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[dragonfly.git] / secure / lib / libcrypto / man / BN_mod_mul_montgomery.3
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80.\" If the F register is turned on, we'll generate
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82.\" TH Title
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96.TH BN_mod_mul_montgomery 3 "0.9.7d" "2/Sep/2004" "OpenSSL"
97.UC
98.if n .hy 0
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189.rm #[ #] #H #V #F C
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190.SH "NAME"
191BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
192BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
193BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication
194.SH "SYNOPSIS"
74dab6c2 195.PP
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196.Vb 1
197\& #include <openssl/bn.h>
198.Ve
199.Vb 3
200\& BN_MONT_CTX *BN_MONT_CTX_new(void);
201\& void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
202\& void BN_MONT_CTX_free(BN_MONT_CTX *mont);
203.Ve
204.Vb 2
205\& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
206\& BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
207.Ve
208.Vb 2
209\& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
210\& BN_MONT_CTX *mont, BN_CTX *ctx);
211.Ve
212.Vb 2
213\& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
214\& BN_CTX *ctx);
215.Ve
216.Vb 2
217\& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
218\& BN_CTX *ctx);
219.Ve
220.SH "DESCRIPTION"
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221These functions implement Montgomery multiplication. They are used
222automatically when BN_mod_exp(3) is called with suitable input,
223but they may be useful when several operations are to be performed
224using the same modulus.
225.PP
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226\fIBN_MONT_CTX_new()\fR allocates and initializes a \fBBN_MONT_CTX\fR structure.
227\fIBN_MONT_CTX_init()\fR initializes an existing uninitialized \fBBN_MONT_CTX\fR.
984263bc 228.PP
74dab6c2 229\fIBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR
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230by precomputing its inverse and a value R.
231.PP
74dab6c2 232\fIBN_MONT_CTX_copy()\fR copies the \fBBN_MONT_CTX\fR \fIfrom\fR to \fIto\fR.
984263bc 233.PP
74dab6c2 234\fIBN_MONT_CTX_free()\fR frees the components of the \fBBN_MONT_CTX\fR, and, if
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235it was created by \fIBN_MONT_CTX_new()\fR, also the structure itself.
236.PP
74dab6c2 237\fIBN_mod_mul_montgomery()\fR computes \fIMont\fR\|(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places
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238the result in \fIr\fR.
239.PP
74dab6c2 240\fIBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1.
984263bc 241.PP
74dab6c2 242\fIBN_to_montgomery()\fR computes \fIMont\fR\|(\fIa\fR,R^2), i.e. \fIa\fR*R.
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243Note that \fIa\fR must be non-negative and smaller than the modulus.
244.PP
74dab6c2 245For all functions, \fIctx\fR is a previously allocated \fBBN_CTX\fR used for
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246temporary variables.
247.PP
74dab6c2 248The \fBBN_MONT_CTX\fR structure is defined as follows:
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249.PP
250.Vb 10
251\& typedef struct bn_mont_ctx_st
252\& {
253\& int ri; /* number of bits in R */
254\& BIGNUM RR; /* R^2 (used to convert to Montgomery form) */
255\& BIGNUM N; /* The modulus */
256\& BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
257\& * (Ni is only stored for bignum algorithm) */
258\& BN_ULONG n0; /* least significant word of Ni */
259\& int flags;
260\& } BN_MONT_CTX;
261.Ve
74dab6c2 262\fIBN_to_montgomery()\fR is a macro.
984263bc 263.SH "RETURN VALUES"
74dab6c2 264\fIBN_MONT_CTX_new()\fR returns the newly allocated \fBBN_MONT_CTX\fR, and NULL
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265on error.
266.PP
74dab6c2 267\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_free()\fR have no return values.
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268.PP
269For the other functions, 1 is returned for success, 0 on error.
270The error codes can be obtained by ERR_get_error(3).
271.SH "WARNING"
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272The inputs must be reduced modulo \fBm\fR, otherwise the result will be
273outside the expected range.
274.SH "SEE ALSO"
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275bn(3), ERR_get_error(3), BN_add(3),
276BN_CTX_new(3)
277.SH "HISTORY"
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278\fIBN_MONT_CTX_new()\fR, \fIBN_MONT_CTX_free()\fR, \fIBN_MONT_CTX_set()\fR,
279\fIBN_mod_mul_montgomery()\fR, \fIBN_from_montgomery()\fR and \fIBN_to_montgomery()\fR
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280are available in all versions of SSLeay and OpenSSL.
281.PP
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282\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b.
283
284.rn }` ''
285.IX Title "BN_mod_mul_montgomery 3"
286.IX Name "BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
287BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
288BN_from_montgomery, BN_to_montgomery - Montgomery multiplication"
289
290.IX Header "NAME"
291
292.IX Header "SYNOPSIS"
293
294.IX Header "DESCRIPTION"
295
296.IX Header "RETURN VALUES"
297
298.IX Header "WARNING"
299
300.IX Header "SEE ALSO"
301
302.IX Header "HISTORY"
303