.rn '' }`
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'''     Set up \*(-- to give an unbreakable dash;
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'''     Bell System Logo is used as a dummy character.
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.ie n \{\
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.\"	If the F register is turned on, we'll generate
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.\"	Of course, you have to process the output yourself
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.TH BN_add 3 "0.9.7d" "2/Sep/2004" "OpenSSL"
.UC
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.rm #[ #] #H #V #F C
.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"
.PP
.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 1
\& int BN_sqr(BIGNUM *r, BIGNUM *a, 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_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
.Ve
.Vb 1
\& int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
.Ve
.Vb 2
\& int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
\&         BN_CTX *ctx);
.Ve
.Vb 2
\& int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
\&         BN_CTX *ctx);
.Ve
.Vb 2
\& int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
\&         BN_CTX *ctx);
.Ve
.Vb 1
\& int BN_mod_sqr(BIGNUM *r, BIGNUM *a, 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"
\fIBN_add()\fR adds \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CWr=a+b\fR).
\fIr\fR may be the same \fBBIGNUM\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(CWr=a-b\fR).
.PP
\fIBN_mul()\fR multiplies \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CWr=a*b\fR).
\fIr\fR may be the same \fBBIGNUM\fR as \fIa\fR or \fIb\fR.
For multiplication by powers of 2, use BN_lshift(3).
.PP
\fIBN_sqr()\fR takes the square of \fIa\fR and places the result in \fIr\fR
(\f(CWr=a^2\fR). \fIr\fR and \fIa\fR may be the same \fBBIGNUM\fR.
This function is faster than \fIBN_mul\fR\|(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(CWdv=a/d, rem=a%d\fR). Either of \fIdv\fR and \fIrem\fR may
be \fBNULL\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 \fBNULL\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(CWr=(a*b) mod m\fR). \fIr\fR may be
the same \fBBIGNUM\fR as \fIa\fR or \fIb\fR. For more efficient algorithms for
repeated computations using the same modulus, see
BN_mod_mul_montgomery(3) and
BN_mod_mul_reciprocal(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(CWr=a^p\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(CWr=a^p %
m\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 \fBBIGNUM\fR as \fIa\fR or
\fIb\fR.
.PP
For all functions, \fIctx\fR is a previously allocated \fBBN_CTX\fR used for
temporary variables; see BN_CTX_new(3).
.PP
Unless noted otherwise, the result \fBBIGNUM\fR must be different from
the arguments.
.SH "RETURN VALUES"
For all functions, 1 is returned for success, 0 on error. The return
value should always be checked (e.g., \f(CWif (!BN_add(r,a,b)) goto err;\fR).
The error codes can be obtained by ERR_get_error(3).
.SH "SEE ALSO"
bn(3), ERR_get_error(3), BN_CTX_new(3),
BN_add_word(3), BN_set_bit(3)
.SH "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.

.rn }` ''
.IX Title "BN_add 3"
.IX 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"

.IX Header "NAME"

.IX Header "SYNOPSIS"

.IX Header "DESCRIPTION"

.IX Header "RETURN VALUES"

.IX Header "SEE ALSO"

.IX Header "HISTORY"