253 lines
8.8 KiB
Groff
Executable File
253 lines
8.8 KiB
Groff
Executable File
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.\" ========================================================================
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.\"
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.IX Title "BN_ADD 3"
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.TH BN_ADD 3 "2020-03-02" "3.0.0-dev" "OpenSSL"
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.\" For nroff, turn off justification. Always turn off hyphenation; it makes
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.\" way too many mistakes in technical documents.
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.if n .ad l
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.nh
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.SH "NAME"
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BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add,
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BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd \-
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arithmetic operations on BIGNUMs
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.SH "SYNOPSIS"
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.IX Header "SYNOPSIS"
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.Vb 1
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\& #include <openssl/bn.h>
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\&
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\& int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
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\&
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\& int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
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\&
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\& int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
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\&
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\& int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
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\&
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\& int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
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\& BN_CTX *ctx);
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\&
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\& int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
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\&
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\& int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
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\&
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\& int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
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\& BN_CTX *ctx);
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\&
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\& int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
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\& BN_CTX *ctx);
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\&
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\& int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
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\& BN_CTX *ctx);
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\&
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\& int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
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\&
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\& int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
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\&
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\& int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
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\& const BIGNUM *m, BN_CTX *ctx);
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\&
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\& int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
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.Ve
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.SH "DESCRIPTION"
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.IX Header "DESCRIPTION"
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\&\fIBN_add()\fR adds \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CW\*(C`r=a+b\*(C'\fR).
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\&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
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.PP
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\&\fIBN_sub()\fR subtracts \fIb\fR from \fIa\fR and places the result in \fIr\fR (\f(CW\*(C`r=a\-b\*(C'\fR).
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\&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
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.PP
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\&\fIBN_mul()\fR multiplies \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CW\*(C`r=a*b\*(C'\fR).
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\&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
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For multiplication by powers of 2, use \fIBN_lshift\fR\|(3).
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.PP
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\&\fIBN_sqr()\fR takes the square of \fIa\fR and places the result in \fIr\fR
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(\f(CW\*(C`r=a^2\*(C'\fR). \fIr\fR and \fIa\fR may be the same \fB\s-1BIGNUM\s0\fR.
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This function is faster than BN_mul(r,a,a).
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.PP
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\&\fIBN_div()\fR divides \fIa\fR by \fId\fR and places the result in \fIdv\fR and the
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remainder in \fIrem\fR (\f(CW\*(C`dv=a/d, rem=a%d\*(C'\fR). Either of \fIdv\fR and \fIrem\fR may
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be \fB\s-1NULL\s0\fR, in which case the respective value is not returned.
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The result is rounded towards zero; thus if \fIa\fR is negative, the
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remainder will be zero or negative.
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For division by powers of 2, use \fIBN_rshift\fR\|(3).
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.PP
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\&\fIBN_mod()\fR corresponds to \fIBN_div()\fR with \fIdv\fR set to \fB\s-1NULL\s0\fR.
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.PP
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\&\fIBN_nnmod()\fR reduces \fIa\fR modulo \fIm\fR and places the non-negative
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remainder in \fIr\fR.
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.PP
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\&\fIBN_mod_add()\fR adds \fIa\fR to \fIb\fR modulo \fIm\fR and places the non-negative
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result in \fIr\fR.
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.PP
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\&\fIBN_mod_sub()\fR subtracts \fIb\fR from \fIa\fR modulo \fIm\fR and places the
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non-negative result in \fIr\fR.
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.PP
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\&\fIBN_mod_mul()\fR multiplies \fIa\fR by \fIb\fR and finds the non-negative
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remainder respective to modulus \fIm\fR (\f(CW\*(C`r=(a*b) mod m\*(C'\fR). \fIr\fR may be
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the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR. For more efficient algorithms for
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repeated computations using the same modulus, see
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\&\fIBN_mod_mul_montgomery\fR\|(3) and
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\&\fIBN_mod_mul_reciprocal\fR\|(3).
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.PP
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\&\fIBN_mod_sqr()\fR takes the square of \fIa\fR modulo \fBm\fR and places the
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result in \fIr\fR.
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.PP
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\&\fIBN_exp()\fR raises \fIa\fR to the \fIp\fR\-th power and places the result in \fIr\fR
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(\f(CW\*(C`r=a^p\*(C'\fR). This function is faster than repeated applications of
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\&\fIBN_mul()\fR.
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.PP
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\&\fIBN_mod_exp()\fR computes \fIa\fR to the \fIp\fR\-th power modulo \fIm\fR (\f(CW\*(C`r=a^p %
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m\*(C'\fR). This function uses less time and space than \fIBN_exp()\fR. Do not call this
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function when \fBm\fR is even and any of the parameters have the
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\&\fB\s-1BN_FLG_CONSTTIME\s0\fR flag set.
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.PP
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\&\fIBN_gcd()\fR computes the greatest common divisor of \fIa\fR and \fIb\fR and
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places the result in \fIr\fR. \fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or
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\&\fIb\fR.
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.PP
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For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
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temporary variables; see \fIBN_CTX_new\fR\|(3).
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.PP
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Unless noted otherwise, the result \fB\s-1BIGNUM\s0\fR must be different from
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the arguments.
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.SH "RETURN VALUES"
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.IX Header "RETURN VALUES"
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For all functions, 1 is returned for success, 0 on error. The return
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value should always be checked (e.g., \f(CW\*(C`if (!BN_add(r,a,b)) goto err;\*(C'\fR).
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The error codes can be obtained by \fIERR_get_error\fR\|(3).
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.SH "SEE ALSO"
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.IX Header "SEE ALSO"
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\&\fIERR_get_error\fR\|(3), \fIBN_CTX_new\fR\|(3),
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\&\fIBN_add_word\fR\|(3), \fIBN_set_bit\fR\|(3)
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.SH "COPYRIGHT"
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.IX Header "COPYRIGHT"
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Copyright 2000\-2018 The OpenSSL Project Authors. All Rights Reserved.
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.PP
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Licensed under the Apache License 2.0 (the \*(L"License\*(R"). You may not use
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this file except in compliance with the License. You can obtain a copy
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in the file \s-1LICENSE\s0 in the source distribution or at
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<https://www.openssl.org/source/license.html>.
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