2326 lines
107 KiB
TeX
2326 lines
107 KiB
TeX
\documentclass{book}
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\usepackage{makeidx}
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\usepackage{amssymb}
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\def\union{\cup}
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\def\intersect{\cap}
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\def\getsrandom{\stackrel{\rm R}{\gets}}
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\def\cross{\times}
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\def\cat{\hspace{0.5em} \| \hspace{0.5em}}
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\def\catn{$\|$}
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\def\divides{\hspace{0.3em} | \hspace{0.3em}}
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\def\nequiv{\not\equiv}
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\def\approx{\raisebox{0.2ex}{\mbox{\small $\sim$}}}
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\def\lcm{{\rm lcm}}
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\def\gcd{{\rm gcd}}
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\def\log{{\rm log}}
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\def\ord{{\rm ord}}
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\def\abs{{\mathit abs}}
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\def\rep{{\mathit rep}}
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\def\mod{{\mathit\ mod\ }}
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\renewcommand{\pmod}[1]{\ ({\rm mod\ }{#1})}
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\newcommand{\floor}[1]{\left\lfloor{#1}\right\rfloor}
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\newcommand{\ceil}[1]{\left\lceil{#1}\right\rceil}
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\def\Or{{\rm\ or\ }}
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\def\And{{\rm\ and\ }}
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\def\iff{\hspace{1em}\Longleftrightarrow\hspace{1em}}
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\def\implies{\Rightarrow}
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\def\undefined{{\rm ``undefined"}}
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\def\Proof{\vspace{1ex}\noindent {\bf Proof:}\hspace{1em}}
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\let\oldphi\phi
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\def\phi{\varphi}
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\def\Pr{{\rm Pr}}
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\newcommand{\str}[1]{{\mathbf{#1}}}
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\def\F{{\mathbb F}}
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\def\N{{\mathbb N}}
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\def\Z{{\mathbb Z}}
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\def\R{{\mathbb R}}
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\def\C{{\mathbb C}}
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\def\Q{{\mathbb Q}}
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\newcommand{\url}[1]{\mbox{$<${#1}$>$}}
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\newcommand{\emailaddr}[1]{\mbox{$<${#1}$>$}}
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\def\twiddle{\raisebox{0.3ex}{\mbox{\tiny $\sim$}}}
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\def\gap{\vspace{0.5ex}}
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\makeindex
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\begin{document}
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\title{A Tiny Crypto Library, \\ LibTomCrypt \\ Version 0.80}
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\author{Tom St Denis \\
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Algonquin College \\
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\\
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tomstdenis@yahoo.com \\
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http://libtomcrypt.iahu.ca \\ \\
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Phone: 1-613-836-3160\\
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111 Banning Rd \\
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Kanata, Ontario \\
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K2L 1C3 \\
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Canada
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}
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\maketitle
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\newpage
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\tableofcontents
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\chapter{Introduction}
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\section{What is the Libtomcrypt?}
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Libtomcrypt is a portable ANSI C cryptographic library that supports symmetric ciphers, one-way hashes,
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pseudo-random number generators, public key cryptography (via RSA,DH or ECC/DH) and a plethora of support
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routines. It is designed to compile out of the box with the GNU C Compiler (GCC) version 2.95.3 (and higher)
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and with MSVC version 6 in win32.
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The library is designed so new ciphers/hashes/PRNGs can be added at runtime and the existing API (and helper API functions) will
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be able to use the new designs automatically. There exist self-check functions for each cipher and hash to ensure that
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they compile and execute to the published design specifications. The library also performs extensive parameter error checking
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and will give verbose error messages.
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Essentially the library saves the time of having to implement the ciphers, hashes, prngs yourself. Typically implementing
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useful cryptography is an error prone business which means anything that can save considerable time and effort is a good
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thing.
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\subsection{What the library IS for?}
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The library typically serves as a basis for other protocols and message formats. For example, it should be possible to
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take the RSA routines out of this library, apply the appropriate message padding and get PKCS compliant RSA routines.
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Similarly SSL protocols could be formed on top of the low-level symmetric cipher functions. The goal of this package is
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to provide these low level core functions in a robust and easy to use fashion.
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The library also serves well as a toolkit for applications where they don't need to be OpenPGP, PKCS, etc. compliant.
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Included are fully operational public key routines for encryption, decryption, signature generation and verification.
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These routines are fully portable but are not conformant to any known set of standards. They are all based on established
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number theory and cryptography.
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\subsection{What the library IS NOT for?}
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The library is not designed to be in anyway an implementation of the SSL, PKCS or OpenPGP standards. The library is not
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designed to be compliant with any known form of API or programming hierarchy. It is not a port of any other
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library and it is not platform specific (like the MS CSP). So if you're looking to drop in some buzzword
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compliant crypto this library is not for you. The library has been written from scratch to provide basic
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functions as well as non-standard higher level functions.
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This is not to say that the library is a ``homebrew'' project. All of the symmetric ciphers and one-way hash functions
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conform to published test vectors. The public key functions are derived from publicly available material and the majority
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of the code has been reviewed by a growing community of developers.
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\subsubsection{Why not?}
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You may be asking why I didn't choose to go all out and support standards like P1363, PKCS and the whole lot. The reason
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is quite simple too much money gets in the way. I just recently tried to access the P1363 draft documents and was denied (it
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requires a password). If people are supposed to support these standards they had better make them more accessible.
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\section{Why did I write it?}
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You may be wondering, ``Tom, why did you write a crypto library. I already have one.''. Well the reason falls into
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two categories:
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\begin{enumerate}
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\item I am too lazy to figure out someone else's API. I'd rather invent my own simpler API and use that.
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\item It was (still is) good coding practice.
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\end{enumerate}
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The idea is that I am not striving to replace OpenSSL or Crypto++ or Cryptlib or etc. I'm trying to write my
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{\bf own} crypto library and hopefully along the way others will appreciate the work.
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With this library all core functions (ciphers, hashes, prngs) have the {\bf exact} same prototype definition. They all load
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and store data in a format independent of the platform. This means if you encrypt with Blowfish on a PPC it should decrypt
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on an x86 with zero problems. The consistent API also means that if you learn how to use blowfish with my library you
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know how to use Safer+ or RC6 or Serpent or ... as well. With all of the core functions there are central descriptor tables
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that can be used to make a program automatically pick between ciphers, hashes and PRNGs at runtime. That means your
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application can support all ciphers/hashes/prngs without changing the source code.
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\section{License}
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All of the source code except for the following files have been written by the author or donated to the project
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under the TDCAL license:
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\begin{enumerate}
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\item aes.c
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\item mpi.c
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\item rc2.c
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\item serpent.c
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\item safer.c
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\end{enumerate}
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``aes.c'' and ``serpent.c'' were written by Brian Gladman (gladman@seven77.demon.co.uk). They are copyrighted works
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but were both granted unrestricted usage in any project (commercial or otherwise). ``mpi.c'' was written by Michael
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Fromberger (sting@linguist.dartmouth.edu). Similarly it is copyrighted work but is free for all purposes.
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``rc2.c'' is based on publicly available code that is not attributed to a person from the given source. ``safer.c''
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was written by Richard De Moliner (demoliner@isi.ee.ethz.ch) and is public domain.
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The rest of the code was written either by Tom St Denis or contributed to the project under the ``Tom Doesn't Care
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About Licenses'' (TDCAL) license. Essentially this license grants the user unlimited distribution and usage (including
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commercial usage). I assume no risk from usage of the code nor do I guarantee it works as desired or stated.
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\section{Patent Disclosure}
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The author (Tom St Denis) is not a patent lawyer so this section is not to be treated as legal advice. To the best
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of the authors knowledge the only patent related issues within the library are the RC5 and RC6 symmetric block ciphers.
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They can be removed from a build by simply commenting out the two appropriate lines in the makefile script. The rest
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of the ciphers and hashes are patent free or under patents that have since expired.
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The RC2 and RC4 symmetric ciphers are not under patents but are under trademark regulations. This means you can use
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the ciphers you just can't advertise that you are doing so.
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\section{Building the library}
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To build the library on a GCC equipped platform simply type ``make'' at your command prompt. It will build the library
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file ``libtomcrypt.a''.
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To install the library copy all of the ``.h'' files into your ``\#include'' path and the single libtomcrypt.a file into
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your library path.
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With MSVC you can build the library with ``make -f makefile.vc''. You must use GNU make to build it even with MSVC
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due to the limitations of the MS MAKE.
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\section{Building against the library}
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To build an application against the library you obviously must first compile the library. However, an important
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step is that the build options you use to build the library must be present when you build your application. For
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instance if ``RC5'' is defined in the makefile when you built the library then you must ensure ``RC5'' is defined when
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you build your application.
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The simplest way to work with this library is to take the makefile provided and simply add on your project to it as a
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target (dependent on the library). That way you can be assured that the library and your application are in sync with
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the build options you provide.
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\section{Thanks}
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I would like to give thanks to the following people (in no particular order) for helping me develop this project:
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\begin{enumerate}
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\item Richard van de Laarschot
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\item Richard Heathfield
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\item Ajay K. Agrawal
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\item Brian Gladman
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\item Svante Seleborg
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\item Clay Culver
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\item Jason Klapste
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\item Dobes Vandermeer
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\item Daniel Richards
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\item Wayne Scott
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\item Andrew Tyler
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\item Sky Schulz
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\item Christopher Imes
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\end{enumerate}
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\chapter{The Application Programming Interface (API)}
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\section{Introduction}
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\index{CRYPT\_ERROR} \index{CRYPT\_OK}
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In general the API is very simple to memorize and use. Most of the functions return either {\bf void} or {\bf int}. Functions
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that return {\bf int} will return {\bf CRYPT\_OK} if the function was successful or one of the many error codes
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if it failed. Certain functions that return int will return $-1$ to indicate an error. These functions will be explicitly
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commented upon. When a function does return a CRYPT error code it can be translated into a string with
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\begin{verbatim}
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const char *error_to_string(int errno);
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\end{verbatim}
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An example of handling an error is:
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\begin{verbatim}
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void somefunc(void)
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{
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int errno;
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/* call a cryptographic function */
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if ((errno = some_crypto_function(...)) != CRYPT_OK) {
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printf("A crypto error occured, %s\n", error_to_string(errno));
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/* perform error handling */
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}
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/* continue on if no error occured */
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}
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\end{verbatim}
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There is no initialization routine for the library and for the most part the code is thread safe. The only thread
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related issue is if you use the same symmetric cipher, hash or public key state data in multiple threads. Normally
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that is not an issue.
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To include the prototypes for ``LibTomCrypt.a'' into your own program simply include ``mycrypt.h'' like so:
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\begin{verbatim}
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#include <mycrypt.h>
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int main(void) {
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return 0;
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}
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\end{verbatim}
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The header file ``mycrypt.h'' also includes ``stdio.h'', ``string.h'', ``stdlib.h'', ``time.h'', ``ctype.h'' and ``mpi.h''
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(the bignum library routines).
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\section{Macros}
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There are a few helper macros to make the coding process a bit easier. The first set are related to loading and storing
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32/64-bit words in little/big endian format. The macros are:
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\index{STORE32L} \index{STORE64L} \index{LOAD32L} \index{LOAD64L}
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\index{STORE32H} \index{STORE64H} \index{LOAD32H} \index{LOAD64H} \index{BSWAP}
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\begin{small}
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\begin{center}
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\begin{tabular}{|c|c|c|}
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\hline STORE32L(x, y) & {\bf unsigned long} x, {\bf unsigned char} *y & $x \to y[0 \ldots 3]$ \\
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\hline STORE64L(x, y) & {\bf unsigned long long} x, {\bf unsigned char} *y & $x \to y[0 \ldots 7]$ \\
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\hline LOAD32L(x, y) & {\bf unsigned long} x, {\bf unsigned char} *y & $y[0 \ldots 3] \to x$ \\
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\hline LOAD64L(x, y) & {\bf unsigned long long} x, {\bf unsigned char} *y & $y[0 \ldots 7] \to x$ \\
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\hline STORE32H(x, y) & {\bf unsigned long} x, {\bf unsigned char} *y & $x \to y[3 \ldots 0]$ \\
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\hline STORE64H(x, y) & {\bf unsigned long long} x, {\bf unsigned char} *y & $x \to y[7 \ldots 0]$ \\
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\hline LOAD32H(x, y) & {\bf unsigned long} x, {\bf unsigned char} *y & $y[3 \ldots 0] \to x$ \\
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\hline LOAD64H(x, y) & {\bf unsigned long long} x, {\bf unsigned char} *y & $y[7 \ldots 0] \to x$ \\
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\hline BSWAP(x) & {\bf unsigned long} x & Swaps the byte order of x. \\
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\hline
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\end{tabular}
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\end{center}
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\end{small}
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There are 32-bit cyclic rotations as well:
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\index{ROL} \index{ROR}
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\begin{center}
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\begin{tabular}{|c|c|c|}
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\hline ROL(x, y) & {\bf unsigned long} x, {\bf unsigned long} y & $x << y$ \\
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\hline ROR(x, y) & {\bf unsigned long} x, {\bf unsigned long} y & $x >> y$ \\
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\hline
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\end{tabular}
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\end{center}
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\section{Functions with Variable Length Output}
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Certain functions such as (for example) ``rsa\_export()'' give an output that is variable length. To prevent buffer overflows you
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must pass it the length of the buffer\footnote{Extensive error checking is not in place but it will be in future releases so it is a good idea to follow through with these guidelines.} where
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the output will be stored. For example:
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\begin{small}
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\begin{verbatim}
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#include <mycrypt.h>
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int main(void) {
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rsa_key key;
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unsigned char buffer[1024];
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unsigned long x;
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int errno;
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/* ... Make up the RSA key somehow */
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/* lets export the key, set x to the size of the output buffer */
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x = sizeof(buffer);
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if ((errno = rsa_export(buffer, &x, PK_PUBLIC, &key)) != CRYPT_OK) {
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printf("Export error: %s\n", error_to_string(errno));
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return -1;
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}
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/* if rsa_export() was successful then x will have the size of the output */
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printf("RSA exported key takes %d bytes\n", x);
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/* ... do something with the buffer */
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return 0;
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}
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\end{verbatim}
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\end{small}
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In the above example if the size of the RSA public key was more than 1024 bytes this function would not store anything in
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either ``buffer'' or ``x'' and simply return an error code. If the function suceeds it stores the length of the output
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back into ``x'' so that the calling application will know how many bytes used.
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\section{Functions that need a PRNG}
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Certain functions such as ``rsa\_make\_key()'' require a PRNG. These functions do not setup the PRNG themselves so it is
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the responsibility of the calling function to initialize the PRNG before calling them.
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\section{Functions that use Arrays of Octets}
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Most functions require inputs that are arrays of the data type ``unsigned char''. Whether it is a symmetric key, IV
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for a chaining mode or public key packet it is assumed that regardless of the actual size of ``unsigned char'' only the
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lower eight bits contain data. For example, if you want to pass a 256 bit key to a symmetric ciphers setup routine
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you must pass it in (a pointer to) an array of 32 ``unsigned char'' variables. Certain routines
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(such as SAFER+) take special care to work properly on platforms where an ``unsigned char'' is not eight bits.
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For the purposes of this library the term ``byte'' will refer to an octet or eight bit word. Typically an array of
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type ``byte'' will be synonymous with an array of type ``unsigned char''.
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\chapter{Symmetric Block Ciphers}
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\section{Core Functions}
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Libtomcrypt provides several block ciphers all in a plain vanilla ECB block mode. Its important to first note that you
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should never use the ECB modes directly to encrypt data. Instead you should use the ECB functions to make a chaining mode
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or use one of the provided chaining modes. All of the ciphers are written as ECB interfaces since it allows the rest of
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the API to grow in a modular fashion.
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All ciphers store their scheduled keys in a single data type called ``symmetric\_key''. This allows all ciphers to
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have the same prototype and store their keys as naturally as possible. All ciphers provide five visible functions which
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are (given that XXX is the name of the cipher):
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\index{Cipher Setup}
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\begin{verbatim}
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int XXX_setup(const unsigned char *key, int keylen, int rounds,
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symmetric_key *skey);
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\end{verbatim}
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The XXX\_setup() routine will setup the cipher to be used with a given number of rounds and a given key length (in bytes).
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The number of rounds can be set to zero to use the default, which is generally a good idea.
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If the function returns successfully the variable ``skey'' will have a scheduled key stored in it. Its important to note
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that you should only used this scheduled key with the intended cipher. For example, if you call
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``blowfish\_setup()'' do not pass the scheduled key onto ``rc5\_ecb\_encrypt()''. All setup functions do not allocate
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memory off the heap so when you are done with a key you can simply discard it (e.g. they can be on the stack).
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To encrypt or decrypt a block in ECB mode there are these two functions:
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\index{Cipher Encrypt} \index{Cipher Decrypt}
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\begin{verbatim}
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void XXX_ecb_encrypt(const unsigned char *pt, unsigned char *ct,
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symmetric_key *skey);
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void XXX_ecb_decrypt(const unsigned char *ct, unsigned char *pt,
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symmetric_key *skey);
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\end{verbatim}
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These two functions will encrypt or decrypt (respectively) a single block of text\footnote{The size of which depends on
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which cipher you are using.} and store the result where you want it. It is possible that the input and output buffer are
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the same buffer. For the encrypt function ``pt''\footnote{pt stands for plaintext.} is the input and ``ct'' is the output.
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For the decryption function its the opposite. To test a particular cipher against test vectors\footnote{As published in their design papers.} call: \index{Cipher Testing}
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\begin{verbatim}
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int XXX_test(void);
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\end{verbatim}
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This function will return {\bf CRYPT\_OK} if the cipher matches the test vectors from the design publication it is
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based upon. Finally for each cipher there is a function which will help find a desired key size:
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\begin{verbatim}
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int XXX_keysize(int *keysize);
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\end{verbatim}
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Essentially it will round the input keysize in ``keysize'' down to the next appropriate key size. This function
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return {\bf CRYPT\_OK} if the key size specified is acceptable. For example:
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\begin{small}
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\begin{verbatim}
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|
#include <mycrypt.h>
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int main(void)
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{
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int keysize, errno;
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/* now given a 20 byte key what keysize does Twofish want to use? */
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keysize = 20;
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if ((errno = twofish_keysize(&keysize)) != CRYPT_OK) {
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printf("Error getting key size: %s\n", error_to_string(errno));
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return -1;
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}
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printf("Twofish suggested a key size of %d\n", keysize);
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return 0;
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}
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\end{verbatim}
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\end{small}
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This should indicate a keysize of sixteen bytes is suggested. An example snippet that encodes a block with
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Blowfish in ECB mode is below.
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\begin{small}
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\begin{verbatim}
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#include <mycrypt.h>
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int main(void)
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{
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unsigned char pt[8], ct[8], key[8];
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symmetric_key skey;
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int errno;
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/* ... key is loaded appropriately in ``key'' ... */
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/* ... load a block of plaintext in ``pt'' ... */
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/* schedule the key */
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if ((errno = blowfish_setup(key, 8, 0, &skey)) != CRYPT_OK) {
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printf("Setup error: %s\n", error_to_string(errno));
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return -1;
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}
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/* encrypt the block */
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blowfish_ecb_encrypt(pt, ct, &skey);
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/* decrypt the block */
|
|
blowfish_ecb_decrypt(ct, pt, &skey);
|
|
|
|
return 0;
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
|
|
\section{Key Sizes and Number of Rounds}
|
|
\index{Symmetric Keys}
|
|
As a general rule of thumb do not use symmetric keys under 80 bits if you can. Only a few of the ciphers support smaller
|
|
keys (mainly for test vectors anyways). Ideally your application should be making at least 256 bit keys. This is not
|
|
because you're supposed to be paranoid. Its because if your PRNG has a bias of any sort the more bits the better. For
|
|
example, if you have $\mbox{Pr}\left[X = 1\right] = {1 \over 2} \pm \gamma$ where $\vert \gamma \vert > 0$ then the
|
|
total amount of entropy in N bits is $N \cdot -log_2\left ({1 \over 2} + \vert \gamma \vert \right)$. So if $\gamma$
|
|
were $0.25$ (a severe bias) a 256-bit string would have about 106 bits of entropy whereas a 128-bit string would have
|
|
only 53 bits of entropy.
|
|
|
|
The number of rounds of most ciphers is not an option you can change. Only RC5 allows you to change the number of
|
|
rounds. By passing zero as the number of rounds all ciphers will use their default number of rounds. Generally the
|
|
ciphers are configured such that the default number of rounds provide adequate security for the given block size.
|
|
|
|
\section{The Cipher Descriptors}
|
|
\index{Cipher Descriptor}
|
|
To facilitate automatic routines an array of cipher descriptors is provided in the array ``cipher\_descriptor''. An element
|
|
of this array has the following format:
|
|
|
|
\begin{verbatim}
|
|
struct _cipher_descriptor {
|
|
char *name;
|
|
unsigned long min_key_length, max_key_length,
|
|
block_length, default_rounds;
|
|
int (*setup) (const unsigned char *key, int keylength,
|
|
int num_rounds, symmetric_key *skey);
|
|
void (*ecb_encrypt)(const unsigned char *pt, unsigned char *ct,
|
|
symmetric_key *key);
|
|
void (*ecb_decrypt)(const unsigned char *ct, unsigned char *pt,
|
|
symmetric_key *key);
|
|
int (*test) (void);
|
|
int (*keysize) (int *desired_keysize);
|
|
};
|
|
\end{verbatim}
|
|
|
|
Where ``name'' is the lower case ASCII version of the name. The fields ``min\_key\_length'', ``max\_key\_length'' and
|
|
``block\_length'' are all the number of bytes not bits. As a good rule of thumb it is assumed that the cipher supports
|
|
the min and max key lengths but not always everything in between. The ``default\_rounds'' field is the default number
|
|
of rounds that will be used.
|
|
|
|
The remaining fields are all pointers to the core functions for each cipher. The end of the cipher\_descriptor array is
|
|
marked when ``name'' equals {\bf NULL}.
|
|
|
|
As of this release the current cipher\_descriptors elements are
|
|
|
|
\begin{small}
|
|
\begin{center}
|
|
\begin{tabular}{|c|c|c|c|c|c|}
|
|
\hline Name & Descriptor Name & Block Size (bytes) & Key Range (bytes) & Rounds \\
|
|
\hline Blowfish & blowfish\_desc & 8 & 8 ... 56 & 16 \\
|
|
\hline X-Tea & xtea\_desc & 8 & 16 & 32 \\
|
|
\hline RC2 & rc2\_desc & 8 & 8 .. 128 & 16 \\
|
|
\hline RC5-32/12/b & rc5\_desc & 8 & 8 ... 128 & 12 ... 24 \\
|
|
\hline RC6-32/20/b & rc6\_desc & 16 & 8 ... 128 & 20 \\
|
|
\hline SAFER+ & saferp\_desc &16 & 16, 24, 32 & 8, 12, 16 \\
|
|
\hline Safer K64 & safer\_k64\_desc & 8 & 8 & 6 .. 13 \\
|
|
\hline Safer SK64 & safer\_sk64\_desc & 8 & 8 & 6 .. 13 \\
|
|
\hline Safer K128 & safer\_k128\_desc & 8 & 16 & 6 .. 13 \\
|
|
\hline Safer SK128 & safer\_sk128\_desc & 8 & 16 & 6 .. 13 \\
|
|
\hline Serpent & serpent\_desc & 16 & 16 .. 32 & 32 \\
|
|
\hline AES & aes\_desc & 16 & 16, 24, 32 & 10, 12, 14 \\
|
|
\hline Twofish & twofish\_desc & 16 & 16, 24, 32 & 16 \\
|
|
\hline DES & des\_desc & 8 & 7 & 16 \\
|
|
\hline 3DES (EDE mode) & des3\_desc & 8 & 21 & 16 \\
|
|
\hline CAST5 (CAST-128) & cast5\_desc & 8 & 5 .. 16 & 12, 16 \\
|
|
\hline Noekeon & noekeon\_desc & 16 & 16 & 16 \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\end{small}
|
|
|
|
\subsection{Notes}
|
|
For the 64-bit SAFER famliy of ciphers (e.g K64, SK64, K128, SK128) the ecb\_encrypt() and ecb\_decrypt()
|
|
functions are the same. So if you want to use those functions directly just call safer\_ecb\_encrypt()
|
|
or safer\_ecb\_decrypt() respectively.
|
|
|
|
Note that for ``DES'' and ``3DES'' they use 8 and 24 byte keys but only 7 and 21 [respectively] bytes of the keys are in
|
|
fact used for the purposes of encryption. My suggestion is just to use random 8/24 byte keys instead of trying to make a 8/24
|
|
byte string from the real 7/21 byte key.
|
|
|
|
Note that ``Twofish'' has additional configuration options that take place at build time. These options are found in
|
|
the file ``mycrypt\_cfg.h''. The first option is ``TWOFISH\_SMALL'' which when defined will force the Twofish code
|
|
to not pre-compute the Twofish ``$g(X)$'' function as a set of four $8 \times 32$ s-boxes. This means that a scheduled
|
|
key will require less ram but the resulting cipher will be slower. The second option is ``TWOFISH\_TABLES'' which when
|
|
defined will force the Twofish code to use pre-computed tables for the two s-boxes $q_0, q_1$ as well as the multiplication
|
|
by the polynomials 5B and EF used in the MDS multiplication. As a result the code is faster and slightly larger. The
|
|
speed increase is useful when ``TWOFISH\_SMALL'' is defined since the s-boxes and MDS multiply form the heart of the
|
|
Twofish round function.
|
|
|
|
\begin{small}
|
|
\begin{center}
|
|
\begin{tabular}{|l|l|l|}
|
|
\hline TWOFISH\_SMALL & TWOFISH\_TABLES & Speed and Memory (per key) \\
|
|
\hline undefined & undefined & Very fast, 4.2KB of ram. \\
|
|
\hline undefined & defined & As above, faster keysetup, larger code (1KB more). \\
|
|
\hline defined & undefined & Very slow, 0.2KB of ram. \\
|
|
\hline defined & defined & Somewhat faster, 0.2KB of ram, larger code. \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\end{small}
|
|
|
|
To work with the cipher\_descriptor array there is a function:
|
|
\begin{verbatim}
|
|
int find_cipher(char *name)
|
|
\end{verbatim}
|
|
Which will search for a given name in the array. It returns negative one if the cipher is not found, otherwise it returns
|
|
the location in the array where the cipher was found. For example, to indirectly setup Blowfish you can also use:
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
#include <mycrypt.h>
|
|
int main(void)
|
|
{
|
|
unsigned char key[8];
|
|
symmetric_key skey;
|
|
int errno;
|
|
|
|
/* you must register a cipher before you use it */
|
|
if (register_cipher(&blowfish_desc)) == -1) {
|
|
printf("Unable to register Blowfish cipher.");
|
|
return -1;
|
|
}
|
|
|
|
/* generic call to function (assuming the key in key[] was already setup) */
|
|
if ((errno = cipher_descriptor[find_cipher("blowfish")].setup(key, 8, 0, &skey)) != CRYPT_OK) {
|
|
printf("Error setting up Blowfish: %s\n", error_to_string(errno));
|
|
return -1;
|
|
}
|
|
|
|
/* ... use cipher ... */
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
|
|
A good safety would be to check the return value of ``find\_cipher()'' before accessing the desired function. In order
|
|
to use a cipher with the descriptor table you must register it first using:
|
|
\begin{verbatim}
|
|
int register_cipher(const struct _cipher_descriptor *cipher);
|
|
\end{verbatim}
|
|
Which accepts a pointer to a descriptor and returns the index into the global descriptor table. If an error occurs such
|
|
as there is no more room (it can have 32 ciphers at most) it will return {\bf{-1}}. If you try to add the same cipher more
|
|
than once it will just return the index of the first copy. To remove a cipher call:
|
|
\begin{verbatim}
|
|
int unregister_cipher(const struct _cipher_descriptor *cipher);
|
|
\end{verbatim}
|
|
Which returns {\bf CRYPT\_OK} if it removes it otherwise it returns {\bf CRYPT\_ERROR}. Consider:
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
#include <mycrypt.h>
|
|
int main(void)
|
|
{
|
|
int errno;
|
|
|
|
/* register the cipher */
|
|
if (register_cipher(&rijndael_desc) == -1) {
|
|
printf("Error registering Rijndael\n");
|
|
return -1;
|
|
}
|
|
|
|
/* use Rijndael */
|
|
|
|
/* remove it */
|
|
if ((errno = unregister_cipher(&rijndael_desc)) != CRYPT_OK) {
|
|
printf("Error removing Rijndael: %s\n", error_to_string(errno));
|
|
return -1;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
This snippet is a small program that registers only Rijndael only. Note you must register ciphers before
|
|
using the PK code since all of the PK code (RSA, DH and ECC) rely heavily on the descriptor tables.
|
|
|
|
\section{Symmetric Modes of Operations}
|
|
\subsection{Background}
|
|
A typical symmetric block cipher can be used in chaining modes to effectively encrypt messages larger than the block
|
|
size of the cipher. Given a key $k$, a plaintext $P$ and a cipher $E$ we shall denote the encryption of the block
|
|
$P$ under the key $k$ as $E_k(P)$. In some modes there exists an initial vector denoted as $C_{-1}$.
|
|
|
|
\subsubsection{ECB Mode}
|
|
ECB or Electronic Codebook Mode is the simplest method to use. It is given as:
|
|
\begin{equation}
|
|
C_i = E_k(P_i)
|
|
\end{equation}
|
|
This mode is very weak since it allows people to swap blocks and perform replay attacks if the same key is used more
|
|
than once.
|
|
|
|
\subsubsection{CBC Mode}
|
|
CBC or Cipher Block Chaining mode is a simple mode designed to prevent trivial forms of replay and swap attacks on ciphers.
|
|
It is given as:
|
|
\begin{equation}
|
|
C_i = E_k(P_i \oplus C_{i - 1})
|
|
\end{equation}
|
|
It is important that the initial vector be unique and preferably random for each message encrypted under the same key.
|
|
|
|
\subsubsection{CTR Mode}
|
|
CTR or Counter Mode is a mode which only uses the encryption function of the cipher. Given a initial vector which is
|
|
treated as a large binary counter the CTR mode is given as:
|
|
\begin{eqnarray}
|
|
C_{-1} = C_{-1} + 1\mbox{ }(\mbox{mod }2^W) \nonumber \\
|
|
C_i = P_i \oplus E_k(C_{-1})
|
|
\end{eqnarray}
|
|
Where $W$ is the size of a block in bits (e.g. 64 for Blowfish). As long as the initial vector is random for each message
|
|
encrypted under the same key replay and swap attacks are infeasible. CTR mode may look simple but it is as secure
|
|
as the block cipher is under a chosen plaintext attack (provided the initial vector is unique).
|
|
|
|
\subsubsection{CFB Mode}
|
|
CFB or Ciphertext Feedback Mode is a mode akin to CBC. It is given as:
|
|
\begin{eqnarray}
|
|
C_i = P_i \oplus C_{-1} \nonumber \\
|
|
C_{-1} = E_k(C_i)
|
|
\end{eqnarray}
|
|
Note that in this library the output feedback width is equal to the size of the block cipher. That is this mode is used
|
|
to encrypt whole blocks at a time. However, the library will buffer data allowing the user to encrypt or decrypt partial
|
|
blocks without a delay. When this mode is first setup it will initially encrypt the initial vector as required.
|
|
|
|
\subsubsection{OFB Mode}
|
|
OFB or Output Feedback Mode is a mode akin to CBC as well. It is given as:
|
|
\begin{eqnarray}
|
|
C_{-1} = E_k(C_{-1}) \nonumber \\
|
|
C_i = P_i \oplus C_{-1}
|
|
\end{eqnarray}
|
|
Like the CFB mode the output width in CFB mode is the same as the width of the block cipher. OFB mode will also
|
|
buffer the output which will allow you to encrypt or decrypt partial blocks without delay.
|
|
|
|
\subsection{Choice of Mode}
|
|
My personal preference is for the CTR mode since it has several key benefits:
|
|
\begin{enumerate}
|
|
\item No short cycles which is possible in the OFB and CFB modes.
|
|
\item Provably as secure as the block cipher being used under a chosen plaintext attack.
|
|
\item Technically does not require the decryption routine of the cipher.
|
|
\item Allows random access to the plaintext.
|
|
\item Allows the encryption of block sizes that are not equal to the size of the block cipher.
|
|
\end{enumerate}
|
|
The CTR, CFB and OFB routines provided allow you to encrypt block sizes that differ from the ciphers block size. They
|
|
accomplish this by buffering the data required to complete a block. This allows you to encrypt or decrypt any size
|
|
block of memory with either of the three modes.
|
|
|
|
The ECB and CBC modes process blocks of the same size as the cipher at a time. Therefore they are less flexible than the
|
|
other modes.
|
|
|
|
\subsection{Implementation}
|
|
\index{CBC Mode} \index{CTR Mode}
|
|
\index{OFB Mode} \index{CFB Mode}
|
|
The library provides simple support routines for handling CBC, CTR, CFB, OFB and ECB encoded messages. Assuming the mode
|
|
you want is XXX there is a structure called ``symmetric\_XXX'' that will contain the information required to
|
|
use that mode. They have identical setup routines (except ECB mode for obvious reasons):
|
|
\begin{verbatim}
|
|
int XXX_start(int cipher, const unsigned char *IV,
|
|
const unsigned char *key, int keylen,
|
|
int num_rounds, symmetric_XXX *XXX);
|
|
|
|
int ecb_start(int cipher, const unsigned char *key, int keylen,
|
|
int num_rounds, symmetric_ECB *ecb);
|
|
\end{verbatim}
|
|
|
|
In each case ``cipher'' is the index into the cipher\_descriptor array of the cipher you want to use. The ``IV'' value is
|
|
the initialization vector to be used with the cipher. You must fill the IV yourself and it is assumed they are the same
|
|
length as the block size\footnote{In otherwords the size of a block of plaintext for the cipher, e.g. 8 for DES, 16 for AES, etc.}
|
|
of the cipher you choose. It is important that the IV be random for each unique message you want to encrypt. The
|
|
parameters ``key'', ``keylen'' and ``num\_rounds'' are the same as in the XXX\_setup() function call. The final parameter
|
|
is a pointer to the structure you want to hold the information for the mode of operation.
|
|
|
|
Both routines return {\bf CRYPT\_OK} if the cipher initialized correctly, otherwise they return an error code. To
|
|
actually encrypt or decrypt the following routines are provided:
|
|
\begin{verbatim}
|
|
int XXX_encrypt(const unsigned char *pt, unsigned char *ct,
|
|
symmetric_XXX *XXX);
|
|
int XXX_decrypt(const unsigned char *ct, unsigned char *pt,
|
|
symmetric_XXX *XXX);
|
|
|
|
int YYY_encrypt(const unsigned char *pt, unsigned char *ct,
|
|
unsigned long len, symmetric_YYY *YYY);
|
|
int YYY_decrypt(const unsigned char *ct, unsigned char *pt,
|
|
unsigned long len, symmetric_YYY *YYY);
|
|
\end{verbatim}
|
|
Where ``XXX'' is one of (ecb, cbc) and ``YYY'' is one of (ctr, ofb, cfb). In the CTR, OFB and CFB cases ``len'' is the
|
|
size of the buffer (as number of chars) to encrypt or decrypt. The CTR, OFB and CFB modes are order sensitive but not
|
|
chunk sensitive. That is you can encrypt ``ABCDEF'' in three calls like ``AB'', ``CD'', ``EF'' or two like ``ABCDE'' and ``F''
|
|
and end up with the same ciphertext. However, encrypting ``ABC'' and ``DABC'' will result in different ciphertexts. All
|
|
five of the modes will return {\bf CRYPT\_OK} on success from the encrypt or decrypt functions.
|
|
|
|
To decrypt in either mode you simply perform the setup like before (recall you have to fetch the IV value you used)
|
|
and use the decrypt routine on all of the blocks. When you are done working with either mode you should wipe the
|
|
memory (using ``zeromem()'') to help prevent the key from leaking. For example:
|
|
\newpage
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
#include <mycrypt.h>
|
|
int main(void)
|
|
{
|
|
unsigned char key[16], IV[16], buffer[512];
|
|
symmetric_CTR ctr;
|
|
int x, errno;
|
|
|
|
/* register twofish first */
|
|
if (register_cipher(&twofish_desc) == -1) {
|
|
printf("Error registering cipher.\n");
|
|
return -1;
|
|
}
|
|
|
|
/* somehow fill out key and IV */
|
|
|
|
/* start up CTR mode */
|
|
if ((errno = ctr_start(find_cipher("twofish"), IV, key, 16, 0, &ctr)) != CRYPT_OK) {
|
|
printf("ctr_start error: %s\n", error_to_string(errno));
|
|
return -1;
|
|
}
|
|
|
|
/* somehow fill buffer than encrypt it */
|
|
if ((errno = ctr_encrypt(buffer, buffer, sizeof(buffer), &ctr)) != CRYPT_OK) {
|
|
printf("ctr_encrypt error: %s\n", error_to_string(errno));
|
|
return -1;
|
|
}
|
|
|
|
/* make use of ciphertext... */
|
|
|
|
/* clear up and return */
|
|
zeromem(key, sizeof(key));
|
|
zeromem(&ctr, sizeof(ctr));
|
|
|
|
return 0;
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
|
|
\chapter{One-Way Cryptographic Hash Functions}
|
|
\section{Core Functions}
|
|
|
|
Like the ciphers there are hash core functions and a universal data type to hold the hash state called ``hash\_state''.
|
|
To initialize hash XXX (where XXX is the name) call:
|
|
\index{Hash Functions}
|
|
\begin{verbatim}
|
|
void XXX_init(hash_state *md);
|
|
\end{verbatim}
|
|
|
|
This simply sets up the hash to the default state governed by the specifications of the hash. To add data to the
|
|
message being hashed call:
|
|
\begin{verbatim}
|
|
void XXX_process(hash_state *md, const unsigned char *in, unsigned long len);
|
|
\end{verbatim}
|
|
|
|
Essentially all hash messages are virtually infinitely\footnote{Most hashes are limited to $2^{64}$ bits or 2,305,843,009,213,693,952 bytes.} long message which
|
|
are buffered. The data can be passed in any sized chunks as long as the order of the bytes are the same the message digest
|
|
(hash output) will be the same. For example, this means that:
|
|
\begin{verbatim}
|
|
md5_process(&md, "hello ", 6);
|
|
md5_process(&md, "world", 5);
|
|
\end{verbatim}
|
|
Will produce the same message digest as the single call:
|
|
\index{Message Digest}
|
|
\begin{verbatim}
|
|
md5_process(&md, "hello world", 11);
|
|
\end{verbatim}
|
|
|
|
To finally get the message digest (the hash) call:
|
|
\begin{verbatim}
|
|
void XXX_done(hash_state *md,
|
|
unsigned char *out);
|
|
\end{verbatim}
|
|
|
|
This function will finish up the hash and store the result in the ``out'' array. You must ensure that ``out'' is long
|
|
enough for the hash in question. Often hashes are used to get keys for symmetric ciphers so the ``XXX\_done()'' functions
|
|
will wipe the ``md'' variable before returning automatically.
|
|
|
|
To test a hash function call:
|
|
\begin{verbatim}
|
|
int XXX_test(void);
|
|
\end{verbatim}
|
|
|
|
This will return {\bf CRYPTO\_OK} if the hash matches the test vectors, otherwise it returns an error code. An
|
|
example snippet that hashes a message with md5 is given below.
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
#include <mycrypt.h>
|
|
int main(void)
|
|
{
|
|
hash_state md;
|
|
unsigned char *in = "hello world", out[16];
|
|
|
|
/* setup the hash */
|
|
md5_init(&md);
|
|
|
|
/* add the message */
|
|
md5_process(&md, in, strlen(in));
|
|
|
|
/* get the hash */
|
|
md5_done(&md, out);
|
|
|
|
return 0;
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
|
|
\section{Hash Descriptors}
|
|
\index{Hash Descriptors}
|
|
Like the set of ciphers the set of hashes have descriptors too. They are stored in an array called ``hash\_descriptor'' and
|
|
are defined by:
|
|
\begin{verbatim}
|
|
struct _hash_descriptor {
|
|
char *name;
|
|
unsigned long hashsize; /* digest output size in bytes */
|
|
unsigned long blocksize; /* the block size the hash uses */
|
|
void (*init) (hash_state *);
|
|
void (*process)(hash_state *, const unsigned char *, unsigned long);
|
|
void (*done) (hash_state *, unsigned char *);
|
|
int (*test) (void);
|
|
};
|
|
\end{verbatim}
|
|
|
|
Similarly ``name'' is the name of the hash function in ASCII (all lowercase). ``hashsize'' is the size of the digest output
|
|
in bytes. The remaining fields are pointers to the functions that do the respective tasks. There is a function to
|
|
search the array as well called ``int find\_hash(char *name)''. It returns -1 if the hash is not found, otherwise the
|
|
position in the descriptor table of the hash.
|
|
|
|
You can use the table to indirectly call a hash function that is chosen at runtime. For example:
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
#include <mycrypt.h>
|
|
int main(void)
|
|
{
|
|
unsigned char buffer[100], hash[MAXBLOCKSIZE];
|
|
int idx, x;
|
|
hash_state md;
|
|
|
|
/* register hashes .... */
|
|
if (register_hash(&md5_desc) == -1) {
|
|
printf("Error registering MD5.\n");
|
|
return -1;
|
|
}
|
|
|
|
/* register other hashes ... */
|
|
|
|
/* prompt for name and strip newline */
|
|
printf("Enter hash name: \n");
|
|
fgets(buffer, sizeof(buffer), stdin);
|
|
buffer[strlen(buffer) - 1] = 0;
|
|
|
|
/* get hash index */
|
|
idx = find_hash(buffer);
|
|
if (idx == -1) {
|
|
printf("Invalid hash name!\n");
|
|
return -1;
|
|
}
|
|
|
|
/* hash input until blank line */
|
|
hash_descriptor[idx].init(&md);
|
|
while (fgets(buffer, sizeof(buffer), stdin) != NULL)
|
|
hash_descriptor[idx].process(&md, buffer, strlen(buffer));
|
|
hash_descriptor[idx].done(&md, hash);
|
|
|
|
/* dump to screen */
|
|
for (x = 0; x < hash_descriptor[idx].hashsize; x++)
|
|
printf("%02x ", hash[x]);
|
|
printf("\n");
|
|
return 0;
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
|
|
Note the usage of ``MAXBLOCKSIZE''. In Libtomcrypt no symmetric block, key or hash digest is larger than MAXBLOCKSIZE in
|
|
length. This provides a simple size you can set your automatic arrays to that will not get overrun.
|
|
|
|
There are three helper functions as well:
|
|
\index{hash\_memory()} \index{hash\_file()}
|
|
\begin{verbatim}
|
|
int hash_memory(int hash, const unsigned char *data,
|
|
unsigned long len, unsigned char *dst,
|
|
unsigned long *outlen);
|
|
|
|
int hash_file(int hash, const char *fname,
|
|
unsigned char *dst,
|
|
unsigned long *outlen);
|
|
|
|
int hash_filehandle(int hash, FILE *in,
|
|
unsigned char *dst, unsigned long *outlen);
|
|
\end{verbatim}
|
|
|
|
Both functions return {\bf CRYPT\_OK} on success, otherwise they return an error code. The ``hash'' parameter is
|
|
the location in the descriptor table of the hash. The ``*outlen'' variable is used to keep track of the output size. You
|
|
must set it to the size of your output buffer before calling the functions. When they complete succesfully they store
|
|
the length of the message digest back in it. The functions are otherwise straightforward. The ``hash\_filehandle'' function
|
|
assumes that ``in'' is an file handle opened in binary mode. It will not reset the file position after hashing the content.
|
|
|
|
To perform the above hash with md5 the following code could be used:
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
#include <mycrypt.h>
|
|
int main(void)
|
|
{
|
|
int idx, errno;
|
|
unsigned long len;
|
|
unsigned char out[MAXBLOCKSIZE];
|
|
|
|
/* register the hash */
|
|
if (register_hash(&md5_desc) == -1) {
|
|
printf("Error registering MD5.\n");
|
|
return -1;
|
|
}
|
|
|
|
/* get the index of the hash */
|
|
idx = find_hash("md5");
|
|
|
|
/* call the hash */
|
|
len = sizeof(out);
|
|
if ((errno = hash_memory(idx, "hello world", 11, out, &len)) != CRYPT_OK) {
|
|
printf("Error hashing data: %s\n", error_to_string(errno));
|
|
return -1;
|
|
}
|
|
return 0;
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
|
|
The following hashes are provided as of this release:
|
|
\begin{center}
|
|
\begin{tabular}{|c|c|c|}
|
|
\hline Name & Descriptor Name & Size of Message Digest (bytes) \\
|
|
\hline SHA-512 & sha512\_desc & 64 \\
|
|
\hline SHA-384 & sha384\_desc & 48 \\
|
|
\hline SHA-256 & sha256\_desc & 32 \\
|
|
\hline TIGER-192 & tiger\_desc & 24 \\
|
|
\hline SHA-1 & sha1\_desc & 20 \\
|
|
\hline MD5 & md5\_desc & 16 \\
|
|
\hline MD4 & md4\_desc & 16 \\
|
|
\hline MD2 & md2\_desc & 16 \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
|
|
Similar to the cipher descriptor table you must register your hash algorithms before you can use them. These functions
|
|
work exactly like those of the cipher registration code. The functions are:
|
|
\begin{verbatim}
|
|
int register_hash(const struct _hash_descriptor *hash);
|
|
int unregister_hash(const struct _hash_descriptor *hash);
|
|
\end{verbatim}
|
|
|
|
\subsection{Notice}
|
|
It is highly recommended that you not use the MD4 or MD5 hashes for the purposes of digital signatures or authentication codes.
|
|
These hashes are provided for completeness and they still can be used for the purposes of password hashing or one-way accumulators
|
|
(e.g. Yarrow).
|
|
|
|
The other hashes such as the SHA-1, SHA-2 (that includes SHA-512, SHA-384 and SHA-256) and TIGER-192 are still considered secure
|
|
for all purposes you would normally use a hash for.
|
|
|
|
\section{Hash based Message Authenication Codes}
|
|
Thanks to Dobes Vandermeer the library now includes support for hash based message authenication codes or HMAC for short. An HMAC
|
|
of a message is a keyed authenication code that only the owner of a private symmetric key will be able to verify. The purpose is
|
|
to allow an owner of a private symmetric key to produce an HMAC on a message then later verify if it is correct. Any impostor or
|
|
eavesdropper will not be able to verify the authenticity of a message.
|
|
|
|
The HMAC support works much like the normal hash functions except that the initialization routine requires you to pass a key
|
|
and its length. The key is much like a key you would pass to a cipher. That is, it is simply an array of octets stored in
|
|
chars. The initialization routine is:
|
|
\begin{verbatim}
|
|
int hmac_init(hmac_state *hmac, int hash,
|
|
const unsigned char *key, unsigned long keylen);
|
|
\end{verbatim}
|
|
The ``hmac'' parameter is the state for the HMAC code. ``hash'' is the index into the descriptor table of the hash you want
|
|
to use to authenticate the message. ``key'' is the pointer to the array of chars that make up the key. ``keylen'' is the
|
|
length (in octets) of the key you want to use to authenticate the message. To send octets of a message through the HMAC system you must use the following function:
|
|
\begin{verbatim}
|
|
int hmac_process(hmac_state *hmac, const unsigned char *buf,
|
|
unsigned long len);
|
|
\end{verbatim}
|
|
``hmac'' is the HMAC state you are working with. ``buf'' is the array of octets to send into the HMAC process. ``len'' is the
|
|
number of octets to process. Like the hash process routines you can send the data in arbitrarly sized chunks. When you
|
|
are finished with the HMAC process you must call the following function to get the HMAC code:
|
|
\begin{verbatim}
|
|
int hmac_done(hmac_state *hmac, unsigned char *hash);
|
|
\end{verbatim}
|
|
``hmac'' is the HMAC state you are working with. ``hash'' is the array of octets where the HMAC code should be stored. You
|
|
must ensure that your destination array is the right size (or just make it of size MAXBLOCKSIZE to be sure). There are
|
|
two utility functions provided to make using HMACs easier todo.
|
|
\begin{verbatim}
|
|
int hmac_memory(int hash, const unsigned char *key, unsigned long keylen,
|
|
const unsigned char *data, unsigned long len,
|
|
unsigned char *dst);
|
|
\end{verbatim}
|
|
This will produce an HMAC code for the array of octets in ``data'' of length ``len''. The index into the hash descriptor table must be provided in ``hash''
|
|
It uses the key from ``key'' with a key length of ``keylen''. The result is stored in the array of octets``dst''.
|
|
Similarly for files there is the following function:
|
|
\begin{verbatim}
|
|
int hmac_file(int hash, const char *fname, const unsigned char *key,
|
|
unsigned long keylen, unsigned char *dst);
|
|
\end{verbatim}
|
|
``hash'' is the index into the hash descriptor table of the hash you want to use. ``fname'' is the filename to process. ``key''
|
|
is the array of octets to use as the key. ``keylen'' is the length of the key. ``dst'' is the array of octets where the result
|
|
should be stored.
|
|
|
|
To test if the HMAC code is working there is the following function:
|
|
\begin{verbatim}
|
|
int hmac_test(void);
|
|
\end{verbatim}
|
|
Which returns {\bf CRYPT\_OK} if the code passes otherwise it returns an error code. Some example code for using the
|
|
HMAC system is given below.
|
|
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
#include <mycrypt.h>
|
|
int main(void)
|
|
{
|
|
int idx, errno;
|
|
hmac_state hmac;
|
|
unsigned char key[16], dst[MAXBLOCKSIZE];
|
|
|
|
/* register SHA-1 */
|
|
if (register_hash(&sha1_desc) == -1) {
|
|
printf("Error registering SHA1\n");
|
|
return -1;
|
|
}
|
|
|
|
/* get index of SHA1 in hash descriptor table */
|
|
idx = find_hash("sha1");
|
|
|
|
/* we would make up our symmetric key in "key[]" here */
|
|
|
|
/* start the HMAC */
|
|
if ((errno = hmac_init(&hmac, idx, key, 16)) != CRYPT_OK) {
|
|
printf("Error setting up hmac: %s\n", error_to_string(errno));
|
|
return -1;
|
|
}
|
|
|
|
/* process a few octets */
|
|
if((errno = hmac_process(&hmac, "hello", 5) != CRYPT_OK) {
|
|
printf("Error processing hmac: %s\n", error_to_string(errno));
|
|
return -1;
|
|
}
|
|
|
|
/* get result (presumably to use it somehow...) */
|
|
if ((errno = hmac_done(&hmac, dst)) != CRYPT_OK) {
|
|
printf("Error finishing hmac: %s\n", error_to_string(errno));
|
|
return -1;
|
|
}
|
|
|
|
/* return */
|
|
return 0;
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
|
|
\chapter{Pseudo-Random Number Generators}
|
|
\section{Core Functions}
|
|
|
|
The library provides an array of core functions for Pseudo-Random Number Generators (PRNGs) as well. A cryptographic PRNG is
|
|
used to expand a shorter bit string into a longer bit string. PRNGs are used wherever random data is required such as Public Key (PK)
|
|
key generation. There is a universal structure called ``prng\_state''. To initialize a PRNG call:
|
|
\begin{verbatim}
|
|
int XXX_start(prng_state *prng);
|
|
\end{verbatim}
|
|
|
|
This will setup the PRNG for future use and not seed it. In order
|
|
for the PRNG to be cryptographically useful you must give it entropy. Ideally you'd have some OS level source to tap
|
|
like in UNIX (see section 5.3). To add entropy to the PRNG call:
|
|
\begin{verbatim}
|
|
int XXX_add_entropy(const unsigned char *in, unsigned long len,
|
|
prng_state *prng);
|
|
\end{verbatim}
|
|
|
|
Which returns {\bf CRYPTO\_OK} if the entropy was accepted. Once you think you have enough entropy you call another
|
|
function to put the entropy into action.
|
|
\begin{verbatim}
|
|
int XXX_ready(prng_state *prng);
|
|
\end{verbatim}
|
|
|
|
Which returns {\bf CRYPTO\_OK} if it is ready. Finally to actually read bytes call:
|
|
\begin{verbatim}
|
|
unsigned long XXX_read(unsigned char *out, unsigned long len,
|
|
prng_state *prng);
|
|
\end{verbatim}
|
|
|
|
Which returns the number of bytes read from the PRNG.
|
|
|
|
\subsection{Remarks}
|
|
|
|
It is possible to be adding entropy and reading from a PRNG at the same time. For example, if you first seed the PRNG
|
|
and call ready() you can now read from it. You can also keep adding new entropy to it. The new entropy will not be used
|
|
in the PRNG until ready() is called again. This allows the PRNG to be used and re-seeded at the same time. No real error
|
|
checking is guaranteed to see if the entropy is sufficient or if the PRNG is even in a ready state before reading.
|
|
|
|
\subsection{Example}
|
|
|
|
Below is a simple snippet to read 10 bytes from yarrow. Its important to note that this snippet is {\bf NOT} secure since
|
|
the entropy added is not random.
|
|
|
|
\begin{verbatim}
|
|
#include <mycrypt.h>
|
|
int main(void)
|
|
{
|
|
prng_state prng;
|
|
unsigned char buf[10];
|
|
int errno;
|
|
|
|
/* start it */
|
|
if ((errno = yarrow_start(&prng)) != CRYPT_OK) {
|
|
printf("Start error: %s\n", error_to_string(errno));
|
|
}
|
|
/* add entropy */
|
|
if ((errno = yarrow_add_entropy("hello world", 11, &prng)) != CRYPT_OK) {
|
|
printf("Add_entropy error: %s\n", error_to_string(errno));
|
|
}
|
|
/* ready and read */
|
|
if ((errno = yarrow_ready(&prng)) != CRYPT_OK) {
|
|
printf("Ready error: %s\n", error_to_string(errno));
|
|
}
|
|
printf("Read %lu bytes from yarrow\n", yarrow_read(buf, 10, &prng));
|
|
return 0;
|
|
}
|
|
\end{verbatim}
|
|
|
|
\section{PRNG Descriptors}
|
|
\index{PRNG Descriptor}
|
|
PRNGs have descriptors too (surprised?). Stored in the structure ``prng\_descriptor''. The format of an element is:
|
|
\begin{verbatim}
|
|
struct _prng_descriptor {
|
|
char *name;
|
|
int (*start) (prng_state *);
|
|
int (*add_entropy)(const unsigned char *, unsigned long, prng_state *);
|
|
int (*ready) (prng_state *);
|
|
unsigned long (*read)(unsigned char *, unsigned long len, prng_state *);
|
|
};
|
|
\end{verbatim}
|
|
|
|
There is a ``int find\_prng(char *name)'' function as well. Returns -1 if the PRNG is not found, otherwise it returns
|
|
the position in the prng\_descriptor array.
|
|
|
|
Just like the ciphers and hashes you must register your prng before you can use it. The two functions provided work
|
|
exactly as those for the cipher registry functions. They are:
|
|
\begin{verbatim}
|
|
int register_prng(const struct _prng_descriptor *prng);
|
|
int unregister_prng(const struct _prng_descriptor *prng);
|
|
\end{verbatim}
|
|
|
|
\subsubsection{PRNGs Provided}
|
|
Currently Yarrow (yarrow\_desc), RC4 (rc4\_desc) and the secure RNG (sprng\_desc) are provided as PRNGs within the
|
|
library.
|
|
|
|
RC4 is provided with a PRNG interface because it is a stream cipher and not well suited for the symmetric block cipher
|
|
interface. You provide the key for RC4 via the rc4\_add\_entropy() function. By calling rc4\_ready() the key will be used
|
|
to setup the RC4 state for encryption or decryption. The rc4\_read() function has been modified from RC4 since it will
|
|
XOR the output of the RC4 keystream generator against the input buffer you provide. The following snippet will demonstrate
|
|
how to encrypt a buffer with RC4:
|
|
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
#include <mycrypt.h>
|
|
int main(void)
|
|
{
|
|
prng_state prng;
|
|
unsigned char buf[32];
|
|
int errno;
|
|
|
|
if ((errno = rc4_start(&prng)) != CRYPT_OK) {
|
|
printf("RC4 init error: %s\n", error_to_string(errno));
|
|
exit(-1);
|
|
}
|
|
|
|
/* use ``key'' as the key */
|
|
if ((errno = rc4_add_entropy("key", 3, &prng)) != CRYPT_OK) {
|
|
printf("RC4 add entropy error: %s\n", error_to_string(errno));
|
|
exit(-1);
|
|
}
|
|
|
|
/* setup RC4 for use */
|
|
if ((errno = rc4_ready(&prng)) != CRYPT_OK) {
|
|
printf("RC4 ready error: %s\n", error_to_string(errno));
|
|
exit(-1);
|
|
}
|
|
|
|
/* encrypt buffer */
|
|
strcpy(buf,"hello world");
|
|
if (rc4_read(buf, 11, &prng) != 11) {
|
|
printf("RC4 read error\n");
|
|
exit(-1);
|
|
}
|
|
return 0;
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
To decrypt you have to do the exact same steps.
|
|
|
|
\section{The Secure RNG}
|
|
\index{Secure RNG}
|
|
An RNG is related to a PRNG except that it doesn't expand a smaller seed to get the data. They generate their random bits
|
|
by performing some computation on fresh input bits. Possibly the hardest thing to get correctly in a cryptosystem is the
|
|
PRNG. Computers are deterministic beasts that try hard not to stray from pre-determined paths. That makes gathering
|
|
entropy needed to seed the PRNG a hard task.
|
|
|
|
There is one small function that may help on certain platforms:
|
|
\index{rng\_get\_bytes()}
|
|
\begin{verbatim}
|
|
unsigned long rng_get_bytes(unsigned char *buf, unsigned long len,
|
|
void (*callback)(void));
|
|
\end{verbatim}
|
|
|
|
Which will try one of three methods of getting random data. The first is to open the popular ``/dev/random'' device which
|
|
on most *NIX platforms provides cryptographic random bits\footnote{This device is available in Windows through the Cygwin compiler suite. It emulates ``/dev/random'' via the Microsoft CSP.}.
|
|
The second method is to try the Microsoft Cryptographic Service Provider and read the RNG. The third method is an ANSI C
|
|
clock drift method that is also somewhat popular but gives bits of lower entropy. The ``callback'' parameter is a pointer to a function that returns void. Its used when the slower ANSI C RNG must be
|
|
used so the calling application can still work. This is useful since the ANSI C RNG has a throughput of three
|
|
bytes a second. The callback pointer may be set to {\bf NULL} to avoid using it if you don't want to. The function
|
|
returns the number of bytes actually read from any RNG source. There is a function to help setup a PRNG as well:
|
|
\index{rng\_make\_prng()}
|
|
\begin{verbatim}
|
|
int rng_make_prng(int bits, int wprng, prng_state *prng,
|
|
void (*callback)(void));
|
|
\end{verbatim}
|
|
This will try to setup the prng with a state of at least ``bits'' of entropy. The ``callback'' parameter works much like
|
|
the callback in ``rng\_get\_bytes()''. It is highly recommended that you use this function to setup your PRNGs unless you have a
|
|
platform where the RNG doesn't work well. Example usage of this function is given below.
|
|
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
#include <mycrypt.h>
|
|
int main(void)
|
|
{
|
|
ecc_key mykey;
|
|
prng_state prng;
|
|
int errno;
|
|
|
|
/* register yarrow */
|
|
if (register_prng(&yarrow_desc) == -1) {
|
|
printf("Error registering Yarrow\n");
|
|
return -1;
|
|
}
|
|
|
|
/* setup the PRNG */
|
|
if ((errno = rng_make_prng(128, find_prng("yarrow"), &prng, NULL)) != CRYPT_OK) {
|
|
printf("Error setting up PRNG, %s\n", error_to_string(errno));
|
|
return -1;
|
|
}
|
|
|
|
/* make a 192-bit ECC key */
|
|
if ((errno = ecc_make_key(&prng, find_prng("yarrow"), 24, &mykey)) != CRYPT_OK) {
|
|
printf("Error making key: %s\n", error_to_string(errno));
|
|
return -1;
|
|
}
|
|
return 0;
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
|
|
\subsection{The Secure PRNG Interface}
|
|
It is possible to access the secure RNG through the PRNG interface and in turn use it within dependent functions such
|
|
as the PK API. This simplifies the cryptosystem on platforms where the secure RNG is fast. The secure PRNG never
|
|
requires to be started, that is you need not call the start, add\_entropy or ready functions. For example, consider
|
|
the previous example using this PRNG.
|
|
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
#include <mycrypt.h>
|
|
int main(void)
|
|
{
|
|
ecc_key mykey;
|
|
int errno;
|
|
|
|
/* register SPRNG */
|
|
if (register_prng(&sprng_desc) == -1) {
|
|
printf("Error registering SPRNG\n");
|
|
return -1;
|
|
}
|
|
|
|
/* make a 192-bit ECC key */
|
|
if ((errno = ecc_make_key(NULL, find_prng("sprng"), 24, &mykey)) != CRYPT_OK) {
|
|
printf("Error making key: %s\n", error_to_string(errno));
|
|
return -1;
|
|
}
|
|
return 0;
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
|
|
\chapter{RSA Routines}
|
|
|
|
\section{Background}
|
|
|
|
RSA is a public key algorithm that is based on the inability to find the ``e-th'' root modulo a composite of unknown
|
|
factorization. Normally the difficulty of breaking RSA is associated with the integer factoring problem but they are
|
|
not strictly equivalent.
|
|
|
|
The system begins with with two primes $p$ and $q$ and their product $N = pq$. The order or ``Euler totient'' of the
|
|
multiplicative sub-group formed modulo $N$ is given as $\phi(N) = (p - 1)(q - 1)$ which can be reduced to
|
|
$\mbox{lcm}(p - 1, q - 1)$. The public key consists of the composite $N$ and some integer $e$ such that
|
|
$\mbox{gcd}(e, \phi(N)) = 1$. The private key consists of the composite $N$ and the inverse of $e$ modulo $\phi(N)$
|
|
often simply denoted as $de \equiv 1\mbox{ }(\mbox{mod }\phi(N))$.
|
|
|
|
A person who wants to encrypt with your public key simply forms an integer (the plaintext) $M$ such that
|
|
$1 < M < N-2$ and computes the ciphertext $C = M^e\mbox{ }(\mbox{mod }N)$. Since finding the inverse exponent $d$
|
|
given only $N$ and $e$ appears to be intractable only the owner of the private key can decrypt the ciphertext and compute
|
|
$C^d \equiv \left (M^e \right)^d \equiv M^1 \equiv M\mbox{ }(\mbox{mod }N)$. Similarly the owner of the private key
|
|
can sign a message by ``decrypting'' it. Others can verify it by ``encrypting'' it.
|
|
|
|
Currently RSA is a difficult system to cryptanalyze provided that both primes are large and not close to each other.
|
|
Ideally $e$ should be larger than $100$ to prevent direct analysis. For example, if $e$ is three and you do not pad
|
|
the plaintext to be encrypted than it is possible that $M^3 < N$ in which case finding the cube-root would be trivial.
|
|
The most often suggested value for $e$ is $65537$ since it is large enough to make such attacks impossible and also well
|
|
designed for fast exponentiation (requires 16 squarings and one multiplication).
|
|
|
|
It is important to pad the input to RSA since it has particular mathematical structure. For instance
|
|
$M_1^dM_2^d = (M_1M_2)^d$ which can be used to forge a signature. Suppose $M_3 = M_1M_2$ is a message you want
|
|
to have a forged signature for. Simply get the signatures for $M_1$ and $M_2$ on their own and multiply the result
|
|
together. Similar tricks can be used to deduce plaintexts from ciphertexts. It is important not only to sign
|
|
the hash of documents only but also to pad the inputs with data to remove such structure.
|
|
|
|
\section{Core Functions}
|
|
|
|
For RSA routines a single ``rsa\_key'' structure is used. To make a new RSA key call:
|
|
\index{rsa\_make\_key()}
|
|
\begin{verbatim}
|
|
int rsa_make_key(prng_state *prng,
|
|
int wprng, int size,
|
|
long e, rsa_key *key);
|
|
\end{verbatim}
|
|
|
|
Where ``wprng'' is the index into the PRNG descriptor array. ``size'' is the size in bytes of the RSA modulus desired.
|
|
``e'' is the encryption exponent desired, typical values are 3, 17, 257 and 65537. I suggest you stick with 65537 since its big
|
|
enough to prevent trivial math attacks and not super slow. ``key'' is where the key is placed. All keys must be at
|
|
least 128 bytes and no more than 512 bytes in size (that is from 1024 to 4096 bits).
|
|
|
|
Note that the ``rsa\_make\_key()'' function allocates memory at runtime when you make the key. Make sure to call
|
|
``rsa\_free()'' (see below) when you are finished with the key. If ``rsa\_make\_key()'' fails it will automatically
|
|
free the ram allocated itself.
|
|
|
|
There are three types of RSA keys. The types are {\bf PK\_PRIVATE\_OPTIMIZED}, {\bf PK\_PRIVATE} and {\bf PK\_PUBLIC}. The first
|
|
two are private keys where the ``optimized'' type uses the Chinese Remainder Theorem to speed up decryption/signatures. By
|
|
default all new keys are of the ``optimized'' type. The non-optimized private type is provided for backwards compatibility
|
|
as well as to save space since the optimized key requires about four times as much memory.
|
|
|
|
To do raw work with the RSA function call:
|
|
\index{rsa\_exptmod()}
|
|
\begin{verbatim}
|
|
int rsa_exptmod(const unsigned char *in, unsigned long inlen,
|
|
unsigned char *out, unsigned long *outlen,
|
|
int which, rsa_key *key);
|
|
\end{verbatim}
|
|
This loads the bignum from ``in'' as a big endian word in the format PKCS specifies, raises it to either ``e'' or ``d'' and stores the result
|
|
in ``out'' and the size of the result in ``outlen''. ``which'' is set to {\bf PK\_PUBLIC} to use ``e''
|
|
(i.e. for encryption/verifying) and set to {\bf PK\_PRIVATE} to use ``d'' as the exponent (i.e. for decrypting/signing).
|
|
|
|
\section{Packet Routines}
|
|
To encrypt or decrypt a symmetric key using RSA the following functions are provided. The idea is that you make up
|
|
a random symmetric key and use that to encode your message. By RSA encrypting the symmetric key you can send it to a
|
|
recipient who can RSA decrypt it and symmetrically decrypt the message.
|
|
\begin{verbatim}
|
|
int rsa_encrypt_key(const unsigned char *inkey, unsigned long inlen,
|
|
unsigned char *outkey, unsigned long *outlen,
|
|
prng_state *prng, int wprng, rsa_key *key);
|
|
|
|
int rsa_decrypt_key(const unsigned char *in, unsigned long inlen,
|
|
unsigned char *outkey, unsigned long *keylen,
|
|
rsa_key *key);
|
|
\end{verbatim}
|
|
|
|
The ``rsa\_encrypt\_key()'' function accepts a symmetric key (limited to 32 bytes) as input in ``inkey''. ``inlen''
|
|
is the size of the input key in bytes. The function will then ``rsa\_pad()'' the key and encrypt it using the RSA
|
|
algorithm. It will store the result in ``outkey'' along with the length in ``outlen''.
|
|
|
|
The ``rsa\_decrypt\_key()'' function performs the opposite. The ``in'' variable is where the RSA packet of length
|
|
``inlen'' goes and it will store the original symmetric key in the ``outkey'' variable along with its length in
|
|
``keylen''.
|
|
|
|
Similarly to sign or verify a hash of a message the following two messages are provided. The idea is to hash your
|
|
message then use these functions to RSA sign the hash.
|
|
\begin{verbatim}
|
|
int rsa_sign_hash(const unsigned char *in, unsigned long inlen,
|
|
unsigned char *out, unsigned long *outlen,
|
|
rsa_key *key);
|
|
|
|
int rsa_verify_hash(const unsigned char *sig, unsigned long siglen,
|
|
const unsigned char *hash, int *stat, rsa_key *key);
|
|
\end{verbatim}
|
|
For ``rsa\_sign\_hash'' the input is intended to be the hash of a message the user wants to sign. The output is the
|
|
RSA signed packet which ``rsa\_verify\_hash'' can verify. For the verification function ``sig'' is the RSA signature
|
|
and ``hash'' is the hash of the message. The integer ``stat'' is set to non-zero if the signature is valid or zero
|
|
otherwise.
|
|
|
|
To import/export RSA keys as a memory buffer (e.g. to store them to disk) call:
|
|
\begin{verbatim}
|
|
int rsa_export(unsigned char *out, unsigned long *outlen,
|
|
int type, rsa_key *key);
|
|
|
|
int rsa_import(const unsigned char *in, unsigned long inlen, rsa_key *key);
|
|
\end{verbatim}
|
|
|
|
The ``type'' parameter is {\bf PK\_PUBLIC}, {\bf PK\_PRIVATE} or {\bf PK\_PRIVATE\_OPTIMIZED} to export either a public or
|
|
private key. The latter type will export a key with the optimized parameters. To free the memory used by an RSA key call:
|
|
\index{rsa\_free()}
|
|
\begin{verbatim}
|
|
void rsa_free(rsa_key *key);
|
|
\end{verbatim}
|
|
|
|
Note that if the key fails to ``rsa\_import()'' you do not have to free the memory allocated for it.
|
|
|
|
\section{Remarks}
|
|
It is important that you match your RSA key size with the function you are performing. The internal padding for both
|
|
signatures and encryption triple the size of the plaintext. This means to encrypt or sign
|
|
a message of N bytes you must have a modulus of 1+3N bytes. Note that this doesn't affect the length of the plaintext
|
|
you pass into functions like rsa\_encrypt(). This restriction applies only to data that is passed through the
|
|
internal RSA routines directly directly.
|
|
|
|
The following table gives the size requirements for various hashes.
|
|
\begin{center}
|
|
\begin{tabular}{|c|c|c|}
|
|
\hline Name & Size of Message Digest (bytes) & RSA Key Size (bits)\\
|
|
\hline SHA-512 & 64 & 1544\\
|
|
\hline SHA-384 & 48 & 1160 \\
|
|
\hline SHA-256 & 32 & 776\\
|
|
\hline TIGER-192 & 24 & 584\\
|
|
\hline SHA-1 & 20 & 488\\
|
|
\hline MD5 & 16 & 392\\
|
|
\hline MD4 & 16 & 392\\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
|
|
The symmetric ciphers will use at a maximum a 256-bit key which means at the least a 776-bit RSA key is
|
|
required to use all of the symmetric ciphers with the RSA routines. If you want to use any of the large size
|
|
message digests (SHA-512 or SHA-384) you will have to use a larger key. Or to be simple just make 2048-bit or larger
|
|
keys. None of the hashes will have problems with such key sizes.
|
|
|
|
\chapter{Diffie-Hellman Key Exchange}
|
|
|
|
\section{Background}
|
|
|
|
Diffie-Hellman was the original public key system proposed. The system is based upon the group structure
|
|
of finite fields. For Diffie-Hellman a prime $p$ is chosen and a ``base'' $b$ such that $b^x\mbox{ }(\mbox{mod }p)$
|
|
generates a large sub-group of prime order (for unique values of $x$).
|
|
|
|
A secret key is an exponent $x$ and a public key is the value of $y \equiv g^x\mbox{ }(\mbox{mod }p)$. The term
|
|
``discrete logarithm'' denotes the action of finding $x$ given only $y$, $g$ and $p$. The key exchange part of
|
|
Diffie-Hellman arises from the fact that two users A and B with keys $(A_x, A_y)$ and $(B_x, B_y)$ can exchange
|
|
a shared key $K \equiv B_y^{A_x} \equiv A_y^{B_x} \equiv g^{A_xB_x}\mbox{ }(\mbox{mod }p)$.
|
|
|
|
From this public encryption and signatures can be developed. The trivial way to encrypt (for example) using a public key
|
|
$y$ is to perform the key exchange offline. The sender invents a key $k$ and its public copy
|
|
$k' \equiv g^k\mbox{ }(\mbox{mod }p)$ and uses $K \equiv k'^{A_x}\mbox{ }(\mbox{mod }p)$ as a key to encrypt
|
|
the message with. Typically $K$ would be sent to a one-way hash and the message digested used as a key in a
|
|
symmetric cipher.
|
|
|
|
It is important that the order of the sub-group that $g$ generates not only be large but also prime. There are
|
|
discrete logarithm algorithms that take $\sqrt r$ time given the order $r$. The discrete logarithm can be computed
|
|
modulo each prime factor of $r$ and the results combined using the Chinese Remainder Theorem. In the cases where
|
|
$r$ is ``B-Smooth'' (e.g. all small factors or powers of small prime factors) the solution is trivial to find.
|
|
|
|
To thwart such attacks the primes and bases in the library have been designed and fixed. Given a prime $p$ the order of
|
|
the sub-group generated is a large prime namely ${p - 1} \over 2$. Such primes are known as ``strong primes'' and the
|
|
smaller prime (e.g. the order of the base) are known as Sophie-Germaine primes.
|
|
|
|
\section{Core Functions}
|
|
|
|
This library also provides core Diffie-Hellman functions so you can negotiate keys over insecure mediums. The routines
|
|
provided are relatively easy to use and only take two function calls to negotiate a shared key. There is a structure
|
|
called ``dh\_key'' which stores the Diffie-Hellman key in a format these routines can use. The first routine is to
|
|
make a Diffie-Hellman private key pair:
|
|
\index{dh\_make\_key()}
|
|
\begin{verbatim}
|
|
int dh_make_key(prng_state *prng, int wprng,
|
|
int keysize, dh_key *key);
|
|
\end{verbatim}
|
|
The ``keysize'' is the size of the modulus you want in bytes. Currently support sizes are 96 to 512 bytes which correspond
|
|
to key sizes of 768 to 4096 bits. The smaller the key the faster it is to use however it will be less secure. When
|
|
specifying a size not explicitly supported by the library it will round {\em up} to the next key size. If the size is
|
|
above 512 it will return an error. So if you pass ``keysize == 32'' it will use a 768 bit key but if you pass
|
|
``keysize == 20000'' it will return an error. The primes and generators used are built-into the library and were designed
|
|
to meet very specific goals. The primes are strong primes which means that if $p$ is the prime then
|
|
$p-1$ is equal to $2r$ where $r$ is a large prime. The bases are chosen to generate a group of order $r$ to prevent
|
|
leaking a bit of the key. This means the bases generate a very large prime order group which is good to make cryptanalysis
|
|
hard.
|
|
|
|
The next two routines are for exporting/importing Diffie-Hellman keys in a binary format. This is useful for transport
|
|
over communication mediums.
|
|
|
|
\index{dh\_export()} \index{dh\_import()}
|
|
\begin{verbatim}
|
|
int dh_export(unsigned char *out, unsigned long *outlen,
|
|
int type, dh_key *key);
|
|
|
|
int dh_import(const unsigned char *in, unsigned long inlen, dh_key *key);
|
|
\end{verbatim}
|
|
|
|
These two functions work just like the ``rsa\_export()'' and ``rsa\_import()'' functions except these work with
|
|
Diffie-Hellman keys. Its important to note you do not have to free the ram for a ``dh\_key'' if an import fails. You can free a
|
|
``dh\_key'' using:
|
|
\begin{verbatim}
|
|
void dh_free(dh_key *key);
|
|
\end{verbatim}
|
|
After you have exported a copy of your public key (using {\bf PK\_PUBLIC} as ``type'') you can now create a shared secret
|
|
with the other user using:
|
|
\index{dh\_shared\_secret()}
|
|
\begin{verbatim}
|
|
int dh_shared_secret(dh_key *private_key,
|
|
dh_key *public_key,
|
|
unsigned char *out, unsigned long *outlen);
|
|
\end{verbatim}
|
|
|
|
Where ``private\_key'' is the key you made and ``public\_key'' is the copy of the public key the other user sent you. The result goes
|
|
into ``out'' and the length into ``outlen''. If all went correctly the data in ``out'' should be identical for both parties. It is important to
|
|
note that the two keys have to be the same size in order for this to work. There is a function to get the size of a
|
|
key:
|
|
\index{dh\_get\_size()}
|
|
\begin{verbatim}
|
|
int dh_get_size(dh_key *key);
|
|
\end{verbatim}
|
|
This returns the size in bytes of the modulus chosen for that key.
|
|
|
|
\subsection{Remarks on Usage}
|
|
Its important that you hash the shared key before trying to use it as a key for a symmetric cipher or something. An
|
|
example program that communicates over sockets, using MD5 and 1024-bit DH keys is\footnote{This function is a small example. It is suggested that proper packaging be used. For example, if the public key sent is truncated these routines will not detect that.}:
|
|
\newpage
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
int establish_secure_socket(int sock, int mode, unsigned char *key,
|
|
prng_state *prng, int wprng)
|
|
{
|
|
unsigned char buf[4096], buf2[4096];
|
|
unsigned long x, len;
|
|
int res, errno, inlen;
|
|
dh_key mykey, theirkey;
|
|
|
|
/* make up our private key */
|
|
if ((errno = dh_make_key(prng, wprng, 128, &mykey)) != CRYPT_OK) {
|
|
return errno;
|
|
}
|
|
|
|
/* export our key as public */
|
|
x = sizeof(buf);
|
|
if ((errno = dh_export(buf, &x, PK_PUBLIC, &mykey)) != CRYPT_OK) {
|
|
res = errno;
|
|
goto done2;
|
|
}
|
|
|
|
if (mode == 0) {
|
|
/* mode 0 so we send first */
|
|
if (send(sock, buf, x, 0) != x) {
|
|
res = CRYPT_ERROR;
|
|
goto done2;
|
|
}
|
|
|
|
/* get their key */
|
|
if ((inlen = recv(sock, buf2, sizeof(buf2), 0)) <= 0) {
|
|
res = CRYPT_ERROR;
|
|
goto done2;
|
|
}
|
|
} else {
|
|
/* mode >0 so we send second */
|
|
if ((inlen = recv(sock, buf2, sizeof(buf2), 0)) <= 0) {
|
|
res = CRYPT_ERROR;
|
|
goto done2;
|
|
}
|
|
|
|
if (send(sock, buf, x, 0) != x) {
|
|
res = CRYPT_ERROR;
|
|
goto done2;
|
|
}
|
|
}
|
|
|
|
if ((errno = dh_import(buf2, inlen, &theirkey)) != CRYPT_OK) {
|
|
res = errno;
|
|
goto done2;
|
|
}
|
|
|
|
/* make shared secret */
|
|
x = sizeof(buf);
|
|
if ((errno = dh_shared_secret(&mykey, &theirkey, buf, &x)) != CRYPT_OK) {
|
|
res = errno;
|
|
goto done;
|
|
}
|
|
|
|
/* hash it */
|
|
len = 16; /* default is MD5 so "key" must be at least 16 bytes long */
|
|
if ((errno = hash_memory(find_hash("md5"), buf, x, key, &len)) != CRYPT_OK) {
|
|
res = errno;
|
|
goto done;
|
|
}
|
|
|
|
/* clean up and return */
|
|
res = CRYPT_OK;
|
|
done:
|
|
dh_free(&theirkey);
|
|
done2:
|
|
dh_free(&mykey);
|
|
zeromem(buf, sizeof(buf));
|
|
zeromem(buf2, sizeof(buf2));
|
|
return res;
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
\newpage
|
|
\subsection{Remarks on The Snippet}
|
|
When the above code snippet is done (assuming all went well) their will be a shared 128-bit key in the ``key'' array
|
|
passed to ``establish\_secure\_socket()''.
|
|
|
|
\section{Other Diffie-Hellman Functions}
|
|
In order to test the Diffie-Hellman function internal workings (e.g. the primes and bases) their is a test function made
|
|
available:
|
|
\index{dh\_test()}
|
|
\begin{verbatim}
|
|
int dh_test(void);
|
|
\end{verbatim}
|
|
|
|
This function returns {\bf CRYPT\_OK} if the bases and primes in the library are correct. There is one last helper
|
|
function:
|
|
\index{dh\_sizes()}
|
|
\begin{verbatim}
|
|
void dh_sizes(int *low, int *high);
|
|
\end{verbatim}
|
|
Which stores the smallest and largest key sizes support into the two variables.
|
|
|
|
\section{DH Packet}
|
|
Similar to the RSA related functions there are functions to encrypt or decrypt symmetric keys using the DH public key
|
|
algorithms.
|
|
\begin{verbatim}
|
|
int dh_encrypt_key(const unsigned char *inkey, unsigned long keylen,
|
|
unsigned char *out, unsigned long *len,
|
|
prng_state *prng, int wprng, int hash,
|
|
dh_key *key);
|
|
|
|
int dh_decrypt_key(const unsigned char *in, unsigned long inlen,
|
|
unsigned char *outkey, unsigned long *keylen,
|
|
dh_key *key);
|
|
\end{verbatim}
|
|
Where ``inkey'' is an input symmetric key of no more than 32 bytes. Essentially these routines created a random public key
|
|
and find the hash of the shared secret. The message digest is than XOR'ed against the symmetric key. All of the
|
|
required data is placed in ``out'' by ``dh\_encrypt\_key()''. The hash must produce a message digest at least as large
|
|
as the symmetric key you are trying to share.
|
|
|
|
Similar to the RSA system you can sign and verify a hash of a message.
|
|
\begin{verbatim}
|
|
int dh_sign_hash(const unsigned char *in, unsigned long inlen,
|
|
unsigned char *out, unsigned long *outlen,
|
|
prng_state *prng, int wprng, dh_key *key);
|
|
|
|
int dh_verify_hash(const unsigned char *sig, unsigned long siglen,
|
|
const unsigned char *hash, unsigned long hashlen,
|
|
int *stat, dh_key *key);
|
|
\end{verbatim}
|
|
|
|
The ``dh\_sign\_hash'' function signs the message hash in ``in'' of length ``inlen'' and forms a DH packet in ``out''.
|
|
The ``dh\_verify\_hash'' function verifies the DH signature in ``sig'' against the hash in ``hash''. It sets ``stat''
|
|
to non-zero if the signature passes or zero if it fails.
|
|
|
|
\chapter{Elliptic Curve Cryptography}
|
|
|
|
\section{Background}
|
|
The library provides a set of core ECC functions as well that are designed to be the Elliptic Curve analogy of all of the
|
|
Diffie-Hellman routines in the previous chapter. Elliptic curves (of certain forms) have the benefit that they are harder
|
|
to attack (no sub-exponential attacks exist unlike normal DH crypto) in fact the fastest attack requires the square root
|
|
of the order of the base point in time. That means if you use a base point of order $2^{192}$ (which would represent a
|
|
192-bit key) then the work factor is $2^{96}$ in order to find the secret key.
|
|
|
|
The curves in this library are taken from the following website:
|
|
\begin{verbatim}
|
|
http://csrc.nist.gov/cryptval/dss.htm
|
|
\end{verbatim}
|
|
|
|
They are all curves over the integers modulo a prime. The curves have the basic equation that is:
|
|
\begin{equation}
|
|
y^2 = x^3 - 3x + b\mbox{ }(\mbox{mod }p)
|
|
\end{equation}
|
|
|
|
The variable $b$ is chosen such that the number of points is nearly maximal. In fact the order of the base points $\beta$
|
|
provided are very close to $p$ that is $\vert \vert \phi(\beta) \vert \vert \approx \vert \vert p \vert \vert$. The curves
|
|
range in order from $\approx 2^{192}$ points to $\approx 2^{521}$. According to the source document any key size greater
|
|
than or equal to 256-bits is sufficient for long term security.
|
|
|
|
\section{Core Functions}
|
|
|
|
Like the DH routines there is a key structure ``ecc\_key'' used by the functions. There is a function to make a key:
|
|
\index{ecc\_make\_key()}
|
|
\begin{verbatim}
|
|
int ecc_make_key(prng_state *prng, int wprng,
|
|
int keysize, ecc_key *key);
|
|
\end{verbatim}
|
|
|
|
The ``keysize'' is the size of the modulus in bytes desired. Currently directly supported values are 20, 24, 28, 32, 48 and 65 bytes which
|
|
correspond to key sizes of 160, 192, 224, 256, 384 and 521 bits respectively. If you pass a key size that is between any key size
|
|
it will round the keysize up to the next available one. The rest of the parameters work like they do in the ``dh\_make\_key()'' function.
|
|
To free the ram allocated by a key call:
|
|
\index{ecc\_free()}
|
|
\begin{verbatim}
|
|
void ecc_free(ecc_key *key);
|
|
\end{verbatim}
|
|
|
|
To import and export a key there are:
|
|
\index{ecc\_export()}
|
|
\index{ecc\_import()}
|
|
\begin{verbatim}
|
|
int ecc_export(unsigned char *out, unsigned long *outlen,
|
|
int type, ecc_key *key);
|
|
|
|
int ecc_import(const unsigned char *in, unsigned long inlen, ecc_key *key);
|
|
\end{verbatim}
|
|
These two work exactly like there DH counterparts. Finally when you share your public key you can make a shared secret
|
|
with:
|
|
\index{ecc\_shared\_secret()}
|
|
\begin{verbatim}
|
|
int ecc_shared_secret(ecc_key *private_key,
|
|
ecc_key *public_key,
|
|
unsigned char *out, unsigned long *outlen);
|
|
\end{verbatim}
|
|
Which works exactly like the DH counterpart, the ``private\_key'' is your own key and ``public\_key'' is the key the other
|
|
user sent you. Note that this function stores both $x$ and $y$ co-ordinates of the shared
|
|
elliptic point. You should hash the output to get a shared key in a more compact and useful form (most of the entropy is
|
|
in $x$ anyways). Both keys have to be the same size for this to work, to help there is a function to get the size in bytes
|
|
of a key.
|
|
\index{ecc\_get\_size()}
|
|
\begin{verbatim}
|
|
int ecc_get_size(ecc_key *key);
|
|
\end{verbatim}
|
|
|
|
To test the ECC routines and to get the minimum and maximum key sizes there are these two functions:
|
|
\index{ecc\_test()}
|
|
\begin{verbatim}
|
|
int ecc_test(void);
|
|
void ecc_sizes(int *low, int *high);
|
|
\end{verbatim}
|
|
Which both work like their DH counterparts.
|
|
|
|
\section{ECC Packet}
|
|
Similar to the RSA API there are two functions which encrypt and decrypt symmetric keys using the ECC public key
|
|
algorithms.
|
|
\begin{verbatim}
|
|
int ecc_encrypt_key(const unsigned char *inkey, unsigned long keylen,
|
|
unsigned char *out, unsigned long *len,
|
|
prng_state *prng, int wprng, int hash,
|
|
ecc_key *key);
|
|
|
|
int ecc_decrypt_key(const unsigned char *in, unsigned long inlen,
|
|
unsigned char *outkey, unsigned long *keylen,
|
|
ecc_key *key);
|
|
\end{verbatim}
|
|
|
|
Where ``inkey'' is an input symmetric key of no more than 32 bytes. Essentially these routines created a random public key
|
|
and find the hash of the shared secret. The message digest is than XOR'ed against the symmetric key. All of the required
|
|
data is placed in ``out'' by ``ecc\_encrypt\_key()''. The hash chosen must produce a message digest at least as large
|
|
as the symmetric key you are trying to share.
|
|
|
|
There are also functions to sign and verify the hash of a message.
|
|
\begin{verbatim}
|
|
int ecc_sign_hash(const unsigned char *in, unsigned long inlen,
|
|
unsigned char *out, unsigned long *outlen,
|
|
prng_state *prng, int wprng, ecc_key *key);
|
|
|
|
int ecc_verify_hash(const unsigned char *sig, unsigned long siglen,
|
|
const unsigned char *hash, unsigned long hashlen,
|
|
int *stat, ecc_key *key);
|
|
\end{verbatim}
|
|
|
|
The ``ecc\_sign\_hash'' function signs the message hash in ``in'' of length ``inlen'' and forms a ECC packet in ``out''.
|
|
The ``ecc\_verify\_hash'' function verifies the ECC signature in ``sig'' against the hash in ``hash''. It sets ``stat''
|
|
to non-zero if the signature passes or zero if it fails.
|
|
|
|
|
|
\section{ECC Keysizes}
|
|
With ECC if you try and sign a hash that is bigger than your ECC key you can run into problems. The math will still work
|
|
and in effect the signature will still work. With ECC keys the strength of the signature is limited by the size of
|
|
the hash or the size of they key, whichever is smaller. For example, if you sign with SHA256 and a ECC-160 key in effect
|
|
you have 160-bits of security (e.g. as if you signed with SHA-1).
|
|
|
|
The library will not warn you if you make this mistake so it is important to check yourself before using the
|
|
signatures.
|
|
|
|
\chapter{Public Keyrings}
|
|
\section{Introduction}
|
|
In order to simplify the usage of the public key algorithms a set of keyring routines have been developed. They let the
|
|
developer manage asymmetric keys by providing load, save, export, import routines as well as encrypt, decrypt, sign, verify
|
|
routines in a unified API. That is all three types of PK systems can be used within the same keyring with the same API.
|
|
|
|
To define types of keys there are four enumerations used globaly:
|
|
\begin{verbatim}
|
|
enum {
|
|
NON_KEY=0,
|
|
RSA_KEY,
|
|
DH_KEY,
|
|
ECC_KEY
|
|
};
|
|
\end{verbatim}
|
|
|
|
To make use of the system the developer has to know how link-lists work. The main structure that the keyring routines use
|
|
is the ``pk\_key'' defined as:
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
typedef struct Pk_key {
|
|
int key_type, /* PUBLIC, PRIVATE, PRIVATE_OPTIMIZED */
|
|
system; /* RSA, ECC or DH ? */
|
|
|
|
char name[MAXLEN], /* various info's about this key */
|
|
email[MAXLEN],
|
|
description[MAXLEN];
|
|
|
|
unsigned long ID; /* CRC32 of the name/email/description together */
|
|
|
|
_pk_key key;
|
|
|
|
struct Pk_key *next; /* linked list chain */
|
|
} pk_key;
|
|
\end{verbatim}
|
|
\end{small}
|
|
|
|
The list is chained via the ``next'' member and terminated with the node of the list that has ``system'' equal to
|
|
{\bf NON\_KEY}.
|
|
|
|
\section{The Keyring API}
|
|
To initialize a blank keyring the function ``kr\_init()'' is used.
|
|
\begin{verbatim}
|
|
int kr_init(pk_key **pk);
|
|
\end{verbatim}
|
|
You pass it a pointer to a pointer of type ``pk\_key'' where it will allocate ram for one node of the keyring and sets the
|
|
pointer.
|
|
|
|
Now instead of calling the PK specific ``make\_key'' functions there is one function that can make all three types of keys.
|
|
\begin{verbatim}
|
|
int kr_make_key(pk_key *pk, prng_state *prng, int wprng,
|
|
int system, int keysize, const char *name,
|
|
const char *email, const char *description);
|
|
\end{verbatim}
|
|
The ``name'', ``email'' and ``description'' parameters are simply little pieces of information that you can tag along with a
|
|
key. They can each be either blank or any string less than 256 bytes. ``system'' is one of the enumeration elements, that
|
|
is {\bf RSA\_KEY}, {\bf DH\_KEY} or {\bf ECC\_KEY}. ``keysize'' is the size of the key you desire which is regulated by
|
|
the individual systems, for example, RSA keys are limited in keysize from 128 to 512 bytes.
|
|
|
|
To find keys along a keyring there are two functions provided:
|
|
\begin{verbatim}
|
|
pk_key *kr_find(pk_key *pk, unsigned long ID);
|
|
|
|
pk_key *kr_find_name(pk_key *pk, const char *name);
|
|
\end{verbatim}
|
|
The first searches by the 32-bit ID provided and the latter checks the name against the keyring. They both return a pointer
|
|
to the node in the ring of a match or {\bf NULL} if no match is found.
|
|
|
|
To export or import a single node of a keyring the two functions are provided:
|
|
\begin{verbatim}
|
|
int kr_export(pk_key *pk, unsigned long ID, int key_type,
|
|
unsigned char *out, unsigned long *outlen);
|
|
|
|
int kr_import(pk_key *pk, const unsigned char *in);
|
|
\end{verbatim}
|
|
The export function exports the key with an ID provided and of a specific type much like the normal PK export routines. The
|
|
``key\_type'' is one of {\bf PK\_PUBLIC} or {\bf PK\_PRIVATE}. In this function with RSA keys the type
|
|
{\bf PK\_PRIVATE\_OPTIMIZED} is the same as the {\bf PK\_PRIVATE} type. The import function will read in a packet and
|
|
add it to the keyring.
|
|
|
|
To load and save whole keyrings from disk:
|
|
\begin{verbatim}
|
|
int kr_load(pk_key **pk, FILE *in, symmetric_CTR *ctr);
|
|
|
|
int kr_save(pk_key *pk, FILE *out, symmetric_CTR *ctr);
|
|
\end{verbatim}
|
|
Both take file pointers to allow the user to pre-append data to the stream. The ``ctr'' parameter should be setup with
|
|
``ctr\_start'' or set to NULL. This parameter lets the user encrypt the keyring as its written to disk, if it is set
|
|
to NULL the data is written without being encrypted. The load function assumes the list has not been initialized yet
|
|
and will reset the pointer given to it.
|
|
|
|
There are the four encrypt, decrypt, sign and verify functions as well
|
|
\begin{verbatim}
|
|
int kr_encrypt_key(pk_key *pk, unsigned long ID,
|
|
const unsigned char *in, unsigned long inlen,
|
|
unsigned char *out, unsigned long *outlen,
|
|
prng_state *prng, int wprng, int hash);
|
|
|
|
int kr_decrypt_key(pk_key *pk, const unsigned char *in,
|
|
unsigned char *out, unsigned long *outlen);
|
|
\end{verbatim}
|
|
|
|
The kr\_encrypt\_key() routine is designed to encrypt a symmetric key with a specified users public key. The symmetric
|
|
key is then used with a block cipher to encode the message. The recipient can call kr\_decrypt\_key() to get the original
|
|
symmetric key back and decode the message. The hash specified must produce a message digest longer than symmetric key
|
|
provided.
|
|
|
|
\begin{verbatim}
|
|
int kr_sign_hash(pk_key *pk, unsigned long ID,
|
|
const unsigned char *in, unsigned long inlen,
|
|
unsigned char *out, unsigned long *outlen,
|
|
prng_state *prng, int wprng);
|
|
|
|
int kr_verify_hash(pk_key *pk, const unsigned char *in,
|
|
const unsigned char *hash, unsigned long hashlen,
|
|
int *stat);
|
|
\end{verbatim}
|
|
|
|
Similar to the two previous these are used to sign a message digest or verify one. This requires hashing the message
|
|
first then passing the output in.
|
|
|
|
To delete keys and clear rings there are:
|
|
\begin{verbatim}
|
|
int kr_del(pk_key **_pk, unsigned long ID);
|
|
int kr_clear(pk_key **pk);
|
|
\end{verbatim}
|
|
``kr\_del'' will try to remove a key with a given ID from the ring and ``kr\_clear'' will completely empty a list and free
|
|
the memory associated with it. Below is small example using the keyring API:
|
|
|
|
\begin{small}
|
|
\begin{verbatim}
|
|
#include <mycrypt.h>
|
|
int main(void)
|
|
{
|
|
pk_key *kr;
|
|
unsigned char buf[4096], buf2[4096];
|
|
unsigned long len;
|
|
int errno;
|
|
|
|
/* make a new list */
|
|
if ((errno = kr_init(&kr)) != CRYPT_OK) {
|
|
printf("kr_init: %s\n", error_to_string(errno));
|
|
exit(-1);
|
|
}
|
|
|
|
/* add a key to it */
|
|
register_prng(&sprng_desc);
|
|
if ((errno = kr_make_key(kr, NULL, find_prng("sprng"), RSA_KEY, 128,
|
|
"TomBot", "tomstdenis@yahoo.com", "test key")) == CRYPT_OK) {
|
|
printf("kr_make_key: %s\n", error_to_string(errno));
|
|
exit(-1);
|
|
}
|
|
|
|
/* export the first key */
|
|
len = sizeof(buf);
|
|
if ((errno = kr_export(kr, kr->ID, PK_PRIVATE, buf, &len)) != CRYPT_OK) {
|
|
printf("kr_export: %s\n", error_to_string(errno));
|
|
exit(-1);
|
|
}
|
|
|
|
/* ... */
|
|
}
|
|
\end{verbatim}
|
|
\end{small}
|
|
|
|
\chapter{$GF(2^w)$ Math Routines}
|
|
|
|
The library provides a set of polynomial-basis $GF(2^w)$ routines to help facilitate algorithms such as ECC over such
|
|
fields. Note that the current implementation of ECC in the library is strictly over the integers only. The routines
|
|
are simple enough to use for other purposes outside of ECC.
|
|
|
|
At the heart of all of the GF routines is the data type ``gf\_int'. It is simply a type definition for an array of
|
|
$L$ 32-bit words. You can configure the maximum size $L$ of the ``gf\_int'' type by opening the file ``mycrypt.h'' and
|
|
changing ``LSIZE''. Note that if you set it to $n$ then you can only multiply upto two $n \over 2$ bit polynomials without
|
|
an overflow. The type ``gf\_intp'' is associated with a pointer to an ``unsigned long'' as required in the algorithms.
|
|
|
|
There are no initialization routines for ``gf\_int'' variables and you can simply use them after declaration. There are five
|
|
low level functions:
|
|
\index{gf\_copy()} \index{gf\_zero()} \index{gf\_iszero()} \index{gf\_isone()}
|
|
\index{gf\_deg()}
|
|
\begin{verbatim}
|
|
void gf_copy(gf_intp a, gf_intp b);
|
|
void gf_zero(gf_intp a);
|
|
int gf_iszero(gf_intp a);
|
|
int gf_isone(gf_intp a);
|
|
int gf_deg(gf_intp a);
|
|
\end{verbatim}
|
|
There are all fairly self-explanatory. ``gf\_copy(a, b)'' copies the contents of ``a'' into ``b''. ``gf\_zero()'' simply
|
|
zeroes the entire polynomial. ``gf\_iszero()'' tests to see if the polynomial is all zero and ``gf\_isone()'' tests to see
|
|
if the polynomial is equal to the multiplicative identity. ``gf\_deg()'' returns the degree of the polynomial or $-1$ if its
|
|
a zero polynomial.
|
|
|
|
There are five core math routines as well:
|
|
\index{gf\_shl()} \index{gf\_shr()} \index{gf\_add()} \index{gf\_mul()} \index{gf\_div()}
|
|
\begin{verbatim}
|
|
void gf_shl(gf_intp a, gf_intp b);
|
|
void gf_shr(gf_intp a, gf_intp b);
|
|
void gf_add(gf_intp a, gf_intp b, gf_intp c);
|
|
void gf_mul(gf_intp a, gf_intp b, gf_intp c);
|
|
void gf_div(gf_intp a, gf_intp b, gf_intp q, gf_intp r);
|
|
\end{verbatim}
|
|
|
|
Which are all fairly obvious. ``gf\_shl(a,b)'' multiplies the polynomial ``a'' by $x$ and stores it in ``b''.
|
|
``gf\_shl(a,b)'' divides the polynomial ``a'' by $x$ and stores it in ``b''. ``gf\_add(a,b,c)'' adds the polynomial
|
|
``a'' to ``b'' and stores the sum in ``c''. Similarly for ``gf\_mul(a,b,c)''. The ``gf\_div(a,b,q,r)'' function divides
|
|
``a'' by ``b'' and stores the quotient in ``q'' and the remainder in ``r''.
|
|
|
|
There are six number theoretic functions as well:
|
|
\index{gf\_mod()} \index{gf\_mulmod()} \index{gf\_invmod()} \index{gf\_gcd()} \index{gf\_is\_prime()}
|
|
\index{gf\_sqrt()}
|
|
\begin{verbatim}
|
|
void gf_mod(gf_intp a, gf_intp m, gf_intp b);
|
|
void gf_mulmod(gf_intp a, gf_intp b, gf_intp m, gf_intp c);
|
|
void gf_invmod(gf_intp A, gf_intp M, gf_intp B);
|
|
void gf_sqrt(gf_intp a, gf_intp m, gf_intp b);
|
|
void gf_gcd(gf_intp A, gf_intp B, gf_intp c);
|
|
int gf_is_prime(gf_intp a);
|
|
\end{verbatim}
|
|
|
|
Which all work similarly except for ``gf\_mulmod(a,b,m,c)'' which computes $c = ab\mbox{ }(\mbox{mod }m)$. The
|
|
``gf\_is\_prime()'' function returns one if the polynomial is primitive, otherwise it returns zero.
|
|
|
|
Finally to read/store a ``gf\_int'' in a binary string use:
|
|
\index{gf\_size()} \index{gf\_toraw()} \index{gf\_readraw()}
|
|
\begin{verbatim}
|
|
int gf_size(gf_intp a);
|
|
void gf_toraw(gf_intp a, unsigned char *dst);
|
|
void gf_readraw(gf_intp a, unsigned char *str, int len);
|
|
\end{verbatim}
|
|
Where ``gf\_size()'' returns the size in bytes required for the data. ``gf\_toraw(a,b)'' stores the polynomial in ``b''
|
|
in binary format (endian neutral). ``gf\_readraw(a,b,c)'' reads the binary string in ``b'' back. Note that the length
|
|
you pass it must be the same as returned by ``gf\_size()'' or it will not load correctly.
|
|
|
|
\chapter{Miscellaneous}
|
|
\section{Base64 Encoding and Decoding}
|
|
The library provides functions to encode and decode a RFC1521 base64 coding scheme. This means that it can decode what it
|
|
encodes but the format used does not comply to any known standard. The characters used in the mappings are:
|
|
\begin{verbatim}
|
|
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/
|
|
\end{verbatim}
|
|
Those characters should are supported in virtually any 7-bit ASCII system which means they can be used for transport over
|
|
common e-mail, usenet and HTTP mediums. The format of an encoded stream is just a literal sequence of ASCII characters
|
|
where a group of four represent 24-bits of input. The first four chars of the encoders output is the length of the
|
|
original input. After the first four characters is the rest of the message.
|
|
|
|
Often it is desirable to line wrap the output to fit nicely in an e-mail or usenet posting. The decoder allows you to
|
|
put any character (that is not in the above sequence) in between any character of the encoders output. You may not however,
|
|
break up the first four characters.
|
|
|
|
To encode a binary string in base64 call:
|
|
\index{base64\_encode()} \index{base64\_decode()}
|
|
\begin{verbatim}
|
|
int base64_encode(const unsigned char *in, unsigned long len,
|
|
unsigned char *out, unsigned long *outlen);
|
|
\end{verbatim}
|
|
Where ``in'' is the binary string and ``out'' is where the ASCII output is placed. You must set the value of ``outlen'' prior
|
|
to calling this function and it sets the length of the base64 output in ``outlen'' when it is done. To decode a base64
|
|
string call:
|
|
\begin{verbatim}
|
|
int base64_decode(const unsigned char *in, unsigned long len,
|
|
unsigned char *out, unsigned long *outlen);
|
|
\end{verbatim}
|
|
|
|
\section{The Multiple Precision Integer Library (MPI)}
|
|
The library comes with a copy of Michael Fromberger's\footnote{Michael J. Fromberger, sting@linguist.Thayer.dartmouth.edu} multiple
|
|
precision integer library MPI. MPI is a trivial to use ANSI C compatible large integer library. It is free for all uses and
|
|
is distributed freely.
|
|
|
|
At the heart of all MPI functions is the data type ``mp\_int'' (defined in mpi.h). This data type is what will hold all large
|
|
integers. In order to use an mp\_int one must initialize it first, for example:
|
|
\begin{verbatim}
|
|
#include <mycrypt.h> /* mycrypt.h includes mpi.h automatically */
|
|
int main(void)
|
|
{
|
|
mp_int bignum;
|
|
|
|
/* initialize it */
|
|
mp_init(&bignum);
|
|
|
|
return 0;
|
|
}
|
|
\end{verbatim}
|
|
If you are unfamiliar with the syntax of C the \& symbol is used to pass the address of ``bignum'' to the function. All
|
|
MPI functions require the address of the parameters. To free the memory of a mp\_int use (for example):
|
|
\begin{verbatim}
|
|
mp_clear(&bignum);
|
|
\end{verbatim}
|
|
|
|
All MPI functions have the basic form of one of the following:
|
|
\begin{verbatim}
|
|
mp_XXX(mp_int *a);
|
|
mp_XXX(mp_int *a, mp_int *b, mp_int *c);
|
|
mp_XXX(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
|
|
\end{verbatim}
|
|
|
|
Where they perform some operation and store the result in the mp\_int variable passed on the far right. For example, to
|
|
compute $c = a + b \mbox{ }(\mbox{mod }m)$ you would call:
|
|
\begin{verbatim}
|
|
mp_addmod(&a, &b, &m, &c);
|
|
\end{verbatim}
|
|
|
|
The simplest way to get a complete listing of all MPI functions is to open ``mpi.h'' and look. They're all fairly
|
|
well documented.
|
|
|
|
\subsection{Binary Forms of ``mp\_int'' Variables}
|
|
|
|
Often it is required to store a ``mp\_int'' in binary form for transport (e.g. exporting a key, packet encryption, etc.).
|
|
MPI includes two functions to help when exporting numbers:
|
|
\begin{verbatim}
|
|
int mp_raw_size(mp_int *num);
|
|
mp_toraw(&num, buf);
|
|
\end{verbatim}
|
|
|
|
The former function gives the size in bytes of the raw format and the latter function actually stores the raw data. All
|
|
``mp\_int'' numbers are stored in big endian form (like PKCS demands) with the first byte being the sign of the number. The
|
|
``rsa\_exptmod()'' function differs slightly since it will take the input in the form exactly as PKCS demands (without the
|
|
leading sign byte). All other functions include the sign byte (since its much simpler just to include it). The sign byte
|
|
must be zero for positive numbers and non-zero for negative numbers. For example,
|
|
the sequence:
|
|
\begin{verbatim}
|
|
00 FF 30 04
|
|
\end{verbatim}
|
|
Represents the integer $255 \cdot 256^2 + 48 \cdot 256^1 + 4 \cdot 256^0$ or 16,723,972.
|
|
|
|
To read a binary string back into a ``mp\_int'' call:
|
|
\begin{verbatim}
|
|
mp_read_raw(mp_int *num, unsigned char *str, int len);
|
|
\end{verbatim}
|
|
Where ``num'' is where to store it, ``str'' is the binary string (including the leading sign byte) and ``len'' is the
|
|
length of the binary string.
|
|
|
|
\subsection{Primality Testing}
|
|
\index{Primality Testing}
|
|
The library includes primality testing and random prime functions as well. The primality tester will perform the test in
|
|
two phases. First it will perform trial division by the first few primes. Second it will perform eight rounds of the
|
|
Rabin-Miller primality testing algorithm. If the candidate passes both phases it is declared prime otherwise it is declared
|
|
composite. No prime number will fail the two phases but composites can. Each round of the Rabin-Miller algorithm reduces
|
|
the probability of a pseudo-prime by $1 \over 4$ therefore after sixteen rounds the probability is no more than
|
|
$\left ( { 1 \over 4 } \right )^{8} = 2^{-16}$. In practice the probability of error is in fact much lower than that.
|
|
|
|
When making random primes the trial division step is in fact an optimized implementation of ``Implementation of Fast RSA Key Generation on Smart Cards''\footnote{Chenghuai Lu, Andre L. M. dos Santos and Francisco R. Pimentel}.
|
|
In essence a table of machine-word sized residues are kept of a candidate modulo a set of primes. When the candiate
|
|
is rejected and ultimately incremented to test the next number the residues are updated without using multi-word precision
|
|
math operations. As a result the routine can scan ahead to the next number required for testing with very little work
|
|
involved.
|
|
|
|
In the event that a composite did make it through it would most likely cause the the algorithm trying to use it to fail. For
|
|
instance, in RSA two primes $p$ and $q$ are required. The order of the multiplicative sub-group (modulo $pq$) is given
|
|
as $\phi(pq)$ or $(p - 1)(q - 1)$. The decryption exponent $d$ is found as $de \equiv 1\mbox{ }(\mbox{mod } \phi(pq))$. If either $p$ or $q$ is composite the value of $d$ will be incorrect and the user
|
|
will not be able to sign or decrypt messages at all. Suppose $p$ was prime and $q$ was composite this is just a variation of
|
|
the multi-prime RSA. Suppose $q = rs$ for two primes $r$ and $s$ then $\phi(pq) = (p - 1)(r - 1)(s - 1)$ which clearly is
|
|
not equal to $(p - 1)(rs - 1)$.
|
|
|
|
These are not technically part of the MPI
|
|
library\footnote{As written by Michael Fromberger} but this is the best place to document them. To test if a ``mp\_int'' is
|
|
prime call:
|
|
\begin{verbatim}
|
|
int is_prime(mp_int *N, int *result);
|
|
\end{verbatim}
|
|
This puts a one in ``result'' if the number is probably prime, otherwise it places a zero in it. It is assumed that if
|
|
it returns an error that the value in ``result'' is undefined. To make
|
|
a random prime call:
|
|
\begin{verbatim}
|
|
int rand_prime(mp_int *N, unsigned long len, prng_state *prng, int wprng);
|
|
\end{verbatim}
|
|
Where ``len'' is the size of the prime in bytes ($2 \le len \le 256$). You can set ``len'' to the negative size you want
|
|
to get a prime of the form $p \equiv 3\mbox{ }(\mbox{mod } 4)$. So if you want a 1024-bit prime of this sort pass
|
|
``len = -128'' to the function. Upon success it will return {\bf CRYPT\_OK} and ``N'' will contain an integer which
|
|
is very likely prime.
|
|
|
|
\chapter{Programming Guidelines}
|
|
|
|
\section{Secure Pseudo Random Number Generators}
|
|
Probably the singal most vulnerable point of any cryptosystem is the PRNG. Without one generating and protecting secrets
|
|
would be impossible. The requirement that one be setup correctly is vitally important and to address this point the library
|
|
does provide two RNG sources that will address the largest amount of end users as possible. The ``sprng'' PRNG provided
|
|
provides and easy to access source of entropy for any application on a *NIX or Windows computer.
|
|
|
|
However, when the end user is not on one of these platforms the application developer must address the issue of finding
|
|
entropy. This manual is not designed to be a text on cryptography. I would just like to highlight that when you design
|
|
a cryptosystem make sure the first problem you solve is getting a fresh source of entropy.
|
|
|
|
\section{Preventing Trivial Errors}
|
|
Two simple ways to prevent trivial errors is to prevent overflows and to check the return values. All of the functions
|
|
which output variable length strings will require you to pass the length of the destination. If the size of your output
|
|
buffer is smaller than the output it will report an error. Therefore, make sure the size you pass is correct!
|
|
|
|
Also virtually all of the functions return an error code or {\bf CRYPT\_OK}. You should detect all errors as simple
|
|
typos or such can cause algorithms to fail to work as desired.
|
|
|
|
\section{Registering Your Algorithms}
|
|
To avoid linking and other runtime errors it is important to register the ciphers, hashes and PRNGs you intend to use
|
|
before you try to use them. This includes any function which would use an algorithm indirectly through a descriptor table.
|
|
|
|
A neat bonus to the registry system is that you can add external algorithms that are not part of the library without
|
|
having to hack the library. For example, suppose you have a hardware specific PRNG on your system. You could easily
|
|
write the few functions required plus a descriptor. After registering your PRNG all of the library functions that
|
|
need a PRNG can instantly take advantage of it.
|
|
|
|
\section{Key Sizes}
|
|
|
|
\subsection{Symmetric Ciphers}
|
|
For symmetric ciphers use as large as of a key as possible. For the most part ``bits are cheap'' so using a 256-bit key
|
|
is not a hard thing todo.
|
|
|
|
\subsection{Assymetric Ciphers}
|
|
The following chart gives the work factor for solving a DH/RSA public key using the NFS. The work factor for a key of order
|
|
$n$ is estimated to be
|
|
\begin{equation}
|
|
e^{1.923 \cdot ln(n)^{1 \over 3} \cdot ln(ln(n))^{2 \over 3}}
|
|
\end{equation}
|
|
|
|
Note that $n$ is not the bit-length but the magnitude. For example, for a 1024-bit key $n = 2^{1024}$. The work required
|
|
is:
|
|
\begin{center}
|
|
\begin{tabular}{|c|c|}
|
|
\hline RSA/DH Key Size (bits) & Work Factor ($log_2$) \\
|
|
\hline 512 & 63.92 \\
|
|
\hline 768 & 76.50 \\
|
|
\hline 1024 & 86.76 \\
|
|
\hline 1536 & 103.37 \\
|
|
\hline 2048 & 116.88 \\
|
|
\hline 2560 & 128.47 \\
|
|
\hline 3072 & 138.73 \\
|
|
\hline 4096 & 156.49 \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
|
|
The work factor for ECC keys is much higher since the best attack is still fully exponentional. Given a key of magnitude
|
|
$n$ it requires $\sqrt n$ work. The following table sumarizes the work required:
|
|
\begin{center}
|
|
\begin{tabular}{|c|c|}
|
|
\hline ECC Key Size (bits) & Work Factor ($log_2$) \\
|
|
\hline 160 & 80 \\
|
|
\hline 192 & 96 \\
|
|
\hline 224 & 112 \\
|
|
\hline 256 & 128 \\
|
|
\hline 384 & 192 \\
|
|
\hline 521 & 260.5 \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
|
|
Using the above tables the following suggestions for key sizes seems appropriate:
|
|
\begin{center}
|
|
\begin{tabular}{|c|c|c|}
|
|
\hline Security Goal & RSA/DH Key Size (bits) & ECC Key Size (bits) \\
|
|
\hline Short term (less than a year) & 1024 & 160 \\
|
|
\hline Short term (less than five years) & 1536 & 192 \\
|
|
\hline Long Term (less than ten years) & 2560 & 256 \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
|
|
\section{Thread Safety}
|
|
The library is not thread safe but several simple precautions can be taken to avoid any problems. The registry functions
|
|
such as register\_cipher() are not thread safe no matter what you do. Its best to call them from your programs initializtion
|
|
code before threads are initiated.
|
|
|
|
The rest of the code uses state variables you must pass it such as hash\_state, hmac\_state, etc. This means that if each
|
|
thread has its own state variables then they will not affect each other. This is fairly simple with symmetric ciphers
|
|
and hashes. However, the keyring and PRNG support is something the threads will want to share. The simplest workaround
|
|
is create semaphores or mutexes around calls to those functions.
|
|
|
|
Since C does not have standard semaphores this support is not native to Libtomcrypt. Even a C based semaphore is not entire
|
|
possible as some compilers may ignore the ``volatile'' keyword or have multiple processors. Provide your host application
|
|
is modular enough putting the locks in the right place should not bloat the code significantly and will solve all thread
|
|
safety issues within the library.
|
|
|
|
\chapter{Configuring the Library}
|
|
\section{Introduction}
|
|
The library is fairly flexible about how it can be built, used and generally distributed. Additions are being made with
|
|
each new release that will make the library even more flexible. Most options are placed in the makefile and others
|
|
are in ``mycrypt\_cfg.h''. All are used when the library is built from scratch.
|
|
|
|
For GCC platforms the file ``makefile'' is the makefile to be used. On MSVC platforms ``makefile.vc'' and on PS2 platforms
|
|
``makefile.ps2''.
|
|
|
|
\section{mycrypt\_cfg.h}
|
|
The file ``mycrypt\_cfg.h'' is what lets you control what functionality you want to remove from the library. By default,
|
|
everything the library has to offer it built.
|
|
|
|
\subsubsection{ARGTYPE}
|
|
This lets you control how the \_ARGCHK macro will behave. The macro is used to check pointers inside the functions against
|
|
NULL. There are three settings for ARGTYPE. When set to 0 it will have the default behaviour of printing a message to
|
|
stderr and raising a SIGABRT signal. This is provided so all platforms that use libtomcrypt can have an error that functions
|
|
similarly. When set to 1 it will simply pass on to the assert() macro. When set to 2 it will resolve to a empty macro
|
|
and no error checking will be performed.
|
|
|
|
\subsubsection{Endianess}
|
|
There are five macros related to endianess issues. For little endian platforms define, ENDIAN\_LITTLE. For big endian
|
|
platforms define ENDIAN\_BIG. Similarly when the default word size of an ``unsigned long'' is 32-bits define ENDIAN\_32BITWORD
|
|
or define ENDIAN\_64BITWORD when its 64-bits. If you do not define any of them the library will automatically use ENDIAN\_NEUTRAL
|
|
which will work on all platforms. Currently the system will automatically detect GCC or MSVC on a windows platform as well
|
|
as GCC on a PS2 platform.
|
|
|
|
\section{The makefile}
|
|
There are also options you can specify from the makefiles themselves.
|
|
|
|
\subsubsection{X memory routines}
|
|
The makefiles must define three macros denoted as XMALLOC, XCALLOC and XFREE which resolve to the name of the respective
|
|
functions. This lets you substitute in your own memory routines. If you substitute in your own functions they must behave
|
|
like the standard C library functions in terms of what they expect as input and output. By default the library uses the
|
|
standard C routines.
|
|
|
|
\subsubsection{X clock routines}
|
|
The rng\_get\_bytes() function can call a function that requires the clock() function. These macros let you override
|
|
the default clock() used with a replacement. By default the standard C library clock() function is used.
|
|
|
|
\subsubsection{NO\_FILE}
|
|
During the build if NO\_FILE is defined then any function in the library that uses file I/O will not call the file I/O
|
|
functions and instead simply return CRYPT\_ERROR. This should help resolve any linker errors stemming from a lack of
|
|
file I/O on embedded platforms.
|
|
|
|
\subsubsection{CLEAN\_STACK}
|
|
When this functions is defined the functions that store key material on the stack will clean up afterwards. Assumes that
|
|
you have no memory paging with the stack.
|
|
|
|
\subsubsection{Symmetric Ciphers, One-way Hashes, PRNGS and Public Key Functions}
|
|
There are a plethora of macros for the ciphers, hashes, PRNGs and public key functions which are fairly self-explanatory.
|
|
When they are defined the functionality is included otherwise it is not. There are some dependency issues which are
|
|
noted in the file. For instance, Yarrow requires CTR chaining mode, a block cipher and a hash function.
|
|
|
|
\subsubsection{TWOFISH\_SMALL and TWOFISH\_TABLES}
|
|
Twofish is a 128-bit symmetric block cipher that is provided within the library. The cipher itself is flexible enough
|
|
to allow some tradeoffs in the implementation. When TWOFISH\_SMALL is defined the scheduled symmetric key for Twofish
|
|
requires only 200 bytes of memory. This is achieved by not pre-computing the substitution boxes. Having this
|
|
defined will also greatly slow down the cipher. When this macro is not defined Twofish will pre-compute the
|
|
tables at a cost of 4KB of memory. The cipher will be much faster as a result.
|
|
|
|
When TWOFISH\_TABLES is defined the cipher will use pre-computed (and fixed in code) tables required to work. This is
|
|
useful when TWOFISH\_SMALL is defined as the table values are computed on the fly. When this is defined the code size
|
|
will increase by approximately 500 bytes. If this is defined but TWOFISH\_SMALL is not the cipher will still work but
|
|
it will not speed up the encryption or decryption functions.
|
|
|
|
\subsubsection{SMALL\_CODE}
|
|
When this is defined some of the code such as the Rijndael and SAFER+ ciphers are replaced with smaller code variants.
|
|
These variants are slower but can save quite a bit of code space.
|
|
|
|
\end{document}
|