mirror of
https://github.com/clearml/dropbear
synced 2025-06-26 18:17:32 +00:00
0.30 release of LibTomMath
--HG-- branch : libtommath-orig extra : convert_revision : be264b7e24d36930eed24f74b3c77a4e437691ab
This commit is contained in:
Matt Johnston
parent
3b2639b9b5
commit
6666e06851
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bn.ilg
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This is makeindex, version 2.14 [02-Oct-2002] (kpathsea + Thai support).
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Scanning input file bn.idx....done (79 entries accepted, 0 rejected).
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Sorting entries....done (511 comparisons).
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Generating output file bn.ind....done (82 lines written, 0 warnings).
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Output written in bn.ind.
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Transcript written in bn.ilg.
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82
bn.ind
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bn.ind
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\begin{theindex}
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\item mp\_add, \hyperpage{25}
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\item mp\_add\_d, \hyperpage{48}
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\item mp\_and, \hyperpage{25}
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\item mp\_clear, \hyperpage{7}
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||||
\item mp\_clear\_multi, \hyperpage{8}
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||||
\item mp\_cmp, \hyperpage{20}
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||||
\item mp\_cmp\_d, \hyperpage{21}
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||||
\item mp\_cmp\_mag, \hyperpage{19}
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||||
\item mp\_div, \hyperpage{26}
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||||
\item mp\_div\_2, \hyperpage{22}
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||||
\item mp\_div\_2d, \hyperpage{24}
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||||
\item mp\_div\_d, \hyperpage{48}
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||||
\item mp\_dr\_reduce, \hyperpage{36}
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||||
\item mp\_dr\_setup, \hyperpage{36}
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||||
\item MP\_EQ, \hyperpage{18}
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||||
\item mp\_error\_to\_string, \hyperpage{6}
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||||
\item mp\_expt\_d, \hyperpage{39}
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||||
\item mp\_exptmod, \hyperpage{39}
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||||
\item mp\_exteuclid, \hyperpage{47}
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||||
\item mp\_gcd, \hyperpage{47}
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||||
\item mp\_get\_int, \hyperpage{16}
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||||
\item mp\_grow, \hyperpage{12}
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||||
\item MP\_GT, \hyperpage{18}
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||||
\item mp\_init, \hyperpage{7}
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||||
\item mp\_init\_copy, \hyperpage{9}
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||||
\item mp\_init\_multi, \hyperpage{8}
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||||
\item mp\_init\_set, \hyperpage{17}
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||||
\item mp\_init\_set\_int, \hyperpage{17}
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||||
\item mp\_init\_size, \hyperpage{10}
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||||
\item mp\_int, \hyperpage{6}
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||||
\item mp\_invmod, \hyperpage{48}
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||||
\item mp\_jacobi, \hyperpage{48}
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||||
\item mp\_lcm, \hyperpage{47}
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||||
\item mp\_lshd, \hyperpage{24}
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||||
\item MP\_LT, \hyperpage{18}
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||||
\item MP\_MEM, \hyperpage{5}
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||||
\item mp\_mod, \hyperpage{31}
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||||
\item mp\_mod\_d, \hyperpage{48}
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||||
\item mp\_montgomery\_calc\_normalization, \hyperpage{34}
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||||
\item mp\_montgomery\_reduce, \hyperpage{33}
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||||
\item mp\_montgomery\_setup, \hyperpage{33}
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||||
\item mp\_mul, \hyperpage{27}
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||||
\item mp\_mul\_2, \hyperpage{22}
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||||
\item mp\_mul\_2d, \hyperpage{24}
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||||
\item mp\_mul\_d, \hyperpage{48}
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||||
\item mp\_n\_root, \hyperpage{40}
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||||
\item mp\_neg, \hyperpage{25}
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||||
\item MP\_NO, \hyperpage{5}
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||||
\item MP\_OKAY, \hyperpage{5}
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||||
\item mp\_or, \hyperpage{25}
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\item mp\_prime\_fermat, \hyperpage{41}
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\item mp\_prime\_is\_divisible, \hyperpage{41}
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||||
\item mp\_prime\_is\_prime, \hyperpage{42}
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\item mp\_prime\_miller\_rabin, \hyperpage{41}
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\item mp\_prime\_next\_prime, \hyperpage{42}
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||||
\item mp\_prime\_rabin\_miller\_trials, \hyperpage{42}
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||||
\item mp\_prime\_random, \hyperpage{43}
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\item mp\_prime\_random\_ex, \hyperpage{43}
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||||
\item mp\_radix\_size, \hyperpage{45}
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||||
\item mp\_read\_radix, \hyperpage{45}
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||||
\item mp\_read\_unsigned\_bin, \hyperpage{46}
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\item mp\_reduce, \hyperpage{32}
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\item mp\_reduce\_2k, \hyperpage{37}
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\item mp\_reduce\_2k\_setup, \hyperpage{37}
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\item mp\_reduce\_setup, \hyperpage{32}
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\item mp\_rshd, \hyperpage{24}
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\item mp\_set, \hyperpage{15}
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\item mp\_set\_int, \hyperpage{16}
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\item mp\_shrink, \hyperpage{11}
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\item mp\_sqr, \hyperpage{29}
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\item mp\_sub, \hyperpage{25}
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\item mp\_sub\_d, \hyperpage{48}
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\item mp\_to\_unsigned\_bin, \hyperpage{46}
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\item mp\_toradix, \hyperpage{45}
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\item mp\_unsigned\_bin\_size, \hyperpage{46}
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\item MP\_VAL, \hyperpage{5}
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\item mp\_xor, \hyperpage{25}
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\item MP\_YES, \hyperpage{5}
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\end{theindex}
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0
poster.out
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poster.out
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poster.pdf
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poster.tex
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\documentclass[landscape,11pt]{article}
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\usepackage{amsmath, amssymb}
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\usepackage{hyperref}
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\begin{document}
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\hspace*{-3in}
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\begin{tabular}{llllll}
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$c = a + b$ & {\tt mp\_add(\&a, \&b, \&c)} & $b = 2a$ & {\tt mp\_mul\_2(\&a, \&b)} & \\
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$c = a - b$ & {\tt mp\_sub(\&a, \&b, \&c)} & $b = a/2$ & {\tt mp\_div\_2(\&a, \&b)} & \\
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$c = ab $ & {\tt mp\_mul(\&a, \&b, \&c)} & $c = 2^ba$ & {\tt mp\_mul\_2d(\&a, b, \&c)} \\
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$b = a^2 $ & {\tt mp\_sqr(\&a, \&b)} & $c = a/2^b, d = a \mod 2^b$ & {\tt mp\_div\_2d(\&a, b, \&c, \&d)} \\
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$c = \lfloor a/b \rfloor, d = a \mod b$ & {\tt mp\_div(\&a, \&b, \&c, \&d)} & $c = a \mod 2^b $ & {\tt mp\_mod\_2d(\&a, b, \&c)} \\
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&& \\
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$a = b $ & {\tt mp\_set\_int(\&a, b)} & $c = a \vee b$ & {\tt mp\_or(\&a, \&b, \&c)} \\
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$b = a $ & {\tt mp\_copy(\&a, \&b)} & $c = a \wedge b$ & {\tt mp\_and(\&a, \&b, \&c)} \\
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&& $c = a \oplus b$ & {\tt mp\_xor(\&a, \&b, \&c)} \\
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& \\
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$b = -a $ & {\tt mp\_neg(\&a, \&b)} & $d = a + b \mod c$ & {\tt mp\_addmod(\&a, \&b, \&c, \&d)} \\
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$b = |a| $ & {\tt mp\_abs(\&a, \&b)} & $d = a - b \mod c$ & {\tt mp\_submod(\&a, \&b, \&c, \&d)} \\
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&& $d = ab \mod c$ & {\tt mp\_mulmod(\&a, \&b, \&c, \&d)} \\
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Compare $a$ and $b$ & {\tt mp\_cmp(\&a, \&b)} & $c = a^2 \mod b$ & {\tt mp\_sqrmod(\&a, \&b, \&c)} \\
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Is Zero? & {\tt mp\_iszero(\&a)} & $c = a^{-1} \mod b$ & {\tt mp\_invmod(\&a, \&b, \&c)} \\
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Is Even? & {\tt mp\_iseven(\&a)} & $d = a^b \mod c$ & {\tt mp\_exptmod(\&a, \&b, \&c, \&d)} \\
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Is Odd ? & {\tt mp\_isodd(\&a)} \\
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&\\
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$\vert \vert a \vert \vert$ & {\tt mp\_unsigned\_bin\_size(\&a)} & $res$ = 1 if $a$ prime to $t$ rounds? & {\tt mp\_prime\_is\_prime(\&a, t, \&res)} \\
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$buf \leftarrow a$ & {\tt mp\_to\_unsigned\_bin(\&a, buf)} & Next prime after $a$ to $t$ rounds. & {\tt mp\_prime\_next\_prime(\&a, t, bbs\_style)} \\
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$a \leftarrow buf[0..len-1]$ & {\tt mp\_read\_unsigned\_bin(\&a, buf, len)} \\
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&\\
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$b = \sqrt{a}$ & {\tt mp\_sqrt(\&a, \&b)} & $c = \mbox{gcd}(a, b)$ & {\tt mp\_gcd(\&a, \&b, \&c)} \\
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$c = a^{1/b}$ & {\tt mp\_n\_root(\&a, b, \&c)} & $c = \mbox{lcm}(a, b)$ & {\tt mp\_lcm(\&a, \&b, \&c)} \\
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&\\
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Greater Than & MP\_GT & Equal To & MP\_EQ \\
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Less Than & MP\_LT & Bits per digit & DIGIT\_BIT \\
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\end{tabular}
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\end{document}
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139
tommath.out
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tommath.out
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\BOOKMARK [0][-]{chapter.1}{Introduction}{}
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\BOOKMARK [1][-]{section.1.1}{Multiple Precision Arithmetic}{chapter.1}
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\BOOKMARK [2][-]{subsection.1.1.1}{What is Multiple Precision Arithmetic?}{section.1.1}
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\BOOKMARK [2][-]{subsection.1.1.2}{The Need for Multiple Precision Arithmetic}{section.1.1}
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\BOOKMARK [2][-]{subsection.1.1.3}{Benefits of Multiple Precision Arithmetic}{section.1.1}
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\BOOKMARK [1][-]{section.1.2}{Purpose of This Text}{chapter.1}
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\BOOKMARK [1][-]{section.1.3}{Discussion and Notation}{chapter.1}
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\BOOKMARK [2][-]{subsection.1.3.1}{Notation}{section.1.3}
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\BOOKMARK [2][-]{subsection.1.3.2}{Precision Notation}{section.1.3}
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||||
\BOOKMARK [2][-]{subsection.1.3.3}{Algorithm Inputs and Outputs}{section.1.3}
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\BOOKMARK [2][-]{subsection.1.3.4}{Mathematical Expressions}{section.1.3}
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\BOOKMARK [2][-]{subsection.1.3.5}{Work Effort}{section.1.3}
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\BOOKMARK [1][-]{section.1.4}{Exercises}{chapter.1}
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\BOOKMARK [1][-]{section.1.5}{Introduction to LibTomMath}{chapter.1}
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\BOOKMARK [2][-]{subsection.1.5.1}{What is LibTomMath?}{section.1.5}
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\BOOKMARK [2][-]{subsection.1.5.2}{Goals of LibTomMath}{section.1.5}
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||||
\BOOKMARK [1][-]{section.1.6}{Choice of LibTomMath}{chapter.1}
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\BOOKMARK [2][-]{subsection.1.6.1}{Code Base}{section.1.6}
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\BOOKMARK [2][-]{subsection.1.6.2}{API Simplicity}{section.1.6}
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||||
\BOOKMARK [2][-]{subsection.1.6.3}{Optimizations}{section.1.6}
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||||
\BOOKMARK [2][-]{subsection.1.6.4}{Portability and Stability}{section.1.6}
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||||
\BOOKMARK [2][-]{subsection.1.6.5}{Choice}{section.1.6}
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\BOOKMARK [0][-]{chapter.2}{Getting Started}{}
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\BOOKMARK [1][-]{section.2.1}{Library Basics}{chapter.2}
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||||
\BOOKMARK [1][-]{section.2.2}{What is a Multiple Precision Integer?}{chapter.2}
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||||
\BOOKMARK [2][-]{subsection.2.2.1}{The mp\137int Structure}{section.2.2}
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||||
\BOOKMARK [1][-]{section.2.3}{Argument Passing}{chapter.2}
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||||
\BOOKMARK [1][-]{section.2.4}{Return Values}{chapter.2}
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||||
\BOOKMARK [1][-]{section.2.5}{Initialization and Clearing}{chapter.2}
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||||
\BOOKMARK [2][-]{subsection.2.5.1}{Initializing an mp\137int}{section.2.5}
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\BOOKMARK [2][-]{subsection.2.5.2}{Clearing an mp\137int}{section.2.5}
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||||
\BOOKMARK [1][-]{section.2.6}{Maintenance Algorithms}{chapter.2}
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||||
\BOOKMARK [2][-]{subsection.2.6.1}{Augmenting an mp\137int's Precision}{section.2.6}
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\BOOKMARK [2][-]{subsection.2.6.2}{Initializing Variable Precision mp\137ints}{section.2.6}
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||||
\BOOKMARK [2][-]{subsection.2.6.3}{Multiple Integer Initializations and Clearings}{section.2.6}
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||||
\BOOKMARK [2][-]{subsection.2.6.4}{Clamping Excess Digits}{section.2.6}
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\BOOKMARK [0][-]{chapter.3}{Basic Operations}{}
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\BOOKMARK [1][-]{section.3.1}{Introduction}{chapter.3}
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||||
\BOOKMARK [1][-]{section.3.2}{Assigning Values to mp\137int Structures}{chapter.3}
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||||
\BOOKMARK [2][-]{subsection.3.2.1}{Copying an mp\137int}{section.3.2}
|
||||
\BOOKMARK [2][-]{subsection.3.2.2}{Creating a Clone}{section.3.2}
|
||||
\BOOKMARK [1][-]{section.3.3}{Zeroing an Integer}{chapter.3}
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||||
\BOOKMARK [1][-]{section.3.4}{Sign Manipulation}{chapter.3}
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||||
\BOOKMARK [2][-]{subsection.3.4.1}{Absolute Value}{section.3.4}
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||||
\BOOKMARK [2][-]{subsection.3.4.2}{Integer Negation}{section.3.4}
|
||||
\BOOKMARK [1][-]{section.3.5}{Small Constants}{chapter.3}
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||||
\BOOKMARK [2][-]{subsection.3.5.1}{Setting Small Constants}{section.3.5}
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||||
\BOOKMARK [2][-]{subsection.3.5.2}{Setting Large Constants}{section.3.5}
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||||
\BOOKMARK [1][-]{section.3.6}{Comparisons}{chapter.3}
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||||
\BOOKMARK [2][-]{subsection.3.6.1}{Unsigned Comparisions}{section.3.6}
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||||
\BOOKMARK [2][-]{subsection.3.6.2}{Signed Comparisons}{section.3.6}
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||||
\BOOKMARK [0][-]{chapter.4}{Basic Arithmetic}{}
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\BOOKMARK [1][-]{section.4.1}{Introduction}{chapter.4}
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||||
\BOOKMARK [1][-]{section.4.2}{Addition and Subtraction}{chapter.4}
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||||
\BOOKMARK [2][-]{subsection.4.2.1}{Low Level Addition}{section.4.2}
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||||
\BOOKMARK [2][-]{subsection.4.2.2}{Low Level Subtraction}{section.4.2}
|
||||
\BOOKMARK [2][-]{subsection.4.2.3}{High Level Addition}{section.4.2}
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||||
\BOOKMARK [2][-]{subsection.4.2.4}{High Level Subtraction}{section.4.2}
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||||
\BOOKMARK [1][-]{section.4.3}{Bit and Digit Shifting}{chapter.4}
|
||||
\BOOKMARK [2][-]{subsection.4.3.1}{Multiplication by Two}{section.4.3}
|
||||
\BOOKMARK [2][-]{subsection.4.3.2}{Division by Two}{section.4.3}
|
||||
\BOOKMARK [1][-]{section.4.4}{Polynomial Basis Operations}{chapter.4}
|
||||
\BOOKMARK [2][-]{subsection.4.4.1}{Multiplication by x}{section.4.4}
|
||||
\BOOKMARK [2][-]{subsection.4.4.2}{Division by x}{section.4.4}
|
||||
\BOOKMARK [1][-]{section.4.5}{Powers of Two}{chapter.4}
|
||||
\BOOKMARK [2][-]{subsection.4.5.1}{Multiplication by Power of Two}{section.4.5}
|
||||
\BOOKMARK [2][-]{subsection.4.5.2}{Division by Power of Two}{section.4.5}
|
||||
\BOOKMARK [2][-]{subsection.4.5.3}{Remainder of Division by Power of Two}{section.4.5}
|
||||
\BOOKMARK [0][-]{chapter.5}{Multiplication and Squaring}{}
|
||||
\BOOKMARK [1][-]{section.5.1}{The Multipliers}{chapter.5}
|
||||
\BOOKMARK [1][-]{section.5.2}{Multiplication}{chapter.5}
|
||||
\BOOKMARK [2][-]{subsection.5.2.1}{The Baseline Multiplication}{section.5.2}
|
||||
\BOOKMARK [2][-]{subsection.5.2.2}{Faster Multiplication by the ``Comba'' Method}{section.5.2}
|
||||
\BOOKMARK [2][-]{subsection.5.2.3}{Polynomial Basis Multiplication}{section.5.2}
|
||||
\BOOKMARK [2][-]{subsection.5.2.4}{Karatsuba Multiplication}{section.5.2}
|
||||
\BOOKMARK [2][-]{subsection.5.2.5}{Toom-Cook 3-Way Multiplication}{section.5.2}
|
||||
\BOOKMARK [2][-]{subsection.5.2.6}{Signed Multiplication}{section.5.2}
|
||||
\BOOKMARK [1][-]{section.5.3}{Squaring}{chapter.5}
|
||||
\BOOKMARK [2][-]{subsection.5.3.1}{The Baseline Squaring Algorithm}{section.5.3}
|
||||
\BOOKMARK [2][-]{subsection.5.3.2}{Faster Squaring by the ``Comba'' Method}{section.5.3}
|
||||
\BOOKMARK [2][-]{subsection.5.3.3}{Polynomial Basis Squaring}{section.5.3}
|
||||
\BOOKMARK [2][-]{subsection.5.3.4}{Karatsuba Squaring}{section.5.3}
|
||||
\BOOKMARK [2][-]{subsection.5.3.5}{Toom-Cook Squaring}{section.5.3}
|
||||
\BOOKMARK [2][-]{subsection.5.3.6}{High Level Squaring}{section.5.3}
|
||||
\BOOKMARK [0][-]{chapter.6}{Modular Reduction}{}
|
||||
\BOOKMARK [1][-]{section.6.1}{Basics of Modular Reduction}{chapter.6}
|
||||
\BOOKMARK [1][-]{section.6.2}{The Barrett Reduction}{chapter.6}
|
||||
\BOOKMARK [2][-]{subsection.6.2.1}{Fixed Point Arithmetic}{section.6.2}
|
||||
\BOOKMARK [2][-]{subsection.6.2.2}{Choosing a Radix Point}{section.6.2}
|
||||
\BOOKMARK [2][-]{subsection.6.2.3}{Trimming the Quotient}{section.6.2}
|
||||
\BOOKMARK [2][-]{subsection.6.2.4}{Trimming the Residue}{section.6.2}
|
||||
\BOOKMARK [2][-]{subsection.6.2.5}{The Barrett Algorithm}{section.6.2}
|
||||
\BOOKMARK [2][-]{subsection.6.2.6}{The Barrett Setup Algorithm}{section.6.2}
|
||||
\BOOKMARK [1][-]{section.6.3}{The Montgomery Reduction}{chapter.6}
|
||||
\BOOKMARK [2][-]{subsection.6.3.1}{Digit Based Montgomery Reduction}{section.6.3}
|
||||
\BOOKMARK [2][-]{subsection.6.3.2}{Baseline Montgomery Reduction}{section.6.3}
|
||||
\BOOKMARK [2][-]{subsection.6.3.3}{Faster ``Comba'' Montgomery Reduction}{section.6.3}
|
||||
\BOOKMARK [2][-]{subsection.6.3.4}{Montgomery Setup}{section.6.3}
|
||||
\BOOKMARK [1][-]{section.6.4}{The Diminished Radix Algorithm}{chapter.6}
|
||||
\BOOKMARK [2][-]{subsection.6.4.1}{Choice of Moduli}{section.6.4}
|
||||
\BOOKMARK [2][-]{subsection.6.4.2}{Choice of k}{section.6.4}
|
||||
\BOOKMARK [2][-]{subsection.6.4.3}{Restricted Diminished Radix Reduction}{section.6.4}
|
||||
\BOOKMARK [2][-]{subsection.6.4.4}{Unrestricted Diminished Radix Reduction}{section.6.4}
|
||||
\BOOKMARK [1][-]{section.6.5}{Algorithm Comparison}{chapter.6}
|
||||
\BOOKMARK [0][-]{chapter.7}{Exponentiation}{}
|
||||
\BOOKMARK [1][-]{section.7.1}{Exponentiation Basics}{chapter.7}
|
||||
\BOOKMARK [2][-]{subsection.7.1.1}{Single Digit Exponentiation}{section.7.1}
|
||||
\BOOKMARK [1][-]{section.7.2}{k-ary Exponentiation}{chapter.7}
|
||||
\BOOKMARK [2][-]{subsection.7.2.1}{Optimal Values of k}{section.7.2}
|
||||
\BOOKMARK [2][-]{subsection.7.2.2}{Sliding-Window Exponentiation}{section.7.2}
|
||||
\BOOKMARK [1][-]{section.7.3}{Modular Exponentiation}{chapter.7}
|
||||
\BOOKMARK [2][-]{subsection.7.3.1}{Barrett Modular Exponentiation}{section.7.3}
|
||||
\BOOKMARK [1][-]{section.7.4}{Quick Power of Two}{chapter.7}
|
||||
\BOOKMARK [0][-]{chapter.8}{Higher Level Algorithms}{}
|
||||
\BOOKMARK [1][-]{section.8.1}{Integer Division with Remainder}{chapter.8}
|
||||
\BOOKMARK [2][-]{subsection.8.1.1}{Quotient Estimation}{section.8.1}
|
||||
\BOOKMARK [2][-]{subsection.8.1.2}{Normalized Integers}{section.8.1}
|
||||
\BOOKMARK [2][-]{subsection.8.1.3}{Radix- Division with Remainder}{section.8.1}
|
||||
\BOOKMARK [1][-]{section.8.2}{Single Digit Helpers}{chapter.8}
|
||||
\BOOKMARK [2][-]{subsection.8.2.1}{Single Digit Addition and Subtraction}{section.8.2}
|
||||
\BOOKMARK [2][-]{subsection.8.2.2}{Single Digit Multiplication}{section.8.2}
|
||||
\BOOKMARK [2][-]{subsection.8.2.3}{Single Digit Division}{section.8.2}
|
||||
\BOOKMARK [2][-]{subsection.8.2.4}{Single Digit Root Extraction}{section.8.2}
|
||||
\BOOKMARK [1][-]{section.8.3}{Random Number Generation}{chapter.8}
|
||||
\BOOKMARK [1][-]{section.8.4}{Formatted Representations}{chapter.8}
|
||||
\BOOKMARK [2][-]{subsection.8.4.1}{Reading Radix-n Input}{section.8.4}
|
||||
\BOOKMARK [2][-]{subsection.8.4.2}{Generating Radix-n Output}{section.8.4}
|
||||
\BOOKMARK [0][-]{chapter.9}{Number Theoretic Algorithms}{}
|
||||
\BOOKMARK [1][-]{section.9.1}{Greatest Common Divisor}{chapter.9}
|
||||
\BOOKMARK [2][-]{subsection.9.1.1}{Complete Greatest Common Divisor}{section.9.1}
|
||||
\BOOKMARK [1][-]{section.9.2}{Least Common Multiple}{chapter.9}
|
||||
\BOOKMARK [1][-]{section.9.3}{Jacobi Symbol Computation}{chapter.9}
|
||||
\BOOKMARK [2][-]{subsection.9.3.1}{Jacobi Symbol}{section.9.3}
|
||||
\BOOKMARK [1][-]{section.9.4}{Modular Inverse}{chapter.9}
|
||||
\BOOKMARK [2][-]{subsection.9.4.1}{General Case}{section.9.4}
|
||||
\BOOKMARK [1][-]{section.9.5}{Primality Tests}{chapter.9}
|
||||
\BOOKMARK [2][-]{subsection.9.5.1}{Trial Division}{section.9.5}
|
||||
\BOOKMARK [2][-]{subsection.9.5.2}{The Fermat Test}{section.9.5}
|
||||
\BOOKMARK [2][-]{subsection.9.5.3}{The Miller-Rabin Test}{section.9.5}
|
||||
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Reference in New Issue
Block a user