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127 .TH BN_add 3 "2007-10-24" "0.9.8g" "OpenSSL"
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133 BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add,
134 BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd \-
135 arithmetic operations on BIGNUMs
137 .IX Header "SYNOPSIS"
139 \& #include <openssl/bn.h>
141 \& int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
143 \& int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
145 \& int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
147 \& int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
149 \& int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
152 \& int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
154 \& int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
156 \& int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
159 \& int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
162 \& int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
165 \& int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
167 \& int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
169 \& int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
170 \& const BIGNUM *m, BN_CTX *ctx);
172 \& int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
175 .IX Header "DESCRIPTION"
176 \&\fIBN_add()\fR adds \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CW\*(C`r=a+b\*(C'\fR).
177 \&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
179 \&\fIBN_sub()\fR subtracts \fIb\fR from \fIa\fR and places the result in \fIr\fR (\f(CW\*(C`r=a\-b\*(C'\fR).
181 \&\fIBN_mul()\fR multiplies \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CW\*(C`r=a*b\*(C'\fR).
182 \&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
183 For multiplication by powers of 2, use \fIBN_lshift\fR\|(3).
185 \&\fIBN_sqr()\fR takes the square of \fIa\fR and places the result in \fIr\fR
186 (\f(CW\*(C`r=a^2\*(C'\fR). \fIr\fR and \fIa\fR may be the same \fB\s-1BIGNUM\s0\fR.
187 This function is faster than BN_mul(r,a,a).
189 \&\fIBN_div()\fR divides \fIa\fR by \fId\fR and places the result in \fIdv\fR and the
190 remainder in \fIrem\fR (\f(CW\*(C`dv=a/d, rem=a%d\*(C'\fR). Either of \fIdv\fR and \fIrem\fR may
191 be \fB\s-1NULL\s0\fR, in which case the respective value is not returned.
192 The result is rounded towards zero; thus if \fIa\fR is negative, the
193 remainder will be zero or negative.
194 For division by powers of 2, use \fIBN_rshift\fR\|(3).
196 \&\fIBN_mod()\fR corresponds to \fIBN_div()\fR with \fIdv\fR set to \fB\s-1NULL\s0\fR.
198 \&\fIBN_nnmod()\fR reduces \fIa\fR modulo \fIm\fR and places the non-negative
199 remainder in \fIr\fR.
201 \&\fIBN_mod_add()\fR adds \fIa\fR to \fIb\fR modulo \fIm\fR and places the non-negative
204 \&\fIBN_mod_sub()\fR subtracts \fIb\fR from \fIa\fR modulo \fIm\fR and places the
205 non-negative result in \fIr\fR.
207 \&\fIBN_mod_mul()\fR multiplies \fIa\fR by \fIb\fR and finds the non-negative
208 remainder respective to modulus \fIm\fR (\f(CW\*(C`r=(a*b) mod m\*(C'\fR). \fIr\fR may be
209 the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR. For more efficient algorithms for
210 repeated computations using the same modulus, see
211 \&\fIBN_mod_mul_montgomery\fR\|(3) and
212 \&\fIBN_mod_mul_reciprocal\fR\|(3).
214 \&\fIBN_mod_sqr()\fR takes the square of \fIa\fR modulo \fBm\fR and places the
217 \&\fIBN_exp()\fR raises \fIa\fR to the \fIp\fR\-th power and places the result in \fIr\fR
218 (\f(CW\*(C`r=a^p\*(C'\fR). This function is faster than repeated applications of
221 \&\fIBN_mod_exp()\fR computes \fIa\fR to the \fIp\fR\-th power modulo \fIm\fR (\f(CW\*(C`r=a^p %
222 m\*(C'\fR). This function uses less time and space than \fIBN_exp()\fR.
224 \&\fIBN_gcd()\fR computes the greatest common divisor of \fIa\fR and \fIb\fR and
225 places the result in \fIr\fR. \fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or
228 For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
229 temporary variables; see \fIBN_CTX_new\fR\|(3).
231 Unless noted otherwise, the result \fB\s-1BIGNUM\s0\fR must be different from
234 .IX Header "RETURN VALUES"
235 For all functions, 1 is returned for success, 0 on error. The return
236 value should always be checked (e.g., \f(CW\*(C`if (!BN_add(r,a,b)) goto err;\*(C'\fR).
237 The error codes can be obtained by \fIERR_get_error\fR\|(3).
239 .IX Header "SEE ALSO"
240 \&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIBN_CTX_new\fR\|(3),
241 \&\fIBN_add_word\fR\|(3), \fIBN_set_bit\fR\|(3)
244 \&\fIBN_add()\fR, \fIBN_sub()\fR, \fIBN_sqr()\fR, \fIBN_div()\fR, \fIBN_mod()\fR, \fIBN_mod_mul()\fR,
245 \&\fIBN_mod_exp()\fR and \fIBN_gcd()\fR are available in all versions of SSLeay and
246 OpenSSL. The \fIctx\fR argument to \fIBN_mul()\fR was added in SSLeay
247 0.9.1b. \fIBN_exp()\fR appeared in SSLeay 0.9.0.
248 \&\fIBN_nnmod()\fR, \fIBN_mod_add()\fR, \fIBN_mod_sub()\fR, and \fIBN_mod_sqr()\fR were added in