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129.\" ========================================================================
130.\"
131.IX Title "BN_mod_mul_montgomery 3"
| 1.\" Automatically generated by Pod::Man 4.07 (Pod::Simple 3.35)
2.\"
3.\" Standard preamble:
4.\" ========================================================================
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6.if t .sp .5v
7.if n .sp
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9.de Vb \" Begin verbatim text
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15.ft R
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20.\" double quote, and \*(R" will give a right double quote. \*(C+ will
21.\" give a nicer C++. Capital omega is used to do unbreakable dashes and
22.\" therefore won't be available. \*(C` and \*(C' expand to `' in nroff,
23.\" nothing in troff, for use with C<>.
24.tr \(*W-
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129.\" ========================================================================
130.\"
131.IX Title "BN_mod_mul_montgomery 3"
|
133.\" For nroff, turn off justification. Always turn off hyphenation; it makes
134.\" way too many mistakes in technical documents.
135.if n .ad l
136.nh
137.SH "NAME"
138BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
139BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
140BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication
141.SH "SYNOPSIS"
142.IX Header "SYNOPSIS"
143.Vb 1
144\& #include <openssl/bn.h>
145\&
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);
149\&
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\&
153\& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
154\& BN_MONT_CTX *mont, BN_CTX *ctx);
155\&
156\& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
157\& BN_CTX *ctx);
158\&
159\& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
160\& BN_CTX *ctx);
161.Ve
162.SH "DESCRIPTION"
163.IX Header "DESCRIPTION"
164These functions implement Montgomery multiplication. They are used
165automatically when \fIBN_mod_exp\fR\|(3) is called with suitable input,
166but they may be useful when several operations are to be performed
167using the same modulus.
168.PP
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.
171.PP
172\&\fIBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR
173by precomputing its inverse and a value R.
174.PP
175\&\fIBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fIfrom\fR to \fIto\fR.
176.PP
177\&\fIBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if
178it was created by \fIBN_MONT_CTX_new()\fR, also the structure itself.
179.PP
180\&\fIBN_mod_mul_montgomery()\fR computes Mont(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places
181the result in \fIr\fR.
182.PP
183\&\fIBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1.
184.PP
185\&\fIBN_to_montgomery()\fR computes Mont(\fIa\fR,R^2), i.e. \fIa\fR*R.
186Note that \fIa\fR must be non-negative and smaller than the modulus.
187.PP
188For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
189temporary variables.
190.PP
191The \fB\s-1BN_MONT_CTX\s0\fR structure is defined as follows:
192.PP
193.Vb 10
194\& typedef struct bn_mont_ctx_st
195\& {
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 */
202\& int flags;
203\& } BN_MONT_CTX;
204.Ve
205.PP
206\&\fIBN_to_montgomery()\fR is a macro.
207.SH "RETURN VALUES"
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
210on error.
211.PP
212\&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_free()\fR have no return values.
213.PP
214For the other functions, 1 is returned for success, 0 on error.
215The error codes can be obtained by \fIERR_get_error\fR\|(3).
216.SH "WARNING"
217.IX Header "WARNING"
218The inputs must be reduced modulo \fBm\fR, otherwise the result will be
219outside the expected range.
220.SH "SEE ALSO"
221.IX Header "SEE ALSO"
222\&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIBN_add\fR\|(3),
223\&\fIBN_CTX_new\fR\|(3)
224.SH "HISTORY"
225.IX Header "HISTORY"
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
228are available in all versions of SSLeay and OpenSSL.
229.PP
230\&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b.
| 133.\" For nroff, turn off justification. Always turn off hyphenation; it makes
134.\" way too many mistakes in technical documents.
135.if n .ad l
136.nh
137.SH "NAME"
138BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
139BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
140BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication
141.SH "SYNOPSIS"
142.IX Header "SYNOPSIS"
143.Vb 1
144\& #include <openssl/bn.h>
145\&
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);
149\&
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\&
153\& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
154\& BN_MONT_CTX *mont, BN_CTX *ctx);
155\&
156\& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
157\& BN_CTX *ctx);
158\&
159\& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
160\& BN_CTX *ctx);
161.Ve
162.SH "DESCRIPTION"
163.IX Header "DESCRIPTION"
164These functions implement Montgomery multiplication. They are used
165automatically when \fIBN_mod_exp\fR\|(3) is called with suitable input,
166but they may be useful when several operations are to be performed
167using the same modulus.
168.PP
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.
171.PP
172\&\fIBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR
173by precomputing its inverse and a value R.
174.PP
175\&\fIBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fIfrom\fR to \fIto\fR.
176.PP
177\&\fIBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if
178it was created by \fIBN_MONT_CTX_new()\fR, also the structure itself.
179.PP
180\&\fIBN_mod_mul_montgomery()\fR computes Mont(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places
181the result in \fIr\fR.
182.PP
183\&\fIBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1.
184.PP
185\&\fIBN_to_montgomery()\fR computes Mont(\fIa\fR,R^2), i.e. \fIa\fR*R.
186Note that \fIa\fR must be non-negative and smaller than the modulus.
187.PP
188For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
189temporary variables.
190.PP
191The \fB\s-1BN_MONT_CTX\s0\fR structure is defined as follows:
192.PP
193.Vb 10
194\& typedef struct bn_mont_ctx_st
195\& {
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 */
202\& int flags;
203\& } BN_MONT_CTX;
204.Ve
205.PP
206\&\fIBN_to_montgomery()\fR is a macro.
207.SH "RETURN VALUES"
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
210on error.
211.PP
212\&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_free()\fR have no return values.
213.PP
214For the other functions, 1 is returned for success, 0 on error.
215The error codes can be obtained by \fIERR_get_error\fR\|(3).
216.SH "WARNING"
217.IX Header "WARNING"
218The inputs must be reduced modulo \fBm\fR, otherwise the result will be
219outside the expected range.
220.SH "SEE ALSO"
221.IX Header "SEE ALSO"
222\&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIBN_add\fR\|(3),
223\&\fIBN_CTX_new\fR\|(3)
224.SH "HISTORY"
225.IX Header "HISTORY"
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
228are available in all versions of SSLeay and OpenSSL.
229.PP
230\&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b.
|