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.\" Automatically generated by Pod::Man 2.27 (Pod::Simple 3.28) .\" .\" Standard preamble: .\" ======================================================================== .de Sp \" Vertical space (when we can't use .PP) .if t .sp .5v .if n .sp .. .de Vb \" Begin verbatim text .ft CW .nf .ne \\$1 .. .de Ve \" End verbatim text .ft R .fi .. .\" Set up some character translations and predefined strings. \(-- will .\" give an unbreakable dash, \(PI will give pi, \(L" will give a left .\" double quote, and \(R" will give a right double quote. \(C+ will .\" give a nicer C++. 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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=ab\(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=(ab) 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. Do not call this function when \fBm\fR is even and any of the parameters have the \&\fB\s-1BN_FLG_CONSTTIME\s0\fR flag set. .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.