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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_mod_sqrt, 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); \& \& BIGNUM *BN_mod_sqrt(BIGNUM *in, BIGNUM *a, const BIGNUM *p, 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" \&\fBBN_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 \&\fBBN_sub()\fR subtracts \fIb\fR from \fIa\fR and places the result in \fIr\fR (\f(CW\*(C`r=a\-b\*(C'\fR). .PP \&\fBBN_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 \fBBN_lshift\fR\|(3). .PP \&\fBBN_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 \&\fBBN_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 \fBBN_rshift\fR\|(3). .PP \&\fBBN_mod()\fR corresponds to \fBBN_div()\fR with \fIdv\fR set to \fB\s-1NULL\s0\fR. .PP \&\fBBN_nnmod()\fR reduces \fIa\fR modulo \fIm\fR and places the non-negative remainder in \fIr\fR. .PP \&\fBBN_mod_add()\fR adds \fIa\fR to \fIb\fR modulo \fIm\fR and places the non-negative result in \fIr\fR. .PP \&\fBBN_mod_sub()\fR subtracts \fIb\fR from \fIa\fR modulo \fIm\fR and places the non-negative result in \fIr\fR. .PP \&\fBBN_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 \&\fBBN_mod_mul_montgomery\fR\|(3) and \&\fBBN_mod_mul_reciprocal\fR\|(3). .PP \&\fBBN_mod_sqr()\fR takes the square of \fIa\fR modulo \fBm\fR and places the result in \fIr\fR. .PP \&\fBBN_mod_sqrt()\fR returns the modular square root of \fIa\fR such that \&\f(CW\*(C`in^2 = a (mod p)\*(C'\fR. The modulus \fIp\fR must be a prime, otherwise an error or an incorrect \*(L"result\*(R" will be returned. The result is stored into \fIin\fR which can be \s-1NULL.\s0 The result will be newly allocated in that case. .PP \&\fBBN_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 \&\fBBN_mul()\fR. .PP \&\fBBN_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 \fBBN_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 \&\fBBN_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 \fBBN_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" The \fBBN_mod_sqrt()\fR returns the result (possibly incorrect if \fIp\fR is not a prime), or \s-1NULL.\s0 .PP For all remaining 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 \fBERR_get_error\fR\|(3). .\" Oracle has added the ARC stability level to this manual page .SH ATTRIBUTES See .BR attributes (7) for descriptions of the following attributes: .sp .TS box; cbp-1 | cbp-1 l | l . ATTRIBUTE TYPE ATTRIBUTE VALUE = Availability library/security/openssl = Stability Pass-through uncommitted .TE .PP .SH "SEE ALSO" .IX Header "SEE ALSO" \&\fBbn\fR\|(3), \fBERR_get_error\fR\|(3), \fBBN_CTX_new\fR\|(3), \&\fBBN_add_word\fR\|(3), \fBBN_set_bit\fR\|(3) .SH "HISTORY" .IX Header "HISTORY" \&\fBBN_add()\fR, \fBBN_sub()\fR, \fBBN_sqr()\fR, \fBBN_div()\fR, \fBBN_mod()\fR, \fBBN_mod_mul()\fR, \&\fBBN_mod_exp()\fR and \fBBN_gcd()\fR are available in all versions of SSLeay and OpenSSL. The \fIctx\fR argument to \fBBN_mul()\fR was added in SSLeay 0.9.1b. \fBBN_exp()\fR appeared in SSLeay 0.9.0. \&\fBBN_nnmod()\fR, \fBBN_mod_add()\fR, \fBBN_mod_sub()\fR, and \fBBN_mod_sqr()\fR were added in OpenSSL 0.9.7. .SH NOTES .\" Oracle has added source availability information to this manual page Source code for open source software components in Oracle Solaris can be found at https://www.oracle.com/downloads/opensource/solaris-source-code-downloads.html. This software was built from source available at https://github.com/oracle/solaris-userland. The original community source was downloaded from https://www.openssl.org/source/openssl-1.0.2zi.tar.gz. Further information about this software can be found on the open source community website at https://www.openssl.org/.