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| 129 | .\" ======================================================================== |
| 130 | .\" |
| 131 | .IX Title "BN_mod_mul_montgomery 3" |
| 132 | .TH BN_mod_mul_montgomery 3 "2004-12-18" "0.9.7e" "OpenSSL" |
| 133 | .SH "NAME" |
| 134 | BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init, |
| 135 | BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy, |
| 136 | BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication |
| 137 | .SH "SYNOPSIS" |
| 138 | .IX Header "SYNOPSIS" |
| 139 | .Vb 1 |
| 140 | \& #include <openssl/bn.h> |
| 141 | .Ve |
| 142 | .PP |
| 143 | .Vb 3 |
| 144 | \& BN_MONT_CTX *BN_MONT_CTX_new(void); |
| 145 | \& void BN_MONT_CTX_init(BN_MONT_CTX *ctx); |
| 146 | \& void BN_MONT_CTX_free(BN_MONT_CTX *mont); |
| 147 | .Ve |
| 148 | .PP |
| 149 | .Vb 2 |
| 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); |
| 152 | .Ve |
| 153 | .PP |
| 154 | .Vb 2 |
| 155 | \& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b, |
| 156 | \& BN_MONT_CTX *mont, BN_CTX *ctx); |
| 157 | .Ve |
| 158 | .PP |
| 159 | .Vb 2 |
| 160 | \& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, |
| 161 | \& BN_CTX *ctx); |
| 162 | .Ve |
| 163 | .PP |
| 164 | .Vb 2 |
| 165 | \& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, |
| 166 | \& BN_CTX *ctx); |
| 167 | .Ve |
| 168 | .SH "DESCRIPTION" |
| 169 | .IX Header "DESCRIPTION" |
| 170 | These functions implement Montgomery multiplication. They are used |
| 171 | automatically when \fIBN_mod_exp\fR\|(3) is called with suitable input, |
| 172 | but they may be useful when several operations are to be performed |
| 173 | using the same modulus. |
| 174 | .PP |
| 175 | \&\fIBN_MONT_CTX_new()\fR allocates and initializes a \fB\s-1BN_MONT_CTX\s0\fR structure. |
| 176 | \&\fIBN_MONT_CTX_init()\fR initializes an existing uninitialized \fB\s-1BN_MONT_CTX\s0\fR. |
| 177 | .PP |
| 178 | \&\fIBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR |
| 179 | by precomputing its inverse and a value R. |
| 180 | .PP |
| 181 | \&\fIBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fIfrom\fR to \fIto\fR. |
| 182 | .PP |
| 183 | \&\fIBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if |
| 184 | it was created by \fIBN_MONT_CTX_new()\fR, also the structure itself. |
| 185 | .PP |
| 186 | \&\fIBN_mod_mul_montgomery()\fR computes Mont(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places |
| 187 | the result in \fIr\fR. |
| 188 | .PP |
| 189 | \&\fIBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1. |
| 190 | .PP |
| 191 | \&\fIBN_to_montgomery()\fR computes Mont(\fIa\fR,R^2), i.e. \fIa\fR*R. |
| 192 | Note that \fIa\fR must be non-negative and smaller than the modulus. |
| 193 | .PP |
| 194 | For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for |
| 195 | temporary variables. |
| 196 | .PP |
| 197 | The \fB\s-1BN_MONT_CTX\s0\fR structure is defined as follows: |
| 198 | .PP |
| 199 | .Vb 10 |
| 200 | \& typedef struct bn_mont_ctx_st |
| 201 | \& { |
| 202 | \& int ri; /* number of bits in R */ |
| 203 | \& BIGNUM RR; /* R^2 (used to convert to Montgomery form) */ |
| 204 | \& BIGNUM N; /* The modulus */ |
| 205 | \& BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 |
| 206 | \& * (Ni is only stored for bignum algorithm) */ |
| 207 | \& BN_ULONG n0; /* least significant word of Ni */ |
| 208 | \& int flags; |
| 209 | \& } BN_MONT_CTX; |
| 210 | .Ve |
| 211 | .PP |
| 212 | \&\fIBN_to_montgomery()\fR is a macro. |
| 213 | .SH "RETURN VALUES" |
| 214 | .IX Header "RETURN VALUES" |
| 215 | \&\fIBN_MONT_CTX_new()\fR returns the newly allocated \fB\s-1BN_MONT_CTX\s0\fR, and \s-1NULL\s0 |
| 216 | on error. |
| 217 | .PP |
| 218 | \&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_free()\fR have no return values. |
| 219 | .PP |
| 220 | For the other functions, 1 is returned for success, 0 on error. |
| 221 | The error codes can be obtained by \fIERR_get_error\fR\|(3). |
| 222 | .SH "WARNING" |
| 223 | .IX Header "WARNING" |
| 224 | The inputs must be reduced modulo \fBm\fR, otherwise the result will be |
| 225 | outside the expected range. |
| 226 | .SH "SEE ALSO" |
| 227 | .IX Header "SEE ALSO" |
| 228 | \&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIBN_add\fR\|(3), |
| 229 | \&\fIBN_CTX_new\fR\|(3) |
| 230 | .SH "HISTORY" |
| 231 | .IX Header "HISTORY" |
| 232 | \&\fIBN_MONT_CTX_new()\fR, \fIBN_MONT_CTX_free()\fR, \fIBN_MONT_CTX_set()\fR, |
| 233 | \&\fIBN_mod_mul_montgomery()\fR, \fIBN_from_montgomery()\fR and \fIBN_to_montgomery()\fR |
| 234 | are available in all versions of SSLeay and OpenSSL. |
| 235 | .PP |
| 236 | \&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b. |