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132 .TH BN_add 3 "2005-02-24" "0.9.7d" "OpenSSL"
134 BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add,
135 BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd \-
136 arithmetic operations on BIGNUMs
138 .IX Header "SYNOPSIS"
140 \& #include <openssl/bn.h>
144 \& int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
148 \& int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
152 \& int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
156 \& int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
160 \& int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
165 \& int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
169 \& int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
173 \& int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
178 \& int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
183 \& int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
188 \& int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
192 \& int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
196 \& int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
197 \& const BIGNUM *m, BN_CTX *ctx);
201 \& int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
204 .IX Header "DESCRIPTION"
205 \&\fIBN_add()\fR adds \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CW\*(C`r=a+b\*(C'\fR).
206 \&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
208 \&\fIBN_sub()\fR subtracts \fIb\fR from \fIa\fR and places the result in \fIr\fR (\f(CW\*(C`r=a\-b\*(C'\fR).
210 \&\fIBN_mul()\fR multiplies \fIa\fR and \fIb\fR and places the result in \fIr\fR (\f(CW\*(C`r=a*b\*(C'\fR).
211 \&\fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR.
212 For multiplication by powers of 2, use \fIBN_lshift\fR\|(3).
214 \&\fIBN_sqr()\fR takes the square of \fIa\fR and places the result in \fIr\fR
215 (\f(CW\*(C`r=a^2\*(C'\fR). \fIr\fR and \fIa\fR may be the same \fB\s-1BIGNUM\s0\fR.
216 This function is faster than BN_mul(r,a,a).
218 \&\fIBN_div()\fR divides \fIa\fR by \fId\fR and places the result in \fIdv\fR and the
219 remainder in \fIrem\fR (\f(CW\*(C`dv=a/d, rem=a%d\*(C'\fR). Either of \fIdv\fR and \fIrem\fR may
220 be \fB\s-1NULL\s0\fR, in which case the respective value is not returned.
221 The result is rounded towards zero; thus if \fIa\fR is negative, the
222 remainder will be zero or negative.
223 For division by powers of 2, use \fIBN_rshift\fR\|(3).
225 \&\fIBN_mod()\fR corresponds to \fIBN_div()\fR with \fIdv\fR set to \fB\s-1NULL\s0\fR.
227 \&\fIBN_nnmod()\fR reduces \fIa\fR modulo \fIm\fR and places the non-negative
228 remainder in \fIr\fR.
230 \&\fIBN_mod_add()\fR adds \fIa\fR to \fIb\fR modulo \fIm\fR and places the non-negative
233 \&\fIBN_mod_sub()\fR subtracts \fIb\fR from \fIa\fR modulo \fIm\fR and places the
234 non-negative result in \fIr\fR.
236 \&\fIBN_mod_mul()\fR multiplies \fIa\fR by \fIb\fR and finds the non-negative
237 remainder respective to modulus \fIm\fR (\f(CW\*(C`r=(a*b) mod m\*(C'\fR). \fIr\fR may be
238 the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or \fIb\fR. For more efficient algorithms for
239 repeated computations using the same modulus, see
240 \&\fIBN_mod_mul_montgomery\fR\|(3) and
241 \&\fIBN_mod_mul_reciprocal\fR\|(3).
243 \&\fIBN_mod_sqr()\fR takes the square of \fIa\fR modulo \fBm\fR and places the
246 \&\fIBN_exp()\fR raises \fIa\fR to the \fIp\fR\-th power and places the result in \fIr\fR
247 (\f(CW\*(C`r=a^p\*(C'\fR). This function is faster than repeated applications of
250 \&\fIBN_mod_exp()\fR computes \fIa\fR to the \fIp\fR\-th power modulo \fIm\fR (\f(CW\*(C`r=a^p %
251 m\*(C'\fR). This function uses less time and space than \fIBN_exp()\fR.
253 \&\fIBN_gcd()\fR computes the greatest common divisor of \fIa\fR and \fIb\fR and
254 places the result in \fIr\fR. \fIr\fR may be the same \fB\s-1BIGNUM\s0\fR as \fIa\fR or
257 For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
258 temporary variables; see \fIBN_CTX_new\fR\|(3).
260 Unless noted otherwise, the result \fB\s-1BIGNUM\s0\fR must be different from
263 .IX Header "RETURN VALUES"
264 For all functions, 1 is returned for success, 0 on error. The return
265 value should always be checked (e.g., \f(CW\*(C`if (!BN_add(r,a,b)) goto err;\*(C'\fR).
266 The error codes can be obtained by \fIERR_get_error\fR\|(3).
268 .IX Header "SEE ALSO"
269 \&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIBN_CTX_new\fR\|(3),
270 \&\fIBN_add_word\fR\|(3), \fIBN_set_bit\fR\|(3)
273 \&\fIBN_add()\fR, \fIBN_sub()\fR, \fIBN_sqr()\fR, \fIBN_div()\fR, \fIBN_mod()\fR, \fIBN_mod_mul()\fR,
274 \&\fIBN_mod_exp()\fR and \fIBN_gcd()\fR are available in all versions of SSLeay and
275 OpenSSL. The \fIctx\fR argument to \fIBN_mul()\fR was added in SSLeay
276 0.9.1b. \fIBN_exp()\fR appeared in SSLeay 0.9.0.
277 \&\fIBN_nnmod()\fR, \fIBN_mod_add()\fR, \fIBN_mod_sub()\fR, and \fIBN_mod_sqr()\fR were added in