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편집 파일: BN_from_montgomery.3ssl

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Always turn off hyphenation; it makes .\" way too many mistakes in technical documents. .if n .ad l .nh .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 "SYNOPSIS" .IX Header "SYNOPSIS" .Vb 1 \& #include <openssl/bn.h> \& \& 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); \& \& 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); \& \& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b, \& BN_MONT_CTX *mont, BN_CTX *ctx); \& \& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, \& BN_CTX *ctx); \& \& 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 \fBBN_mod_exp\fR\|(3) is called with suitable input, but they may be useful when several operations are to be performed using the same modulus. .PP \&\fBBN_MONT_CTX_new()\fR allocates and initializes a \fB\s-1BN_MONT_CTX\s0\fR structure. \&\fBBN_MONT_CTX_init()\fR initializes an existing uninitialized \fB\s-1BN_MONT_CTX\s0\fR. .PP \&\fBBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR by precomputing its inverse and a value R. .PP \&\fBBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fIfrom\fR to \fIto\fR. .PP \&\fBBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if it was created by \fBBN_MONT_CTX_new()\fR, also the structure itself. .PP \&\fBBN_mod_mul_montgomery()\fR computes Mont(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places the result in \fIr\fR. .PP \&\fBBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1. .PP \&\fBBN_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 .PP \&\fBBN_to_montgomery()\fR is a macro. .SH "RETURN VALUES" .IX Header "RETURN VALUES" \&\fBBN_MONT_CTX_new()\fR returns the newly allocated \fB\s-1BN_MONT_CTX\s0\fR, and \s-1NULL\s0 on error. .PP \&\fBBN_MONT_CTX_init()\fR and \fBBN_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 \fBERR_get_error\fR\|(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" \&\fBbn\fR\|(3), \fBERR_get_error\fR\|(3), \fBBN_add\fR\|(3), \&\fBBN_CTX_new\fR\|(3) .SH "HISTORY" .IX Header "HISTORY" \&\fBBN_MONT_CTX_new()\fR, \fBBN_MONT_CTX_free()\fR, \fBBN_MONT_CTX_set()\fR, \&\fBBN_mod_mul_montgomery()\fR, \fBBN_from_montgomery()\fR and \fBBN_to_montgomery()\fR are available in all versions of SSLeay and OpenSSL. .PP \&\fBBN_MONT_CTX_init()\fR and \fBBN_MONT_CTX_copy()\fR were added in SSLeay 0.9.1b.