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131 .IX Title "BN_mod_mul_montgomery 3"
132 .TH BN_mod_mul_montgomery 3 "2018-03-27" "1.0.2o" "OpenSSL"
133 .\" For nroff, turn off justification. Always turn off hyphenation; it makes
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138 BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
139 BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
140 BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication
142 .IX Header "SYNOPSIS"
144 \& #include <openssl/bn.h>
146 \& BN_MONT_CTX *BN_MONT_CTX_new(void);
147 \& void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
148 \& void BN_MONT_CTX_free(BN_MONT_CTX *mont);
150 \& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
151 \& BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
153 \& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
154 \& BN_MONT_CTX *mont, BN_CTX *ctx);
156 \& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
159 \& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
163 .IX Header "DESCRIPTION"
164 These functions implement Montgomery multiplication. They are used
165 automatically when \fIBN_mod_exp\fR\|(3) is called with suitable input,
166 but they may be useful when several operations are to be performed
167 using the same modulus.
169 \&\fIBN_MONT_CTX_new()\fR allocates and initializes a \fB\s-1BN_MONT_CTX\s0\fR structure.
170 \&\fIBN_MONT_CTX_init()\fR initializes an existing uninitialized \fB\s-1BN_MONT_CTX\s0\fR.
172 \&\fIBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR
173 by precomputing its inverse and a value R.
175 \&\fIBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fIfrom\fR to \fIto\fR.
177 \&\fIBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if
178 it was created by \fIBN_MONT_CTX_new()\fR, also the structure itself.
180 \&\fIBN_mod_mul_montgomery()\fR computes Mont(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places
181 the result in \fIr\fR.
183 \&\fIBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1.
185 \&\fIBN_to_montgomery()\fR computes Mont(\fIa\fR,R^2), i.e. \fIa\fR*R.
186 Note that \fIa\fR must be non-negative and smaller than the modulus.
188 For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
191 The \fB\s-1BN_MONT_CTX\s0\fR structure is defined as follows:
194 \& typedef struct bn_mont_ctx_st
196 \& int ri; /* number of bits in R */
197 \& BIGNUM RR; /* R^2 (used to convert to Montgomery form) */
198 \& BIGNUM N; /* The modulus */
199 \& BIGNUM Ni; /* R*(1/R mod N) \- N*Ni = 1
200 \& * (Ni is only stored for bignum algorithm) */
201 \& BN_ULONG n0; /* least significant word of Ni */
206 \&\fIBN_to_montgomery()\fR is a macro.
208 .IX Header "RETURN VALUES"
209 \&\fIBN_MONT_CTX_new()\fR returns the newly allocated \fB\s-1BN_MONT_CTX\s0\fR, and \s-1NULL\s0
212 \&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_free()\fR have no return values.
214 For the other functions, 1 is returned for success, 0 on error.
215 The error codes can be obtained by \fIERR_get_error\fR\|(3).
218 The inputs must be reduced modulo \fBm\fR, otherwise the result will be
219 outside the expected range.
221 .IX Header "SEE ALSO"
222 \&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIBN_add\fR\|(3),
223 \&\fIBN_CTX_new\fR\|(3)
226 \&\fIBN_MONT_CTX_new()\fR, \fIBN_MONT_CTX_free()\fR, \fIBN_MONT_CTX_set()\fR,
227 \&\fIBN_mod_mul_montgomery()\fR, \fIBN_from_montgomery()\fR and \fIBN_to_montgomery()\fR
228 are available in all versions of SSLeay and OpenSSL.
230 \&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b.