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+.\" ========================================================================
+.\"
+.IX Title "BN_add 3"
+.TH BN_add 3 "2014-10-15" "1.0.1j" "OpenSSL"
+.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
+.\" way too many mistakes in technical documents.
+.if n .ad l
+.nh
+.SH "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
+.SH "SYNOPSIS"
+.IX 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
+.SH "DESCRIPTION"
+.IX Header "DESCRIPTION"
+\&\fIBN_add()\fR adds \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CW\*(C`r=a+b\*(C'\fR).
+\&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
+.PP
+\&\fIBN_sub()\fR subtracts \fIb\fR from \fIa\fR and places the result in \fIr\fR (\f(CW\*(C`r=a\-b\*(C'\fR).
+.PP
+\&\fIBN_mul()\fR multiplies \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CW\*(C`r=a*b\*(C'\fR).
+\&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
+For multiplication by powers of 2, use \fIBN_lshift\fR\|(3).
+.PP
+\&\fIBN_sqr()\fR takes the square of \fIa\fR and places the result in \fIr\fR
+(\f(CW\*(C`r=a^2\*(C'\fR). \fIr\fR and \fIa\fR may be the same \fB\s-1BIGNUM\s0\fR.
+This function is faster than BN_mul(r,a,a).
+.PP
+\&\fIBN_div()\fR divides \fIa\fR by \fId\fR and places the result in \fIdv\fR and the
+remainder in \fIrem\fR (\f(CW\*(C`dv=a/d, rem=a%d\*(C'\fR). Either of \fIdv\fR and \fIrem\fR may
+be \fB\s-1NULL\s0\fR, in which case the respective value is not returned.
+The result is rounded towards zero; thus if \fIa\fR is negative, the
+remainder will be zero or negative.
+For division by powers of 2, use \fIBN_rshift\fR\|(3).
+.PP
+\&\fIBN_mod()\fR corresponds to \fIBN_div()\fR with \fIdv\fR set to \fB\s-1NULL\s0\fR.
+.PP
+\&\fIBN_nnmod()\fR reduces \fIa\fR modulo \fIm\fR and places the non-negative
+remainder in \fIr\fR.
+.PP
+\&\fIBN_mod_add()\fR adds \fIa\fR to \fIb\fR modulo \fIm\fR and places the non-negative
+result in \fIr\fR.
+.PP
+\&\fIBN_mod_sub()\fR subtracts \fIb\fR from \fIa\fR modulo \fIm\fR and places the
+non-negative result in \fIr\fR.
+.PP
+\&\fIBN_mod_mul()\fR multiplies \fIa\fR by \fIb\fR and finds the non-negative
+remainder respective to modulus \fIm\fR (\f(CW\*(C`r=(a*b) mod m\*(C'\fR). \fIr\fR may be
+the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR. For more efficient algorithms for
+repeated computations using the same modulus, see
+\&\fIBN_mod_mul_montgomery\fR\|(3) and
+\&\fIBN_mod_mul_reciprocal\fR\|(3).
+.PP
+\&\fIBN_mod_sqr()\fR takes the square of \fIa\fR modulo \fBm\fR and places the
+result in \fIr\fR.
+.PP
+\&\fIBN_exp()\fR raises \fIa\fR to the \fIp\fR\-th power and places the result in \fIr\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 \fIa\fR to the \fIp\fR\-th power modulo \fIm\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 \fIa\fR and \fIb\fR and
+places the result in \fIr\fR. \fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or
+\&\fIb\fR.
+.PP
+For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
+temporary variables; see \fIBN_CTX_new\fR\|(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 \fIERR_get_error\fR\|(3).
+.SH "SEE ALSO"
+.IX Header "SEE ALSO"
+\&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIBN_CTX_new\fR\|(3),
+\&\fIBN_add_word\fR\|(3), \fIBN_set_bit\fR\|(3)
+.SH "HISTORY"
+.IX Header "HISTORY"
+\&\fIBN_add()\fR, \fIBN_sub()\fR, \fIBN_sqr()\fR, \fIBN_div()\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 \fIctx\fR argument to \fIBN_mul()\fR was added in SSLeay
+0.9.1b. \fIBN_exp()\fR appeared in SSLeay 0.9.0.
+\&\fIBN_nnmod()\fR, \fIBN_mod_add()\fR, \fIBN_mod_sub()\fR, and \fIBN_mod_sqr()\fR were added in
+OpenSSL 0.9.7.