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124 | .\" ======================================================================== |
125 | .\" | |
126 | .IX Title "BN_mod_mul_montgomery 3" | |
e3261593 | 127 | .TH BN_mod_mul_montgomery 3 "2012-01-04" "1.0.0f" "OpenSSL" |
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128 | .\" For nroff, turn off justification. Always turn off hyphenation; it makes |
129 | .\" way too many mistakes in technical documents. | |
130 | .if n .ad l | |
131 | .nh | |
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132 | .SH "NAME" |
133 | BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init, | |
134 | BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy, | |
135 | BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication | |
136 | .SH "SYNOPSIS" | |
8b0cefbb | 137 | .IX Header "SYNOPSIS" |
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138 | .Vb 1 |
139 | \& #include <openssl/bn.h> | |
e257b235 | 140 | \& |
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141 | \& BN_MONT_CTX *BN_MONT_CTX_new(void); |
142 | \& void BN_MONT_CTX_init(BN_MONT_CTX *ctx); | |
143 | \& void BN_MONT_CTX_free(BN_MONT_CTX *mont); | |
e257b235 | 144 | \& |
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145 | \& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx); |
146 | \& BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from); | |
e257b235 | 147 | \& |
984263bc MD |
148 | \& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b, |
149 | \& BN_MONT_CTX *mont, BN_CTX *ctx); | |
e257b235 | 150 | \& |
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151 | \& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, |
152 | \& BN_CTX *ctx); | |
e257b235 | 153 | \& |
984263bc MD |
154 | \& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, |
155 | \& BN_CTX *ctx); | |
156 | .Ve | |
157 | .SH "DESCRIPTION" | |
8b0cefbb | 158 | .IX Header "DESCRIPTION" |
984263bc | 159 | These functions implement Montgomery multiplication. They are used |
8b0cefbb | 160 | automatically when \fIBN_mod_exp\fR\|(3) is called with suitable input, |
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161 | but they may be useful when several operations are to be performed |
162 | using the same modulus. | |
163 | .PP | |
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164 | \&\fIBN_MONT_CTX_new()\fR allocates and initializes a \fB\s-1BN_MONT_CTX\s0\fR structure. |
165 | \&\fIBN_MONT_CTX_init()\fR initializes an existing uninitialized \fB\s-1BN_MONT_CTX\s0\fR. | |
984263bc | 166 | .PP |
8b0cefbb | 167 | \&\fIBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR |
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168 | by precomputing its inverse and a value R. |
169 | .PP | |
8b0cefbb | 170 | \&\fIBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fIfrom\fR to \fIto\fR. |
984263bc | 171 | .PP |
8b0cefbb | 172 | \&\fIBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if |
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173 | it was created by \fIBN_MONT_CTX_new()\fR, also the structure itself. |
174 | .PP | |
8b0cefbb | 175 | \&\fIBN_mod_mul_montgomery()\fR computes Mont(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places |
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176 | the result in \fIr\fR. |
177 | .PP | |
8b0cefbb | 178 | \&\fIBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1. |
984263bc | 179 | .PP |
8b0cefbb | 180 | \&\fIBN_to_montgomery()\fR computes Mont(\fIa\fR,R^2), i.e. \fIa\fR*R. |
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181 | Note that \fIa\fR must be non-negative and smaller than the modulus. |
182 | .PP | |
8b0cefbb | 183 | For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for |
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184 | temporary variables. |
185 | .PP | |
8b0cefbb | 186 | The \fB\s-1BN_MONT_CTX\s0\fR structure is defined as follows: |
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187 | .PP |
188 | .Vb 10 | |
189 | \& typedef struct bn_mont_ctx_st | |
190 | \& { | |
191 | \& int ri; /* number of bits in R */ | |
192 | \& BIGNUM RR; /* R^2 (used to convert to Montgomery form) */ | |
193 | \& BIGNUM N; /* The modulus */ | |
e257b235 | 194 | \& BIGNUM Ni; /* R*(1/R mod N) \- N*Ni = 1 |
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195 | \& * (Ni is only stored for bignum algorithm) */ |
196 | \& BN_ULONG n0; /* least significant word of Ni */ | |
197 | \& int flags; | |
198 | \& } BN_MONT_CTX; | |
199 | .Ve | |
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200 | .PP |
201 | \&\fIBN_to_montgomery()\fR is a macro. | |
984263bc | 202 | .SH "RETURN VALUES" |
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203 | .IX Header "RETURN VALUES" |
204 | \&\fIBN_MONT_CTX_new()\fR returns the newly allocated \fB\s-1BN_MONT_CTX\s0\fR, and \s-1NULL\s0 | |
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205 | on error. |
206 | .PP | |
8b0cefbb | 207 | \&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_free()\fR have no return values. |
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208 | .PP |
209 | For the other functions, 1 is returned for success, 0 on error. | |
8b0cefbb | 210 | The error codes can be obtained by \fIERR_get_error\fR\|(3). |
984263bc | 211 | .SH "WARNING" |
8b0cefbb | 212 | .IX Header "WARNING" |
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213 | The inputs must be reduced modulo \fBm\fR, otherwise the result will be |
214 | outside the expected range. | |
215 | .SH "SEE ALSO" | |
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216 | .IX Header "SEE ALSO" |
217 | \&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIBN_add\fR\|(3), | |
218 | \&\fIBN_CTX_new\fR\|(3) | |
984263bc | 219 | .SH "HISTORY" |
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220 | .IX Header "HISTORY" |
221 | \&\fIBN_MONT_CTX_new()\fR, \fIBN_MONT_CTX_free()\fR, \fIBN_MONT_CTX_set()\fR, | |
222 | \&\fIBN_mod_mul_montgomery()\fR, \fIBN_from_montgomery()\fR and \fIBN_to_montgomery()\fR | |
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223 | are available in all versions of SSLeay and OpenSSL. |
224 | .PP | |
8b0cefbb | 225 | \&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b. |