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137 .IX Title "BN_mod_mul_montgomery 3"
138 .TH BN_mod_mul_montgomery 3 "2009-07-19" "1.0.1n" "OpenSSL"
139 .\" For nroff, turn off justification. Always turn off hyphenation; it makes
140 .\" way too many mistakes in technical documents.
141 .if n .ad l
142 .nh
143 .SH "NAME"
144 BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
145 BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
146 BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication
147 .SH "LIBRARY"
148 libcrypto, -lcrypto
149 .SH "SYNOPSIS"
150 .IX Header "SYNOPSIS"
151 .Vb 1
152 \& #include <openssl/bn.h>
153 \&
154 \& BN_MONT_CTX *BN_MONT_CTX_new(void);
155 \& void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
156 \& void BN_MONT_CTX_free(BN_MONT_CTX *mont);
157 \&
158 \& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
159 \& BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
160 \&
161 \& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
162 \& BN_MONT_CTX *mont, BN_CTX *ctx);
163 \&
164 \& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
165 \& BN_CTX *ctx);
166 \&
167 \& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
168 \& BN_CTX *ctx);
169 .Ve
170 .SH "DESCRIPTION"
171 .IX Header "DESCRIPTION"
172 These functions implement Montgomery multiplication. They are used
173 automatically when \fIBN_mod_exp\fR\|(3) is called with suitable input,
174 but they may be useful when several operations are to be performed
175 using the same modulus.
176 .PP
177 \&\fIBN_MONT_CTX_new()\fR allocates and initializes a \fB\s-1BN_MONT_CTX\s0\fR structure.
178 \&\fIBN_MONT_CTX_init()\fR initializes an existing uninitialized \fB\s-1BN_MONT_CTX\s0\fR.
179 .PP
180 \&\fIBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR
181 by precomputing its inverse and a value R.
182 .PP
183 \&\fIBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fIfrom\fR to \fIto\fR.
184 .PP
185 \&\fIBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if
186 it was created by \fIBN_MONT_CTX_new()\fR, also the structure itself.
187 .PP
188 \&\fIBN_mod_mul_montgomery()\fR computes Mont(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places
189 the result in \fIr\fR.
190 .PP
191 \&\fIBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1.
192 .PP
193 \&\fIBN_to_montgomery()\fR computes Mont(\fIa\fR,R^2), i.e. \fIa\fR*R.
194 Note that \fIa\fR must be non-negative and smaller than the modulus.
195 .PP
196 For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
197 temporary variables.
198 .PP
199 The \fB\s-1BN_MONT_CTX\s0\fR structure is defined as follows:
200 .PP
201 .Vb 10
202 \& typedef struct bn_mont_ctx_st
203 \& {
204 \& int ri; /* number of bits in R */
205 \& BIGNUM RR; /* R^2 (used to convert to Montgomery form) */
206 \& BIGNUM N; /* The modulus */
207 \& BIGNUM Ni; /* R*(1/R mod N) \- N*Ni = 1
208 \& * (Ni is only stored for bignum algorithm) */
209 \& BN_ULONG n0; /* least significant word of Ni */
210 \& int flags;
211 \& } BN_MONT_CTX;
212 .Ve
213 .PP
214 \&\fIBN_to_montgomery()\fR is a macro.
215 .SH "RETURN VALUES"
216 .IX Header "RETURN VALUES"
217 \&\fIBN_MONT_CTX_new()\fR returns the newly allocated \fB\s-1BN_MONT_CTX\s0\fR, and \s-1NULL\s0
218 on error.
219 .PP
220 \&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_free()\fR have no return values.
221 .PP
222 For the other functions, 1 is returned for success, 0 on error.
223 The error codes can be obtained by \fIERR_get_error\fR\|(3).
224 .SH "WARNING"
225 .IX Header "WARNING"
226 The inputs must be reduced modulo \fBm\fR, otherwise the result will be
227 outside the expected range.
228 .SH "SEE ALSO"
229 .IX Header "SEE ALSO"
230 \&\fIopenssl_bn\fR\|(3), \fIERR_get_error\fR\|(3), \fIBN_add\fR\|(3),
231 \&\fIBN_CTX_new\fR\|(3)
232 .SH "HISTORY"
233 .IX Header "HISTORY"
234 \&\fIBN_MONT_CTX_new()\fR, \fIBN_MONT_CTX_free()\fR, \fIBN_MONT_CTX_set()\fR,
235 \&\fIBN_mod_mul_montgomery()\fR, \fIBN_from_montgomery()\fR and \fIBN_to_montgomery()\fR
236 are available in all versions of SSLeay and OpenSSL.
237 .PP
238 \&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b.