240 lines
7.3 KiB
Groff
240 lines
7.3 KiB
Groff
.\" $NetBSD: BN_mod_mul_montgomery.3,v 1.7 2002/06/09 16:12:57 itojun Exp $
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.\" ======================================================================
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.\"
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.IX Title "BN_mod_mul_montgomery 3"
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.TH BN_mod_mul_montgomery 3 "0.9.6d" "2001-04-12" "OpenSSL"
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.UC
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.SH "NAME"
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BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
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BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
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BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication
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.SH "LIBRARY"
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libcrypto, -lcrypto
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.SH "SYNOPSIS"
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.IX Header "SYNOPSIS"
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.Vb 1
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\& #include <openssl/bn.h>
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.Ve
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.Vb 3
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\& BN_MONT_CTX *BN_MONT_CTX_new(void);
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\& void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
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\& void BN_MONT_CTX_free(BN_MONT_CTX *mont);
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.Ve
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.Vb 2
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\& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
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\& BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
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.Ve
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.Vb 2
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\& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
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\& BN_MONT_CTX *mont, BN_CTX *ctx);
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.Ve
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.Vb 2
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\& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
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\& BN_CTX *ctx);
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.Ve
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.Vb 2
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\& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
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\& BN_CTX *ctx);
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.Ve
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.SH "DESCRIPTION"
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.IX Header "DESCRIPTION"
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These functions implement Montgomery multiplication. They are used
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automatically when BN_mod_exp(3) is called with suitable input,
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but they may be useful when several operations are to be performed
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using the same modulus.
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.PP
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\&\fIBN_MONT_CTX_new()\fR allocates and initializes a \fB\s-1BN_MONT_CTX\s0\fR structure.
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\&\fIBN_MONT_CTX_init()\fR initializes an existing uninitialized \fB\s-1BN_MONT_CTX\s0\fR.
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.PP
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\&\fIBN_MONT_CTX_set()\fR sets up the \fBmont\fR structure from the modulus \fBm\fR
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by precomputing its inverse and a value R.
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.PP
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\&\fIBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fBfrom\fR to \fBto\fR.
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.PP
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\&\fIBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if
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it was created by \fIBN_MONT_CTX_new()\fR, also the structure itself.
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.PP
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\&\fIBN_mod_mul_montgomery()\fR computes Mont(\fBa\fR,\fBb\fR):=\fBa\fR*\fBb\fR*R^\-1 and places
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the result in \fBr\fR.
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.PP
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\&\fIBN_from_montgomery()\fR performs the Montgomery reduction \fBr\fR = \fBa\fR*R^\-1.
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.PP
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\&\fIBN_to_montgomery()\fR computes Mont(\fBa\fR,R^2), i.e. \fBa\fR*R.
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.PP
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For all functions, \fBctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
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temporary variables.
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.PP
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The \fB\s-1BN_MONT_CTX\s0\fR structure is defined as follows:
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.PP
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.Vb 10
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\& typedef struct bn_mont_ctx_st
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\& {
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\& int ri; /* number of bits in R */
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\& BIGNUM RR; /* R^2 (used to convert to Montgomery form) */
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\& BIGNUM N; /* The modulus */
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\& BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
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\& * (Ni is only stored for bignum algorithm) */
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\& BN_ULONG n0; /* least significant word of Ni */
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\& int flags;
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\& } BN_MONT_CTX;
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.Ve
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\&\fIBN_to_montgomery()\fR is a macro.
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.SH "RETURN VALUES"
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.IX Header "RETURN VALUES"
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\&\fIBN_MONT_CTX_new()\fR returns the newly allocated \fB\s-1BN_MONT_CTX\s0\fR, and \s-1NULL\s0
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on error.
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.PP
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\&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_free()\fR have no return values.
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.PP
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For the other functions, 1 is returned for success, 0 on error.
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The error codes can be obtained by ERR_get_error(3).
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.SH "SEE ALSO"
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.IX Header "SEE ALSO"
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openssl_bn(3), openssl_err(3), BN_add(3),
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BN_CTX_new(3)
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.SH "HISTORY"
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.IX Header "HISTORY"
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\&\fIBN_MONT_CTX_new()\fR, \fIBN_MONT_CTX_free()\fR, \fIBN_MONT_CTX_set()\fR,
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\&\fIBN_mod_mul_montgomery()\fR, \fIBN_from_montgomery()\fR and \fIBN_to_montgomery()\fR
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are available in all versions of SSLeay and OpenSSL.
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.PP
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\&\fIBN_MONT_CTX_init()\fR and \fIBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b.
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