summaryrefslogtreecommitdiffstats
path: root/secure/lib/libcrypto/man/BN_mod_mul_montgomery.3
diff options
context:
space:
mode:
Diffstat (limited to 'secure/lib/libcrypto/man/BN_mod_mul_montgomery.3')
-rw-r--r--secure/lib/libcrypto/man/BN_mod_mul_montgomery.3234
1 files changed, 234 insertions, 0 deletions
diff --git a/secure/lib/libcrypto/man/BN_mod_mul_montgomery.3 b/secure/lib/libcrypto/man/BN_mod_mul_montgomery.3
new file mode 100644
index 0000000..89e295b
--- /dev/null
+++ b/secure/lib/libcrypto/man/BN_mod_mul_montgomery.3
@@ -0,0 +1,234 @@
+.\" Automatically generated by Pod::Man 2.28 (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++. 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 turned on, 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 "2015-12-03" "1.0.2e" "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.
OpenPOWER on IntegriCloud