 1
+\& int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
+.Ve
+.Vb 1
+\& int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
+.Ve
+.Vb 2
+\& int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
+\& BN_CTX *ctx);
+.Ve
+.Vb 1
+\& int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
+.Ve
+.Vb 2
+\& int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
+\& const BIGNUM *m, BN_CTX *ctx);
+.Ve
+.Vb 1
+\& int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
+.Ve
+.SH "DESCRIPTION"
+.IX Header "DESCRIPTION"
+\&\fIBN_add()\fR adds \fBa\fR and \fBb\fR and places the result in \fBr\fR (\f(CW\*(C`r=a+b\*(C'\fR).
+\&\fBr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fBa\fR or \fBb\fR.
+.PP
+\&\fIBN_sub()\fR subtracts \fBb\fR from \fBa\fR and places the result in \fBr\fR (\f(CW\*(C`r=a\-b\*(C'\fR).
+.PP
+\&\fIBN_mul()\fR multiplies \fBa\fR and \fBb\fR and places the result in \fBr\fR (\f(CW\*(C`r=a*b\*(C'\fR).
+\&\fBr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fBa\fR or \fBb\fR.
+For multiplication by powers of 2, use BN_lshift(3).
+.PP
+\&\fIBN_div()\fR divides \fBa\fR by \fBd\fR and places the result in \fBdv\fR and the
+remainder in \fBrem\fR (\f(CW\*(C`dv=a/d, rem=a%d\*(C'\fR). Either of \fBdv\fR and \fBrem\fR may
+be \s-1NULL\s0, in which case the respective value is not returned.
+For division by powers of 2, use \fIBN_rshift\fR\|(3).
+.PP
+\&\fIBN_sqr()\fR takes the square of \fBa\fR and places the result in \fBr\fR
+(\f(CW\*(C`r=a^2\*(C'\fR). \fBr\fR and \fBa\fR may be the same \fB\s-1BIGNUM\s0\fR.
+This function is faster than BN_mul(r,a,a).
+.PP
+\&\fIBN_mod()\fR find the remainder of \fBa\fR divided by \fBm\fR and places it in
+\&\fBrem\fR (\f(CW\*(C`rem=a%m\*(C'\fR).
+.PP
+\&\fIBN_mod_mul()\fR multiplies \fBa\fR by \fBb\fR and finds the remainder when
+divided by \fBm\fR (\f(CW\*(C`r=(a*b)%m\*(C'\fR). \fBr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fBa\fR
+or \fBb\fR. For a more efficient algorithm, see
+BN_mod_mul_montgomery(3); for repeated
+computations using the same modulus, see BN_mod_mul_reciprocal(3).
+.PP
+\&\fIBN_exp()\fR raises \fBa\fR to the \fBp\fR\-th power and places the result in \fBr\fR
+(\f(CW\*(C`r=a^p\*(C'\fR). This function is faster than repeated applications of
+\&\fIBN_mul()\fR.
+.PP
+\&\fIBN_mod_exp()\fR computes \fBa\fR to the \fBp\fR\-th power modulo \fBm\fR (\f(CW\*(C`r=a^p %
+m\*(C'\fR). This function uses less time and space than \fIBN_exp()\fR.
+.PP
+\&\fIBN_gcd()\fR computes the greatest common divisor of \fBa\fR and \fBb\fR and
+places the result in \fBr\fR. \fBr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fBa\fR or
+\&\fBb\fR.
+.PP
+For all functions, \fBctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
+temporary variables; see BN_CTX_new(3).
+.PP
+Unless noted otherwise, the result \fB\s-1BIGNUM\s0\fR must be different from
+the arguments.
+.SH "RETURN VALUES"
+.IX Header "RETURN VALUES"
+For all functions, 1 is returned for success, 0 on error. The return
+value should always be checked (e.g., \f(CW\*(C`if (!BN_add(r,a,b)) goto err;\*(C'\fR).
+The error codes can be obtained by ERR_get_error(3).
+.SH "SEE ALSO"
+.IX Header "SEE ALSO"
+bn(3), err(3), BN_CTX_new(3),
+BN_add_word(3), BN_set_bit(3)
+.SH "HISTORY"
+.IX Header "HISTORY"
+\&\fIBN_add()\fR, \fIBN_sub()\fR, \fIBN_div()\fR, \fIBN_sqr()\fR, \fIBN_mod()\fR, \fIBN_mod_mul()\fR,
+\&\fIBN_mod_exp()\fR and \fIBN_gcd()\fR are available in all versions of SSLeay and
+OpenSSL. The \fBctx\fR argument to \fIBN_mul()\fR was added in SSLeay
+0.9.1b. \fIBN_exp()\fR appeared in SSLeay 0.9.0.
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