Edit File: BN_to_montgomery.3
.\" Automatically generated by Pod::Man 4.11 (Pod::Simple 3.35) .\" .\" 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++. Capital omega is used to do unbreakable dashes and .\" therefore won't be available. \*(C` and \*(C' expand to `' in nroff, .\" nothing in troff, for use with C<>. .tr \(*W- .ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p' .ie n \{\ . ds -- \(*W- . ds PI pi . if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch . if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch . ds L" "" . ds R" "" . ds C` "" . ds C' "" 'br\} .el\{\ . ds -- \|\(em\| . ds PI \(*p . ds L" `` . ds R" '' . ds C` . ds C' 'br\} .\" .\" Escape single quotes in literal strings from groff's Unicode transform. .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" .\" If the F register is >0, we'll generate index entries on stderr for .\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index .\" entries marked with X<> in POD. Of course, you'll have to process the .\" output yourself in some meaningful fashion. .\" .\" Avoid warning from groff about undefined register 'F'. .de IX .. .nr rF 0 .if \n(.g .if rF .nr rF 1 .if (\n(rF:(\n(.g==0)) \{\ . if \nF \{\ . de IX . tm Index:\\$1\t\\n%\t"\\$2" .. . if !\nF==2 \{\ . nr % 0 . nr F 2 . \} . \} .\} .rr rF .\" .\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2). .\" Fear. Run. Save yourself. 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 \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.