.\" $OpenBSD: BN_add.3,v 1.4 2016/11/20 15:57:50 schwarze Exp $ .\" OpenSSL b97fdb57 Nov 11 09:33:09 2016 +0100 .\" .\" This file was written by Ulf Moeller .\" and Bodo Moeller . .\" Copyright (c) 2000, 2001, 2015 The OpenSSL Project. All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions .\" are met: .\" .\" 1. Redistributions of source code must retain the above copyright .\" notice, this list of conditions and the following disclaimer. .\" .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in .\" the documentation and/or other materials provided with the .\" distribution. .\" .\" 3. 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IN NO EVENT SHALL THE OpenSSL PROJECT OR .\" ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, .\" SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT .\" NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; .\" LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) .\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, .\" STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) .\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED .\" OF THE POSSIBILITY OF SUCH DAMAGE. .\" .Dd $Mdocdate: November 20 2016 $ .Dt BN_ADD 3 .Os .Sh NAME .Nm BN_add , .Nm BN_sub , .Nm BN_mul , .Nm BN_sqr , .Nm BN_div , .Nm BN_mod , .Nm BN_nnmod , .Nm BN_mod_add , .Nm BN_mod_sub , .Nm BN_mod_mul , .Nm BN_mod_sqr , .Nm BN_exp , .Nm BN_mod_exp , .Nm BN_gcd .Nd arithmetic operations on BIGNUMs .Sh SYNOPSIS .In openssl/bn.h .Ft int .Fo BN_add .Fa "BIGNUM *r" .Fa "const BIGNUM *a" .Fa "const BIGNUM *b" .Fc .Ft int .Fo BN_sub .Fa "BIGNUM *r" .Fa "const BIGNUM *a" .Fa "const BIGNUM *b" .Fc .Ft int .Fo BN_mul .Fa "BIGNUM *r" .Fa "BIGNUM *a" .Fa "BIGNUM *b" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo BN_sqr .Fa "BIGNUM *r" .Fa "BIGNUM *a" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo BN_div .Fa "BIGNUM *dv" .Fa "BIGNUM *rem" .Fa "const BIGNUM *a" .Fa "const BIGNUM *d" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo BN_mod .Fa "BIGNUM *rem" .Fa "const BIGNUM *a" .Fa "const BIGNUM *m" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo BN_nnmod .Fa "BIGNUM *r" .Fa "const BIGNUM *a" .Fa "const BIGNUM *m" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo BN_mod_add .Fa "BIGNUM *r" .Fa "BIGNUM *a" .Fa "BIGNUM *b" .Fa "const BIGNUM *m" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo BN_mod_sub .Fa "BIGNUM *r" .Fa "BIGNUM *a" .Fa "BIGNUM *b" .Fa "const BIGNUM *m" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo BN_mod_mul .Fa "BIGNUM *r" .Fa "BIGNUM *a" .Fa "BIGNUM *b" .Fa "const BIGNUM *m" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo BN_mod_sqr .Fa "BIGNUM *r" .Fa "BIGNUM *a" .Fa "const BIGNUM *m" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo BN_exp .Fa "BIGNUM *r" .Fa "BIGNUM *a" .Fa "BIGNUM *p" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo BN_mod_exp .Fa "BIGNUM *r" .Fa "BIGNUM *a" .Fa "const BIGNUM *p" .Fa "const BIGNUM *m" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo BN_gcd .Fa "BIGNUM *r" .Fa "BIGNUM *a" .Fa "BIGNUM *b" .Fa "BN_CTX *ctx" .Fc .Sh DESCRIPTION .Fn BN_add adds .Fa a and .Fa b and places the result in .Fa r .Pq Li r=a+b . .Fa r may be the same .Vt BIGNUM as .Fa a or .Fa b . .Pp .Fn BN_sub subtracts .Fa b from .Fa a and places the result in .Fa r .Pq Li r=a-b . .Fa r may be the same .Vt BIGNUM as .Fa a or .Fa b . .Pp .Fn BN_mul multiplies .Fa a and .Fa b and places the result in .Fa r .Pq Li r=a*b . .Fa r may be the same .Vt BIGNUM as .Fa a or .Fa b . For multiplication by powers of 2, use .Xr BN_lshift 3 . .Pp .Fn BN_sqr takes the square of .Fa a and places the result in .Fa r .Pq Li r=a^2 . .Fa r and .Fa a may be the same .Vt BIGNUM . This function is faster than .Fn BN_mul r a a . .Pp .Fn BN_div divides .Fa a by .Fa d and places the result in .Fa dv and the remainder in .Fa rem .Pq Li dv=a/d , rem=a%d . Either of .Fa dv and .Fa rem may be .Dv NULL , in which case the respective value is not returned. The result is rounded towards zero; thus if .Fa a is negative, the remainder will be zero or negative. For division by powers of 2, use .Fn BN_rshift 3 . .Pp .Fn BN_mod corresponds to .Fn BN_div with .Fa dv set to .Dv NULL . .Pp .Fn BN_nnmod reduces .Fa a modulo .Fa m and places the non-negative remainder in .Fa r . .Pp .Fn BN_mod_add adds .Fa a to .Fa b modulo .Fa m and places the non-negative result in .Fa r . .Pp .Fn BN_mod_sub subtracts .Fa b from .Fa a modulo .Fa m and places the non-negative result in .Fa r . .Pp .Fn BN_mod_mul multiplies .Fa a by .Fa b and finds the non-negative remainder respective to modulus .Fa m .Pq Li r=(a*b)%m . .Fa r may be the same .Vt BIGNUM as .Fa a or .Fa b . For more efficient algorithms for repeated computations using the same modulus, see .Xr BN_mod_mul_montgomery 3 and .Xr BN_mod_mul_reciprocal 3 . .Pp .Fn BN_mod_sqr takes the square of .Fa a modulo .Fa m and places the result in .Fa r . .Pp .Fn BN_exp raises .Fa a to the .Fa p Ns -th power and places the result in .Fa r .Pq Li r=a^p . This function is faster than repeated applications of .Fn BN_mul . .Pp .Fn BN_mod_exp computes .Fa a to the .Fa p Ns -th power modulo .Fa m .Pq Li r=(a^p)%m . This function uses less time and space than .Fn BN_exp . .Pp .Fn BN_gcd computes the greatest common divisor of .Fa a and .Fa b and places the result in .Fa r . .Fa r may be the same .Vt BIGNUM as .Fa a or .Fa b . .Pp For all functions, .Fa ctx is a previously allocated .Vt BN_CTX used for temporary variables; see .Xr BN_CTX_new 3 . .Pp Unless noted otherwise, the result .Vt BIGNUM 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, for example: .Pp .Dl if (!BN_add(r,a,b)) goto err; .Pp The error codes can be obtained by .Xr ERR_get_error 3 . .Sh SEE ALSO .Xr bn 3 , .Xr BN_add_word 3 , .Xr BN_CTX_new 3 , .Xr BN_set_bit 3 , .Xr BN_set_negative 3 , .Xr ERR_get_error 3 .Sh HISTORY .Fn BN_add , .Fn BN_sub , .Fn BN_sqr , .Fn BN_div , .Fn BN_mod , .Fn BN_mod_mul , .Fn BN_mod_exp , and .Fn BN_gcd are available in all versions of SSLeay and OpenSSL. The .Fa ctx argument to .Fn BN_mul was added in SSLeay 0.9.1b. .Fn BN_exp appeared in SSLeay 0.9.0. .Fn BN_nnmod , .Fn BN_mod_add , .Fn BN_mod_sub , and .Fn BN_mod_sqr were added in OpenSSL 0.9.7.