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.\" Automatically generated by Pod::Man 2.27 (Pod::Simple 3.28) .\" .\" Standard preamble: .\" ======================================================================== .de Sp \" Vertical space (when we can't use .PP) .if t .sp .5v .if n .sp .. .de Vb \" Begin verbatim text .ft CW .nf .ne \\$1 .. .de Ve \" End verbatim text .ft R .fi .. .\" Set up some character translations and predefined strings. \*(-- will .\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left .\" double quote, and \*(R" will give a right double quote. \*(C+ will .\" give a nicer C++. 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No user-serviceable parts. . \" fudge factors for nroff and troff .if n \{\ . ds #H 0 . ds #V .8m . ds #F .3m . ds #[ \f1 . ds #] \fP .\} .if t \{\ . ds #H ((1u-(\\\\n(.fu%2u))*.13m) . ds #V .6m . ds #F 0 . ds #[ \& . ds #] \& .\} . \" simple accents for nroff and troff .if n \{\ . ds ' \& . ds ` \& . ds ^ \& . ds , \& . ds ~ ~ . ds / .\} .if t \{\ . ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u" . ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u' . ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u' . ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u' . ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u' . ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u' .\} . \" troff and (daisy-wheel) nroff accents .ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V' .ds 8 \h'\*(#H'\(*b\h'-\*(#H' .ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#] .ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H' .ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u' .ds th \*(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u*2/3)'\s-1o\s+1\*(#] .ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#] .ds ae a\h'-(\w'a'u*4/10)'e .ds Ae A\h'-(\w'A'u*4/10)'E . \" corrections for vroff .if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u' .if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u' . \" for low resolution devices (crt and lpr) .if \n(.H>23 .if \n(.V>19 \ \{\ . ds : e . ds 8 ss . ds o a . ds d- d\h'-1'\(ga . ds D- D\h'-1'\(hy . ds th \o'bp' . ds Th \o'LP' . ds ae ae . ds Ae AE .\} .rm #[ #] #H #V #F C .\" ======================================================================== .\" .IX Title "BN_mod_mul_montgomery 3" .TH BN_mod_mul_montgomery 3 "2019-12-20" "1.0.2u" "OpenSSL" .\" For nroff, turn off justification. 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 \fIBN_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 \&\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 .PP \&\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 \fIERR_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" \&\fIbn\fR\|(3), \fIERR_get_error\fR\|(3), \fIBN_add\fR\|(3), \&\fIBN_CTX_new\fR\|(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.