f4401cd869
alter des.h to be friendly with openssl/des.h (you can include both in the same file) make libkrb to depend on libdes. bump major. massage various portioin of heimdal to be friendly with openssl 0.9.7b.
245 lines
7.5 KiB
Groff
245 lines
7.5 KiB
Groff
.\" $NetBSD: BN_mod_mul_montgomery.3,v 1.12 2003/07/24 14:16:37 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 "0.9.7b" "2002-09-25" "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 \fImont\fR structure from the modulus \fIm\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 \fIfrom\fR to \fIto\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(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places
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the result in \fIr\fR.
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.PP
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\&\fIBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1.
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.PP
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\&\fIBN_to_montgomery()\fR computes Mont(\fIa\fR,R^2), i.e. \fIa\fR*R.
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Note that \fIa\fR must be non-negative and smaller than the modulus.
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.PP
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For all functions, \fIctx\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 "WARNING"
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.IX Header "WARNING"
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The inputs must be reduced modulo \fBm\fR, otherwise the result will be
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outside the expected range.
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.SH "SEE ALSO"
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.IX Header "SEE ALSO"
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openssl_bn(3), ERR_get_error(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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