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.\" $NetBSD: BN_mod_mul_montgomery.3,v 1.12 2003/07/24 14:16:37 itojun Exp $
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.\" ======================================================================
.\"
.IX Title "BN_mod_mul_montgomery 3"
.TH BN_mod_mul_montgomery 3 "0.9.7b" "2002-09-25" "OpenSSL"
.UC
.SH "NAME"
BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication
.SH "LIBRARY"
libcrypto, -lcrypto
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\& #include <openssl/bn.h>
.Ve
.Vb 3
\& BN_MONT_CTX *BN_MONT_CTX_new(void);
\& void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
\& void BN_MONT_CTX_free(BN_MONT_CTX *mont);
.Ve
.Vb 2
\& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
\& BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
.Ve
.Vb 2
\& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
\& BN_MONT_CTX *mont, BN_CTX *ctx);
.Ve
.Vb 2
\& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
\& BN_CTX *ctx);
.Ve
.Vb 2
\& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
\& BN_CTX *ctx);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
These functions implement Montgomery multiplication. They are used
automatically when BN_mod_exp(3) is called with suitable input,
but they may be useful when several operations are to be performed
using the same modulus.
.PP
\&\fIBN_MONT_CTX_new()\fR allocates and initializes a \fB\s-1BN_MONT_CTX\s0\fR structure.
\&\fIBN_MONT_CTX_init()\fR initializes an existing uninitialized \fB\s-1BN_MONT_CTX\s0\fR.
.PP
\&\fIBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR
by precomputing its inverse and a value R.
.PP
\&\fIBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fIfrom\fR to \fIto\fR.
.PP
\&\fIBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if
it was created by \fIBN_MONT_CTX_new()\fR, also the structure itself.
.PP
\&\fIBN_mod_mul_montgomery()\fR computes Mont(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places
the result in \fIr\fR.
.PP
\&\fIBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1.
.PP
\&\fIBN_to_montgomery()\fR computes Mont(\fIa\fR,R^2), i.e. \fIa\fR*R.
Note that \fIa\fR must be non-negative and smaller than the modulus.
.PP
For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
temporary variables.
.PP
The \fB\s-1BN_MONT_CTX\s0\fR structure is defined as follows:
.PP
.Vb 10
\& typedef struct bn_mont_ctx_st
\& {
\& int ri; /* number of bits in R */
\& BIGNUM RR; /* R^2 (used to convert to Montgomery form) */
\& BIGNUM N; /* The modulus */
\& BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
\& * (Ni is only stored for bignum algorithm) */
\& BN_ULONG n0; /* least significant word of Ni */
\& int flags;
\& } BN_MONT_CTX;
.Ve
\&\fIBN_to_montgomery()\fR is a macro.
.SH "RETURN VALUES"
.IX Header "RETURN VALUES"
\&\fIBN_MONT_CTX_new()\fR returns the newly allocated \fB\s-1BN_MONT_CTX\s0\fR, and \s-1NULL\s0
on error.
.PP
\&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_free()\fR have no return values.
.PP
For the other functions, 1 is returned for success, 0 on error.
The error codes can be obtained by ERR_get_error(3).
.SH "WARNING"
.IX Header "WARNING"
The inputs must be reduced modulo \fBm\fR, otherwise the result will be
outside the expected range.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
openssl_bn(3), ERR_get_error(3), BN_add(3),
BN_CTX_new(3)
.SH "HISTORY"
.IX Header "HISTORY"
\&\fIBN_MONT_CTX_new()\fR, \fIBN_MONT_CTX_free()\fR, \fIBN_MONT_CTX_set()\fR,
\&\fIBN_mod_mul_montgomery()\fR, \fIBN_from_montgomery()\fR and \fIBN_to_montgomery()\fR
are available in all versions of SSLeay and OpenSSL.
.PP
\&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b.
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