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135 .IX Title "BN_mod_mul_montgomery 3"
136 .TH BN_mod_mul_montgomery 3 "2016-05-03" "1.0.1t" "OpenSSL"
137 .\" For nroff, turn off justification. Always turn off hyphenation; it makes
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142 BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
143 BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
144 BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication
146 .IX Header "SYNOPSIS"
148 \& #include <openssl/bn.h>
150 \& BN_MONT_CTX *BN_MONT_CTX_new(void);
151 \& void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
152 \& void BN_MONT_CTX_free(BN_MONT_CTX *mont);
154 \& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
155 \& BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
157 \& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
158 \& BN_MONT_CTX *mont, BN_CTX *ctx);
160 \& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
163 \& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
167 .IX Header "DESCRIPTION"
168 These functions implement Montgomery multiplication. They are used
169 automatically when \fIBN_mod_exp\fR\|(3) is called with suitable input,
170 but they may be useful when several operations are to be performed
171 using the same modulus.
173 \&\fIBN_MONT_CTX_new()\fR allocates and initializes a \fB\s-1BN_MONT_CTX\s0\fR structure.
174 \&\fIBN_MONT_CTX_init()\fR initializes an existing uninitialized \fB\s-1BN_MONT_CTX\s0\fR.
176 \&\fIBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR
177 by precomputing its inverse and a value R.
179 \&\fIBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fIfrom\fR to \fIto\fR.
181 \&\fIBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if
182 it was created by \fIBN_MONT_CTX_new()\fR, also the structure itself.
184 \&\fIBN_mod_mul_montgomery()\fR computes Mont(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places
185 the result in \fIr\fR.
187 \&\fIBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1.
189 \&\fIBN_to_montgomery()\fR computes Mont(\fIa\fR,R^2), i.e. \fIa\fR*R.
190 Note that \fIa\fR must be non-negative and smaller than the modulus.
192 For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
195 The \fB\s-1BN_MONT_CTX\s0\fR structure is defined as follows:
198 \& typedef struct bn_mont_ctx_st
200 \& int ri; /* number of bits in R */
201 \& BIGNUM RR; /* R^2 (used to convert to Montgomery form) */
202 \& BIGNUM N; /* The modulus */
203 \& BIGNUM Ni; /* R*(1/R mod N) \- N*Ni = 1
204 \& * (Ni is only stored for bignum algorithm) */
205 \& BN_ULONG n0; /* least significant word of Ni */
210 \&\fIBN_to_montgomery()\fR is a macro.
212 .IX Header "RETURN VALUES"
213 \&\fIBN_MONT_CTX_new()\fR returns the newly allocated \fB\s-1BN_MONT_CTX\s0\fR, and \s-1NULL\s0
216 \&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_free()\fR have no return values.
218 For the other functions, 1 is returned for success, 0 on error.
219 The error codes can be obtained by \fIERR_get_error\fR\|(3).
222 The inputs must be reduced modulo \fBm\fR, otherwise the result will be
223 outside the expected range.
225 .IX Header "SEE ALSO"
226 \&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIBN_add\fR\|(3),
227 \&\fIBN_CTX_new\fR\|(3)
230 \&\fIBN_MONT_CTX_new()\fR, \fIBN_MONT_CTX_free()\fR, \fIBN_MONT_CTX_set()\fR,
231 \&\fIBN_mod_mul_montgomery()\fR, \fIBN_from_montgomery()\fR and \fIBN_to_montgomery()\fR
232 are available in all versions of SSLeay and OpenSSL.
234 \&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b.