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-\documentclass{howto}
-
-\title{Python Cryptography Toolkit}
-
-\release{2.0.2}
-
-\author{A.M. Kuchling}
-\authoraddress{\url{www.amk.ca}}
-
-\begin{document}
-\maketitle
-
-\begin{abstract}
-\noindent
-The Python Cryptography Toolkit describes a package containing various
-cryptographic modules for the Python programming language.  This
-documentation assumes you have some basic knowledge about the Python
-language, but not necessarily about cryptography.
-
-\end{abstract}
-
-\tableofcontents
-
-
-%======================================================================
-\section{Introduction}
-
-\subsection{Design Goals}
-The Python cryptography toolkit is intended to provide a reliable and
-stable base for writing Python programs that require cryptographic
-functions.
-
-A central goal of the author's has been to provide a simple,
-consistent interface for similar classes of algorithms.  For example,
-all block cipher objects have the same methods and return values, and
-support the same feedback modes.  Hash functions have a different
-interface, but it too is consistent over all the hash functions
-available.  Some of these interfaces have been codified as Python
-Enhancement Proposal documents, as \pep{247}, ``API for Cryptographic
-Hash Functions'', and \pep{272}, ``API for Block Encryption
-Algorithms''.  
-
-This is intended to make it easy to replace old algorithms with newer,
-more secure ones.  If you're given a bit of portably-written Python
-code that uses the DES encryption algorithm, you should be able to use
-AES instead by simply changing \code{from Crypto.Cipher import DES} to
-\code{from Crypto.Cipher import AES}, and changing all references to
-\code{DES.new()} to \code{AES.new()}.  It's also fairly simple to
-write your own modules that mimic this interface, thus letting you use
-combinations or permutations of algorithms.
-
-Some modules are implemented in C for performance; others are written
-in Python for ease of modification.  Generally, low-level functions
-like ciphers and hash functions are written in C, while less
-speed-critical functions have been written in Python.  This division
-may change in future releases.  When speeds are quoted in this
-document, they were measured on a 500 MHz Pentium II running Linux.
-The exact speeds will obviously vary with different machines,
-different compilers, and the phase of the moon, but they provide a
-crude basis for comparison.  Currently the cryptographic
-implementations are acceptably fast, but not spectacularly good.  I
-welcome any suggestions or patches for faster code.
-
-I have placed the code under no restrictions; you can redistribute the
-code freely or commercially, in its original form or with any
-modifications you make, subject to whatever local laws may apply in your
-jurisdiction.  Note that you still have to come to some agreement with
-the holders of any patented algorithms you're using.  If you're
-intensively using these modules, please tell me about it; there's little
-incentive for me to work on this package if I don't know of anyone using
-it.
-
-I also make no guarantees as to the usefulness, correctness, or legality
-of these modules, nor does their inclusion constitute an endorsement of
-their effectiveness.  Many cryptographic algorithms are patented;
-inclusion in this package does not necessarily mean you are allowed to
-incorporate them in a product and sell it.  Some of these algorithms may
-have been cryptanalyzed, and may no longer be secure.  While I will
-include commentary on the relative security of the algorithms in the
-sections entitled "Security Notes", there may be more recent analyses
-I'm not aware of.  (Or maybe I'm just clueless.)  If you're implementing
-an important system, don't just grab things out of a toolbox and put
-them together; do some research first.  On the other hand, if you're
-just interested in keeping your co-workers or your relatives out of your
-files, any of the components here could be used.
-
-This document is very much a work in progress.  If you have any
-questions, comments, complaints, or suggestions, please send them to me.
-
-\subsection{Acknowledgements}
-Much of the code that actually implements the various cryptographic
-algorithms was not written by me.  I'd like to thank all the people who
-implemented them, and released their work under terms which allowed me
-to use their code.  These individuals are credited in the relevant
-chapters of this documentation.  Bruce Schneier's book \emph{Applied
-Cryptography} was also very useful in writing this toolkit; I highly
-recommend it if you're interested in learning more about cryptography.
-
-Good luck with your cryptography hacking!
-
-A.M.K.
-
-\email{comments@amk.ca}
-
-Washington DC, USA
-
-June 2005
-
-
-%======================================================================
-\section{Crypto.Hash: Hash Functions}
-
-Hash functions take arbitrary strings as input, and produce an output
-of fixed size that is dependent on the input; it should never be
-possible to derive the input data given only the hash function's
-output.  One simple hash function consists of simply adding together
-all the bytes of the input, and taking the result modulo 256.  For a
-hash function to be cryptographically secure, it must be very
-difficult to find two messages with the same hash value, or to find a
-message with a given hash value.  The simple additive hash function
-fails this criterion miserably and the hash functions described below
-meet this criterion (as far as we know).  Examples of
-cryptographically secure hash functions include MD2, MD5, and SHA1.
-
-Hash functions can be used simply as a checksum, or, in association with a
-public-key algorithm, can be used to implement digital signatures.
- 
-The hashing algorithms currently implemented are:
-
-\begin{tableii}{c|l}{}{Hash function}{Digest length}
-\lineii{MD2}{128 bits}
-\lineii{MD4}{128 bits}
-\lineii{MD5}{128 bits}
-\lineii{RIPEMD}{160 bits}
-\lineii{SHA1}{160 bits}
-\lineii{SHA256}{256 bits}
-\end{tableii}
-
-All hashing modules share the same interface.  After importing a given
-hashing module, call the \function{new()} function to create a new
-hashing object. You can now feed arbitrary strings into the object
-with the \method{update()} method, and can ask for the hash value at
-any time by calling the \method{digest()} or \method{hexdigest()}
-methods.  The \function{new()} function can also be passed an optional
-string parameter that will be immediately hashed into the object's
-state.
-
-Hash function modules define one variable:
-
-\begin{datadesc}{digest_size}
-An integer value; the size of the digest
-produced by the hashing objects.  You could also obtain this value by
-creating a sample object, and taking the length of the digest string
-it returns, but using \member{digest_size} is faster.
-\end{datadesc}
-
-The methods for hashing objects are always the following:
-
-\begin{methoddesc}{copy}{}
-Return a separate copy of this hashing object.  An \code{update} to
-this copy won't affect the original object.
-\end{methoddesc}
-
-\begin{methoddesc}{digest}{}
-Return the hash value of this hashing object, as a string containing
-8-bit data.  The object is not altered in any way by this function;
-you can continue updating the object after calling this function.
-\end{methoddesc}
-
-\begin{methoddesc}{hexdigest}{}
-Return the hash value of this hashing object, as a string containing
-the digest data as hexadecimal digits.  The resulting string will be
-twice as long as that returned by \method{digest()}.  The object is not
-altered in any way by this function; you can continue updating the
-object after calling this function.
-\end{methoddesc}
-
-\begin{methoddesc}{update}{arg}
-Update this hashing object with the string \var{arg}.
-\end{methoddesc}
-
-Here's an example, using the MD5 algorithm:
-
-\begin{verbatim}
->>> from Crypto.Hash import MD5
->>> m = MD5.new()
->>> m.update('abc')
->>> m.digest()
-'\x90\x01P\x98<\xd2O\xb0\xd6\x96?}(\xe1\x7fr'
->>> m.hexdigest()
-'900150983cd24fb0d6963f7d28e17f72'
-\end{verbatim}
-
-
-\subsection{Security Notes}
-
-Hashing algorithms are broken by developing an algorithm to compute a
-string that produces a given hash value, or to find two messages that
-produce the same hash value. Consider an example where Alice and Bob
-are using digital signatures to sign a contract.  Alice computes the
-hash value of the text of the contract and signs the hash value with
-her private key.  Bob could then compute a different contract that has
-the same hash value, and it would appear that Alice signed that bogus
-contract; she'd have no way to prove otherwise.  Finding such a
-message by brute force takes \code{pow(2, b-1)} operations, where the
-hash function produces \emph{b}-bit hashes.
-
-If Bob can only find two messages with the same hash value but can't
-choose the resulting hash value, he can look for two messages with
-different meanings, such as "I will mow Bob's lawn for $10" and "I owe
-Bob $1,000,000", and ask Alice to sign the first, innocuous contract.
-This attack is easier for Bob, since finding two such messages by brute
-force will take \code{pow(2, b/2)} operations on average.  However,
-Alice can protect herself by changing the protocol; she can simply
-append a random string to the contract before hashing and signing it;
-the random string can then be kept with the signature.
-
-None of the algorithms implemented here have been completely broken.
-There are no attacks on MD2, but it's rather slow at 1250 K/sec.  MD4
-is faster at 44,500 K/sec but there have been some partial attacks on
-it.  MD4 makes three iterations of a basic mixing operation; two of
-the three rounds have been cryptanalyzed, but the attack can't be
-extended to the full algorithm.  MD5 is a strengthened version of MD4
-with four rounds; an attack against one round has been found XXX
-update this.  MD5 is still believed secure at the moment, but people
-are gravitating toward using SHA1 in new software because there are no
-known attacks against SHA1.  The MD5 implementation is moderately
-well-optimized and thus faster on x86 processors, running at 35,500
-K/sec.  MD5 may even be faster than MD4, depending on the processor
-and compiler you use.
-
-All the MD\var{n} algorithms produce 128-bit hashes; SHA1 produces a
-larger 160-bit hash, and there are no known attacks against it.  The
-first version of SHA had a weakness which was later corrected; the
-code used here implements the second, corrected, version.  It operates
-at 21,000 K/sec.  SHA256 is about as half as fast as SHA1.  RIPEMD has
-a 160-bit output, the same output size as SHA1, and operates at 17,600
-K/sec.
-
-\subsection{Credits}
-The MD2 and MD4 implementations were written by A.M. Kuchling, and the
-MD5 code was implemented by Colin Plumb.  The SHA1 code was originally
-written by Peter Gutmann.  The RIPEMD code was written by Antoon
-Bosselaers, and adapted for the toolkit by Hirendra Hindocha.  The
-SHA256 code was written by Tom St.~Denis and is part of the
-LibTomCrypt library (\url{http://www.libtomcrypt.org/}); it was
-adapted for the toolkit by Jeethu Rao and Taylor Boon.
-
-
-%======================================================================
-\section{Crypto.Cipher: Encryption Algorithms}
-
-Encryption algorithms transform their input data, or \dfn{plaintext},
-in some way that is dependent on a variable \dfn{key}, producing
-\dfn{ciphertext}. This transformation can easily be reversed, if (and,
-hopefully, only if) one knows the key.  The key can be varied by the
-user or application and chosen from some very large space of possible
-keys.
-
-For a secure encryption algorithm, it should be very difficult to
-determine the original plaintext without knowing the key; usually, no
-clever attacks on the algorithm are known, so the only way of breaking
-the algorithm is to try all possible keys. Since the number of possible
-keys is usually of the order of 2 to the power of 56 or 128, this is not
-a serious threat, although 2 to the power of 56 is now considered
-insecure in the face of custom-built parallel computers and distributed
-key guessing efforts.
-
-\dfn{Block ciphers} take multibyte inputs of a fixed size
-(frequently 8 or 16 bytes long) and encrypt them.  Block ciphers can
-be operated in various modes.  The simplest is Electronic Code Book
-(or ECB) mode.  In this mode, each block of plaintext is simply
-encrypted to produce the ciphertext.  This mode can be dangerous,
-because many files will contain patterns greater than the block size;
-for example, the comments in a C program may contain long strings of
-asterisks intended to form a box.  All these identical blocks will
-encrypt to identical ciphertext; an adversary may be able to use this
-structure to obtain some information about the text.
-
-To eliminate this weakness, there are various feedback modes in which
-the plaintext is combined with the previous ciphertext before
-encrypting; this eliminates any repetitive structure in the
-ciphertext.   
-
-One mode is Cipher Block Chaining (CBC mode); another is Cipher
-FeedBack (CFB mode).  CBC mode still encrypts in blocks, and thus is
-only slightly slower than ECB mode.  CFB mode encrypts on a
-byte-by-byte basis, and is much slower than either of the other two
-modes.  The chaining feedback modes require an initialization value to
-start off the encryption; this is a string of the same length as the
-ciphering algorithm's block size, and is passed to the \code{new()}
-function.  There is also a special PGP mode, which is an oddball
-variant of CFB used by the PGP program.  While you can use it in
-non-PGP programs, it's quite non-standard.
-
-The currently available block ciphers are listed in the following table,
-and are in the \code{Crypto.Cipher} package:
-
-\begin{tableii}{c|l}{}{Cipher}{Key Size/Block Size}
-\lineii{AES}{16, 24, or 32 bytes/16 bytes}
-\lineii{ARC2}{Variable/8 bytes}
-\lineii{Blowfish}{Variable/8 bytes}
-\lineii{CAST}{Variable/8 bytes}
-\lineii{DES}{8 bytes/8 bytes}
-\lineii{DES3 (Triple DES)}{16 bytes/8 bytes}
-\lineii{IDEA}{16 bytes/8 bytes}
-\lineii{RC5}{Variable/8 bytes}
-\end{tableii}
-
-In a strict formal sense, \dfn{stream ciphers} encrypt data bit-by-bit;
-practically, stream ciphers work on a character-by-character basis.
-Stream ciphers use exactly the
-same interface as block ciphers, with a block length that will always
-be 1; this is how block and stream ciphers can be distinguished. 
-The only feedback mode available for stream ciphers is ECB mode. 
-
-The currently available stream ciphers are listed in the following table:
-
-\begin{tableii}{c|l}{}{Cipher}{Key Size}
-\lineii{Cipher}{Key Size}
-  \lineii{ARC4}{Variable}
-  \lineii{XOR}{Variable}
-\end{tableii}
-
-ARC4 is short for `Alleged RC4'.  In September of 1994, someone posted
-C code to both the Cypherpunks mailing list and to the Usenet
-newsgroup \code{sci.crypt}, claiming that it implemented the RC4
-algorithm.  This claim turned out to be correct.  Note that there's a
-damaging class of weak RC4 keys; this module won't warn you about such keys.
-% XXX other analyses of RC4?
-
-A similar anonymous posting was made for Alleged RC2 in January, 1996.
-
-An example usage of the DES module:
-\begin{verbatim}
->>> from Crypto.Cipher import DES
->>> obj=DES.new('abcdefgh', DES.MODE_ECB)
->>> plain="Guido van Rossum is a space alien."
->>> len(plain)
-34
->>> obj.encrypt(plain)
-Traceback (innermost last):
-  File "<stdin>", line 1, in ?
-ValueError: Strings for DES must be a multiple of 8 in length
->>> ciph=obj.encrypt(plain+'XXXXXX')
->>> ciph
-'\021,\343Nq\214DY\337T\342pA\372\255\311s\210\363,\300j\330\250\312\347\342I\3215w\03561\303dgb/\006'
->>> obj.decrypt(ciph)
-'Guido van Rossum is a space alien.XXXXXX'
-\end{verbatim}
-
-All cipher algorithms share a common interface.  After importing a
-given module, there is exactly one function and two variables
-available.
-
-\begin{funcdesc}{new}{key, mode\optional{, IV}}
-Returns a ciphering object, using \var{key} and feedback mode
-\var{mode}.  If \var{mode} is \constant{MODE_CBC} or \constant{MODE_CFB}, \var{IV} must be provided,
-and must be a string of the same length as the block size.  Some
-algorithms support additional keyword arguments to this function; see
-the "Algorithm-specific Notes for Encryption Algorithms" section below for the details.
-\end{funcdesc}
-
-\begin{datadesc}{block_size}
-An integer value; the size of the blocks encrypted by this module.
-Strings passed to the \code{encrypt} and \code{decrypt} functions
-must be a multiple of this length.  For stream ciphers,
-\code{block_size} will be 1. 
-\end{datadesc}
-
-\begin{datadesc}{key_size}
-An integer value; the size of the keys required by this module.  If
-\code{key_size} is zero, then the algorithm accepts arbitrary-length
-keys.  You cannot pass a key of length 0 (that is, the null string
-\code{''} as such a variable-length key.  
-\end{datadesc}
-
-All cipher objects have at least three attributes:
-
-\begin{memberdesc}{block_size}
-An integer value equal to the size of the blocks encrypted by this object.
-Identical to the module variable of the same name.
-\end{memberdesc}
-
-\begin{memberdesc}{IV}
-Contains the initial value which will be used to start a cipher
-feedback mode.  After encrypting or decrypting a string, this value
-will reflect the modified feedback text; it will always be one block
-in length.  It is read-only, and cannot be assigned a new value.
-\end{memberdesc}
-
-\begin{memberdesc}{key_size}
-An integer value equal to the size of the keys used by this object.  If
-\code{key_size} is zero, then the algorithm accepts arbitrary-length
-keys.  For algorithms that support variable length keys, this will be 0.
-Identical to the module variable of the same name.  
-\end{memberdesc}
-
-All ciphering objects have the following methods:
-
-\begin{methoddesc}{decrypt}{string}
-Decrypts \var{string}, using the key-dependent data in the object, and
-with the appropriate feedback mode.  The string's length must be an exact
-multiple of the algorithm's block size.  Returns a string containing
-the plaintext.
-\end{methoddesc}
-
-\begin{methoddesc}{encrypt}{string}
-Encrypts a non-null \var{string}, using the key-dependent data in the
-object, and with the appropriate feedback mode.  The string's length
-must be an exact multiple of the algorithm's block size; for stream
-ciphers, the string can be of any length.  Returns a string containing
-the ciphertext.
-\end{methoddesc}
-
-
-\subsection{Algorithm-specific Notes for Encryption Algorithms}
-
-RC5 has a bunch of parameters; see Ronald Rivest's paper at
-\url{http://theory.lcs.mit.edu/~rivest/rc5rev.ps} for the
-implementation details.  The keyword parameters are:
-
-\begin{itemize}
-\item \code{version}:
-The version
-of the RC5 algorithm to use; currently the only legal value is
-\code{0x10} for RC5 1.0.  
-\item \code{wordsize}:
-The word size to use;
-16 or 32 are the only legal values.  (A larger word size is better, so
-usually 32 will be used.  16-bit RC5 is probably only of academic
-interest.)  
-\item \code{rounds}:
-The number of rounds to apply, the larger the more secure: this
-can be any value from 0 to 255, so you will have to choose a value
-balanced between speed and security. 
-\end{itemize}
-
-
-\subsection{Security Notes}
-Encryption algorithms can be broken in several ways.  If you have some
-ciphertext and know (or can guess) the corresponding plaintext, you can
-simply try every possible key in a \dfn{known-plaintext} attack.  Or, it
-might be possible to encrypt text of your choice using an unknown key;
-for example, you might mail someone a message intending it to be
-encrypted and forwarded to someone else.  This is a
-\dfn{chosen-plaintext} attack, which is particularly effective if it's
-possible to choose plaintexts that reveal something about the key when
-encrypted.
-
-DES (5100 K/sec) has a 56-bit key; this is starting to become too small
-for safety.  It has been estimated that it would only cost \$1,000,000 to
-build a custom DES-cracking machine that could find a key in 3 hours.  A
-chosen-ciphertext attack using the technique of \dfn{linear
-cryptanalysis} can break DES in \code{pow(2, 43)} steps.  However,
-unless you're encrypting data that you want to be safe from major
-governments, DES will be fine. DES3 (1830 K/sec) uses three DES
-encryptions for greater security and a 112-bit or 168-bit key, but is
-correspondingly slower.
-
-There are no publicly known attacks against IDEA (3050 K/sec), and
-it's been around long enough to have been examined.  There are no
-known attacks against ARC2 (2160 K/sec), ARC4 (8830 K/sec), Blowfish
-(9250 K/sec), CAST (2960 K/sec), or RC5 (2060 K/sec), but they're all
-relatively new algorithms and there hasn't been time for much analysis
-to be performed; use them for serious applications only after careful
-research.
-
-AES, the Advanced Encryption Standard, was chosen by the US National
-Institute of Standards and Technology from among 6 competitors, and is
-probably your best choice.  It runs at 7060 K/sec, so it's among the
-faster algorithms around.
-
-
-\subsection{Credits}
-The code for Blowfish was written by Bryan Olson, partially based on a
-previous implementation by Bruce Schneier, who also invented the
-algorithm; the Blowfish algorithm has been placed in the public domain
-and can be used freely.  (See \url{http://www.counterpane.com} for more
-information about Blowfish.)  The CAST implementation was written by 
-Wim Lewis.  The DES implementation was written by Eric Young, and the
-IDEA implementation by Colin Plumb. The RC5 implementation
-was written by A.M. Kuchling.
-
-The Alleged RC4 code was posted to the \code{sci.crypt} newsgroup by an
-unknown party, and re-implemented by A.M. Kuchling.  
-
-
-%======================================================================
-\section{Crypto.Protocol: Various Protocols}
-
-\subsection{Crypto.Protocol.AllOrNothing}
-
-This module implements all-or-nothing package transformations.
-An all-or-nothing package transformation is one in which some text is
-transformed into message blocks, such that all blocks must be obtained before
-the reverse transformation can be applied.  Thus, if any blocks are corrupted
-or lost, the original message cannot be reproduced.
-
-An all-or-nothing package transformation is not encryption, although a block
-cipher algorithm is used.  The encryption key is randomly generated and is
-extractable from the message blocks.
-
-\begin{classdesc}{AllOrNothing}{ciphermodule, mode=None, IV=None}
-Class implementing the All-or-Nothing package transform.
-
-\var{ciphermodule} is a module implementing the cipher algorithm to
-use.  Optional arguments \var{mode} and \var{IV} are passed directly
-through to the \var{ciphermodule}.\code{new()} method; they are the
-feedback mode and initialization vector to use.  All three arguments
-must be the same for the object used to create the digest, and to
-undigest'ify the message blocks.
-
-The module passed as \var{ciphermodule} must provide the \pep{272}
-interface.  An encryption key is randomly generated automatically when
-needed.
-\end{classdesc}
-
-The methods of the \class{AllOrNothing} class are:
-
-\begin{methoddesc}{digest}{text}
-Perform the All-or-Nothing package transform on the 
-string \var{text}.  Output is a list of message blocks describing the
-transformed text, where each block is a string of bit length equal
-to the cipher module's block_size.
-\end{methoddesc}
-
-\begin{methoddesc}{undigest}{mblocks}
-Perform the reverse package transformation on a list of message
-blocks.  Note that the cipher module used for both transformations
-must be the same.  \var{mblocks} is a list of strings of bit length
-equal to \var{ciphermodule}'s block_size.  The output is a string object.
-\end{methoddesc}
-
-
-\subsection{Crypto.Protocol.Chaffing}
-
-Winnowing and chaffing is a technique for enhancing privacy without requiring
-strong encryption.  In short, the technique takes a set of authenticated
-message blocks (the wheat) and adds a number of chaff blocks which have
-randomly chosen data and MAC fields.  This means that to an adversary, the
-chaff blocks look as valid as the wheat blocks, and so the authentication
-would have to be performed on every block.  By tailoring the number of chaff
-blocks added to the message, the sender can make breaking the message
-computationally infeasible.  There are many other interesting properties of
-the winnow/chaff technique.
-
-For example, say Alice is sending a message to Bob.  She packetizes the
-message and performs an all-or-nothing transformation on the packets.  Then
-she authenticates each packet with a message authentication code (MAC).  The
-MAC is a hash of the data packet, and there is a secret key which she must
-share with Bob (key distribution is an exercise left to the reader).  She then
-adds a serial number to each packet, and sends the packets to Bob.
-
-Bob receives the packets, and using the shared secret authentication key,
-authenticates the MACs for each packet.  Those packets that have bad MACs are
-simply discarded.  The remainder are sorted by serial number, and passed
-through the reverse all-or-nothing transform.  The transform means that an
-eavesdropper (say Eve) must acquire all the packets before any of the data can
-be read.  If even one packet is missing, the data is useless.
-
-There's one twist: by adding chaff packets, Alice and Bob can make Eve's job
-much harder, since Eve now has to break the shared secret key, or try every
-combination of wheat and chaff packet to read any of the message.  The cool
-thing is that Bob doesn't need to add any additional code; the chaff packets
-are already filtered out because their MACs don't match (in all likelihood --
-since the data and MACs for the chaff packets are randomly chosen it is
-possible, but very unlikely that a chaff MAC will match the chaff data).  And
-Alice need not even be the party adding the chaff!  She could be completely
-unaware that a third party, say Charles, is adding chaff packets to her
-messages as they are transmitted.
-
-\begin{classdesc}{Chaff}{factor=1.0, blocksper=1}
-Class implementing the chaff adding algorithm. 
-\var{factor} is the number of message blocks 
-            to add chaff to, expressed as a percentage between 0.0 and 1.0; the default value is 1.0.
-\var{blocksper} is the number of chaff blocks to include for each block
-            being chaffed, and defaults to 1.  The default settings 
-add one chaff block to every
-            message block.  By changing the defaults, you can adjust how
-            computationally difficult it could be for an adversary to
-            brute-force crack the message.  The difficulty is expressed as:
-
-\begin{verbatim}
-pow(blocksper, int(factor * number-of-blocks))
-\end{verbatim}
-
-For ease of implementation, when \var{factor} < 1.0, only the first
-\code{int(\var{factor}*number-of-blocks)} message blocks are chaffed.
-\end{classdesc}
-
-\class{Chaff} instances have the following methods:
-
-\begin{methoddesc}{chaff}{blocks}
-Add chaff to message blocks.  \var{blocks} is a list of 3-tuples of the
-form (\var{serial-number}, \var{data}, \var{MAC}).
-
-Chaff is created by choosing a random number of the same
-byte-length as \var{data}, and another random number of the same
-byte-length as \var{MAC}.  The message block's serial number is placed
-on the chaff block and all the packet's chaff blocks are randomly
-interspersed with the single wheat block.  This method then
-returns a list of 3-tuples of the same form.  Chaffed blocks will
-contain multiple instances of 3-tuples with the same serial
-number, but the only way to figure out which blocks are wheat and
-which are chaff is to perform the MAC hash and compare values.
-\end{methoddesc}
-
-
-%======================================================================
-\section{Crypto.PublicKey: Public-Key Algorithms}
-So far, the encryption algorithms described have all been \dfn{private
-key} ciphers.  The same key is used for both encryption and decryption
-so all correspondents must know it.  This poses a problem: you may
-want encryption to communicate sensitive data over an insecure
-channel, but how can you tell your correspondent what the key is?  You
-can't just e-mail it to her because the channel is insecure.  One
-solution is to arrange the key via some other way: over the phone or
-by meeting in person.
-
-Another solution is to use \dfn{public-key} cryptography.  In a public
-key system, there are two different keys: one for encryption and one for
-decryption.  The encryption key can be made public by listing it in a
-directory or mailing it to your correspondent, while you keep the
-decryption key secret.  Your correspondent then sends you data encrypted
-with your public key, and you use the private key to decrypt it.  While
-the two keys are related, it's very difficult to derive the private key
-given only the public key; however, deriving the private key is always
-possible given enough time and computing power.  This makes it very
-important to pick keys of the right size: large enough to be secure, but
-small enough to be applied fairly quickly.
-
-Many public-key algorithms can also be used to sign messages; simply
-run the message to be signed through a decryption with your private
-key key.  Anyone receiving the message can encrypt it with your
-publicly available key and read the message.  Some algorithms do only
-one thing, others can both encrypt and authenticate.
-
-The currently available public-key algorithms are listed in the
-following table:
-
-\begin{tableii}{c|l}{}{Algorithm}{Capabilities}
-\lineii{RSA}{Encryption, authentication/signatures}
-\lineii{ElGamal}{Encryption, authentication/signatures}
-\lineii{DSA}{Authentication/signatures}
-\lineii{qNEW}{Authentication/signatures}
-\end{tableii}
-
-Many of these algorithms are patented.  Before using any of them in a
-commercial product, consult a patent attorney; you may have to arrange
-a license with the patent holder.
-
-An example of using the RSA module to sign a message:
-\begin{verbatim}
->>> from Crypto.Hash import MD5
->>> from Crypto.PublicKey import RSA
->>> RSAkey = RSA.generate(384, randfunc)   # This will take a while...
->>> hash = MD5.new(plaintext).digest()
->>> signature = RSAkey.sign(hash, "")
->>> signature   # Print what an RSA sig looks like--you don't really care.
-('\021\317\313\336\264\315' ...,)
->>> RSAkey.verify(hash, signature)     # This sig will check out
-1
->>> RSAkey.verify(hash[:-1], signature)# This sig will fail
-0
-\end{verbatim}
-
-Public-key modules make the following functions available:
-
-\begin{funcdesc}{construct}{tuple}
-Constructs a key object from a tuple of data.  This is
-algorithm-specific; look at the source code for the details.  (To be
-documented later.)
-\end{funcdesc}
-
-\begin{funcdesc}{generate}{size, randfunc, progress_func=\code{None}}
-Generate a fresh public/private key pair.  \var{size} is a
-algorithm-dependent size parameter, usually measured in bits; the
-larger it is, the more difficult it will be to break the key.  Safe
-key sizes vary from algorithm to algorithm; you'll have to research
-the question and decide on a suitable key size for your application.
-An N-bit keys can encrypt messages up to N-1 bits long.
-
-\var{randfunc} is a random number generation function; it should
-accept a single integer \var{N} and return a string of random data
-\var{N} bytes long.  You should always use a cryptographically secure
-random number generator, such as the one defined in the
-\module{Crypto.Util.randpool} module; \emph{don't} just use the
-current time and the \module{random} module. 
-
-\var{progress_func} is an optional function that will be called with a short
-string containing the key parameter currently being generated; it's
-useful for interactive applications where a user is waiting for a key
-to be generated.
-\end{funcdesc}
-
-If you want to interface with some other program, you will have to know
-the details of the algorithm being used; this isn't a big loss.  If you
-don't care about working with non-Python software, simply use the
-\module{pickle} module when you need to write a key or a signature to a
-file.  It's portable across all the architectures that Python supports,
-and it's simple to use.
-
-Public-key objects always support the following methods.  Some of them
-may raise exceptions if their functionality is not supported by the
-algorithm.
-
-\begin{methoddesc}{can_blind}{}
-Returns true if the algorithm is capable of blinding data; 
-returns false otherwise.  
-\end{methoddesc}
-
-\begin{methoddesc}{can_encrypt}{}
-Returns true if the algorithm is capable of encrypting and decrypting
-data; returns false otherwise.  To test if a given key object can encrypt
-data, use \code{key.can_encrypt() and key.has_private()}.
-\end{methoddesc}
-
-\begin{methoddesc}{can_sign}{}
-Returns true if the algorithm is capable of signing data; returns false
-otherwise.  To test if a given key object can sign data, use
-\code{key.can_sign() and key.has_private()}.
-\end{methoddesc}
-
-\begin{methoddesc}{decrypt}{tuple}
-Decrypts \var{tuple} with the private key, returning another string.
-This requires the private key to be present, and will raise an exception
-if it isn't present.  It will also raise an exception if \var{string} is
-too long.
-\end{methoddesc}
-
-\begin{methoddesc}{encrypt}{string, K}
-Encrypts \var{string} with the private key, returning a tuple of
-strings; the length of the tuple varies from algorithm to algorithm.  
-\var{K} should be a string of random data that is as long as
-possible.  Encryption does not require the private key to be present
-inside the key object.  It will raise an exception if \var{string} is
-too long.  For ElGamal objects, the value of \var{K} expressed as a
-big-endian integer must be relatively prime to \code{self.p-1}; an
-exception is raised if it is not.
-\end{methoddesc}
-
-\begin{methoddesc}{has_private}{}
-Returns true if the key object contains the private key data, which
-will allow decrypting data and generating signatures.
-Otherwise this returns false.
-\end{methoddesc}
-
-\begin{methoddesc}{publickey}{}
-Returns a new public key object that doesn't contain the private key
-data. 
-\end{methoddesc}
-
-\begin{methoddesc}{sign}{string, K}
-Sign \var{string}, returning a signature, which is just a tuple; in
-theory the signature may be made up of any Python objects at all; in
-practice they'll be either strings or numbers.  \var{K} should be a
-string of random data that is as long as possible.  Different algorithms
-will return tuples of different sizes.  \code{sign()} raises an
-exception if \var{string} is too long.  For ElGamal objects, the value
-of \var{K} expressed as a big-endian integer must be relatively prime to
-\code{self.p-1}; an exception is raised if it is not.
-\end{methoddesc}
-
-\begin{methoddesc}{size}{}
-Returns the maximum size of a string that can be encrypted or signed,
-measured in bits.  String data is treated in big-endian format; the most
-significant byte comes first.  (This seems to be a \emph{de facto} standard
-for cryptographical software.)  If the size is not a multiple of 8, then
-some of the high order bits of the first byte must be zero.  Usually
-it's simplest to just divide the size by 8 and round down.
-\end{methoddesc}
-
-\begin{methoddesc}{verify}{string, signature}
-Returns true if the signature is valid, and false otherwise.
-\var{string} is not processed in any way; \code{verify} does
-not run a hash function over the data, but you can easily do that yourself.
-\end{methoddesc}
-
-\subsection{The ElGamal and DSA algorithms}
-For RSA, the \var{K} parameters are unused; if you like, you can just
-pass empty strings.  The ElGamal and DSA algorithms require a real
-\var{K} value for technical reasons; see Schneier's book for a detailed
-explanation of the respective algorithms.  This presents a possible
-hazard that can  
-inadvertently reveal the private key.  Without going into the
-mathematical details, the danger is as follows. \var{K} is never derived
-or needed by others; theoretically, it can be thrown away once the
-encryption or signing operation is performed.  However, revealing
-\var{K} for a given message would enable others to derive the secret key
-data; worse, reusing the same value of \var{K} for two different
-messages would also enable someone to derive the secret key data.  An
-adversary could intercept and store every message, and then try deriving
-the secret key from each pair of messages.
-
-This places implementors on the horns of a dilemma.  On the one hand,
-you want to store the \var{K} values to avoid reusing one; on the other
-hand, storing them means they could fall into the hands of an adversary.
-One can randomly generate \var{K} values of a suitable length such as
-128 or 144 bits, and then trust that the random number generator
-probably won't produce a duplicate anytime soon.  This is an
-implementation decision that depends on the desired level of security
-and the expected usage lifetime of a private key.  I can't choose and
-enforce one policy for this, so I've added the \var{K} parameter to the
-\method{encrypt} and \method{sign} methods.  You must choose \var{K} by
-generating a string of random data; for ElGamal, when interpreted as a
-big-endian number (with the most significant byte being the first byte
-of the string), \var{K} must be relatively prime to \code{self.p-1}; any
-size will do, but brute force searches would probably start with small
-primes, so it's probably good to choose fairly large numbers.  It might be
-simplest to generate a prime number of a suitable length using the
-\module{Crypto.Util.number} module.
-
-
-\subsection{Security Notes for Public-key Algorithms}
-Any of these algorithms can be trivially broken; for example, RSA can be
-broken by factoring the modulus \emph{n} into its two prime factors.
-This is easily done by the following code:
-
-\begin{verbatim}
-for i in range(2, n): 
-    if (n%i)==0: 
-        print i, 'is a factor' 
-        break
-\end{verbatim}
-
-However, \emph{n} is usually a few hundred bits long, so this simple
-program wouldn't find a solution before the universe comes to an end.
-Smarter algorithms can factor numbers more quickly, but it's still
-possible to choose keys so large that they can't be broken in a
-reasonable amount of time.  For ElGamal and DSA, discrete logarithms are
-used instead of factoring, but the principle is the same.
-
-Safe key sizes depend on the current state of number theory and
-computer technology.  At the moment, one can roughly define three
-levels of security: low-security commercial, high-security commercial,
-and military-grade.  For RSA, these three levels correspond roughly to
-768, 1024, and 2048-bit keys.
-
-
-%======================================================================
-\section{Crypto.Util: Odds and Ends}
-This chapter contains all the modules that don't fit into any of the
-other chapters.  
-
-\subsection{Crypto.Util.number}
-
-This module contains various number-theoretic functions.  
-
-\begin{funcdesc}{GCD}{x,y}
-Return the greatest common divisor of \var{x} and \var{y}.
-\end{funcdesc}
-
-\begin{funcdesc}{getPrime}{N, randfunc}
-Return an \var{N}-bit random prime number, using random data obtained
-from the function \var{randfunc}.  \var{randfunc} must take a single
-integer argument, and return a string of random data of the
-corresponding length; the \method{get_bytes()} method of a
-\class{RandomPool} object will serve the purpose nicely, as will the
-\method{read()} method of an opened file such as \file{/dev/random}.
-\end{funcdesc}
-
-\begin{funcdesc}{getRandomNumber}{N, randfunc}
-Return an \var{N}-bit random number, using random data obtained from the
-function \var{randfunc}.  As usual, \var{randfunc} must take a single
-integer argument and return a string of random data of the
-corresponding length.
-\end{funcdesc}
-
-\begin{funcdesc}{inverse}{u, v}
-Return the inverse of \var{u} modulo \var{v}.
-\end{funcdesc}
-
-\begin{funcdesc}{isPrime}{N}
-Returns true if the number \var{N} is prime, as determined by a
-Rabin-Miller test.
-\end{funcdesc}
-
-
-\subsection{Crypto.Util.randpool}
-
-For cryptographic purposes, ordinary random number generators are
-frequently insufficient, because if some of their output is known, it
-is frequently possible to derive the generator's future (or past)
-output.  Given the generator's state at some point in time, someone
-could try to derive any keys generated using it.  The solution is to
-use strong encryption or hashing algorithms to generate successive
-data; this makes breaking the generator as difficult as breaking the
-algorithms used.
-
-Understanding the concept of \dfn{entropy} is important for using the
-random number generator properly.  In the sense we'll be using it,
-entropy measures the amount of randomness; the usual unit is in bits.
-So, a single random bit has an entropy of 1 bit; a random byte has an
-entropy of 8 bits.  Now consider a one-byte field in a database containing a
-person's sex, represented as a single character \samp{M} or \samp{F}.
-What's the entropy of this field?  Since there are only two possible
-values, it's not 8 bits, but one; if you were trying to guess the value,
-you wouldn't have to bother trying \samp{Q} or \samp{@}.  
-
-Now imagine running that single byte field through a hash function that
-produces 128 bits of output.  Is the entropy of the resulting hash value
-128 bits?  No, it's still just 1 bit.  The entropy is a measure of how many
-possible states of the data exist.  For English
-text, the entropy of a five-character string is not 40 bits; it's
-somewhat less, because not all combinations would be seen.  \samp{Guido}
-is a possible string, as is \samp{In th}; \samp{zJwvb} is not.
-
-The relevance to random number generation?  We want enough bits of
-entropy to avoid making an attack on our generator possible.  An
-example: One computer system had a mechanism which generated nonsense
-passwords for its users.  This is a good idea, since it would prevent
-people from choosing their own name or some other easily guessed string.
-Unfortunately, the random number generator used only had 65536 states,
-which meant only 65536 different passwords would ever be generated, and
-it was easy to compute all the possible passwords and try them.  The
-entropy of the random passwords was far too low.  By the same token, if
-you generate an RSA key with only 32 bits of entropy available, there
-are only about 4.2 billion keys you could have generated, and an
-adversary could compute them all to find your private key.  See \rfc{1750},
-"Randomness Recommendations for Security", for an interesting discussion
-of the issues related to random number generation.
-
-The \module{randpool} module implements a strong random number generator
-in the \class{RandomPool} class.  The internal state consists of a string
-of random data, which is returned as callers request it.  The class
-keeps track of the number of bits of entropy left, and provides a function to
-add new random data; this data can be obtained in various ways, such as
-by using the variance in a user's keystroke timings.  
-
-\begin{classdesc}{RandomPool}{\optional{numbytes, cipher, hash} }
-An object of the \code{RandomPool} class can be created without
-parameters if desired.  \var{numbytes} sets the number of bytes of
-random data in the pool, and defaults to 160 (1280 bits). \var{hash}
-can be a string containing the module name of the hash function to use
-in stirring the random data, or a module object supporting the hashing
-interface.  The default action is to use SHA.
-
-The \var{cipher} argument is vestigial; it was removed from version
-1.1 so RandomPool would work even in the limited exportable subset of
-the code.  I recommend passing \var{hash} using a keyword argument so
-that someday I can safely delete the \var{cipher} argument
-
-\end{classdesc}
-
-\class{RandomPool} objects define the following variables and methods:
-
-\begin{methoddesc}{add_event}{time\optional{, string}}
-Adds an event to the random pool.  \var{time} should be set to the
-current system time, measured at the highest resolution available.
-\var{string} can be a string of data that will be XORed into the pool,
-and can be used to increase the entropy of the pool.  For example, if
-you're encrypting a document, you might use the hash value of the
-document; an adversary presumably won't have the plaintext of the
-document, and thus won't be able to use this information to break the
-generator.
-\end{methoddesc}
-
-The return value is the value of \member{self.entropy} after the data has
-been added.  The function works in the following manner: the time
-between successive calls to the \method{add_event()} method is determined,
-and the entropy of the data is guessed; the larger the time between
-calls, the better.  The system time is then read and added to the pool,
-along with the \var{string} parameter, if present.  The hope is that the
-low-order bits of the time are effectively random.  In an application,
-it is recommended that \method{add_event()} be called as frequently as
-possible, with whatever random data can be found.
-
-\begin{memberdesc}{bits}
-A constant integer value containing the number of bits of data in
-the pool, equal to the \member{bytes} attribute multiplied by 8.
-\end{memberdesc}
-
-\begin{memberdesc}{bytes}
-A constant integer value containing the number of bytes of data in
-the pool.
-\end{memberdesc}
-
-\begin{memberdesc}{entropy}
-An integer value containing the number of bits of entropy currently in
-the pool.  The value is incremented by the \method{add_event()} method,
-and decreased by the \method{get_bytes()} method.
-\end{memberdesc}
-
-\begin{methoddesc}{get_bytes}{num}
-Returns a string containing \var{num} bytes of random data, and
-decrements the amount of entropy available.  It is not an error to
-reduce the entropy to zero, or to call this function when the entropy
-is zero.  This simply means that, in theory, enough random information has been
-extracted to derive the state of the generator.  It is the caller's
-responsibility to monitor the amount of entropy remaining and decide
-whether it is sufficent for secure operation.
-\end{methoddesc}
-
-\begin{methoddesc}{stir}{}
-Scrambles the random pool using the previously chosen encryption and
-hash function.  An adversary may attempt to learn or alter the state
-of the pool in order to affect its future output; this function
-destroys the existing state of the pool in a non-reversible way.  It
-is recommended that \method{stir()} be called before and after using
-the \class{RandomPool} object.  Even better, several calls to
-\method{stir()} can be interleaved with calls to \method{add_event()}.
-\end{methoddesc}
-
-The \class{PersistentRandomPool} class is a subclass of \class{RandomPool} 
-that adds the capability to save and load the pool from a disk file.
-
-\begin{classdesc}{PersistentRandomPool}{filename, \optional{numbytes, cipher, hash}}
-The path given in \var{filename} will be automatically opened, and an
-existing random pool read; if no such file exists, the pool will be
-initialized as usual.  If omitted, the filename defaults to the empty
-string, which will prevent it from being saved to a file.  These
-arguments are identical to those for the \class{RandomPool}
-constructor.
-\end{classdesc}
-
-\begin{methoddesc}{save}{}
-Opens the file named by the \member{filename} attribute, and saves the
-random data into the file using the \module{pickle} module.
-\end{methoddesc}
-
-The \class{KeyboardRandomPool} class is a subclass of
-\class{PersistentRandomPool} that provides a method to obtain random
-data from the keyboard:
-
-\begin{methoddesc}{randomize}{}
-(Unix systems only)  Obtain random data from the keyboard.  This works
-by prompting the
-user to hit keys at random, and then using the keystroke timings (and
-also the actual keys pressed) to add entropy to the pool.  This works
-similarly to PGP's random pool mechanism.
-\end{methoddesc}
-
-
-\subsection{Crypto.Util.RFC1751}
-The keys for private-key algorithms should be arbitrary binary data.
-Many systems err by asking the user to enter a password, and then
-using the password as the key.  This limits the space of possible
-keys, as each key byte is constrained within the range of possible
-ASCII characters, 32-127, instead of the whole 0-255 range possible
-with ASCII.  Unfortunately, it's difficult for humans to remember 16
-or 32 hex digits.
-
-One solution is to request a lengthy passphrase from the user, and
-then run it through a hash function such as SHA or MD5.  Another
-solution is discussed in RFC 1751, "A Convention for Human-Readable
-128-bit Keys", by Daniel L. McDonald.  Binary keys are transformed
-into a list of short English words that should be easier to remember.
-For example, the hex key EB33F77EE73D4053 is transformed to "TIDE ITCH
-SLOW REIN RULE MOT".
-
-\begin{funcdesc}{key_to_english}{key}
-Accepts a string of arbitrary data \var{key}, and returns a string
-containing uppercase English words separated by spaces.  \var{key}'s
-length must be a multiple of 8.
-\end{funcdesc}
-
-\begin{funcdesc}{english_to_key}{string}
-Accepts \var{string} containing English words, and returns a string of
-binary data representing the key.  Words must be separated by
-whitespace, and can be any mixture of uppercase and lowercase
-characters.  6 words are required for 8 bytes of key data, so
-the number of words in \var{string} must be a multiple of 6.
-\end{funcdesc}
-
-
-%======================================================================
-\section{Extending the Toolkit}
-
-Preserving the a common interface for cryptographic routines is a good
-idea.  This chapter explains how to write new modules for the Toolkit.
-
-The basic process is as follows:
-\begin{enumerate}
-
-\item Add a new \file{.c} file containing an implementation of the new
-algorithm.  
-This file must define 3 or 4 standard functions,
-a few constants, and a C \code{struct} encapsulating the state variables required by the algorithm.
-
-\item  Add the new algorithm to \file{setup.py}.
-
-\item  Send a copy of the code to me, if you like; code for new
-algorithms will be gratefully accepted.
-\end{enumerate}
-
-
-\subsection{Adding Hash Algorithms}
-
-The required constant definitions are as follows:
-
-\begin{verbatim}
-#define MODULE_NAME MD2		/* Name of algorithm */
-#define DIGEST_SIZE 16          /* Size of resulting digest in bytes */
-\end{verbatim}
-
-The C structure must be named \ctype{hash_state}:
-
-\begin{verbatim}
-typedef struct {
-     ... whatever state variables you need ...
-} hash_state;
-\end{verbatim}
-
-There are four functions that need to be written: to initialize the
-algorithm's state, to hash a string into the algorithm's state, to get
-a digest from the current state, and to copy a state.
-
-\begin{itemize}
-  \item \code{void hash_init(hash_state *self);}
-  \item \code{void hash_update(hash_state *self, unsigned char *buffer, int length);}
-  \item \code{PyObject *hash_digest(hash_state *self);}
-  \item \code{void hash_copy(hash_state *source, hash_state *dest);}
-\end{itemize}
-
-Put \code{\#include "hash_template.c"} at the end of the file to
-include the actual implementation of the module.
-
-
-\subsection{Adding Block Encryption Algorithms}
-
-The required constant definitions are as follows:
-
-\begin{verbatim}
-#define MODULE_NAME AES	       /* Name of algorithm */
-#define BLOCK_SIZE 16          /* Size of encryption block */
-#define KEY_SIZE 0             /* Size of key in bytes (0 if not fixed size) */
-\end{verbatim}
-
-The C structure must be named \ctype{block_state}:
-
-\begin{verbatim}
-typedef struct {
-     ... whatever state variables you need ...
-} block_state;
-\end{verbatim}
-
-There are three functions that need to be written: to initialize the
-algorithm's state, and to encrypt and decrypt a single block.
-
-\begin{itemize}
-  \item \code{void block_init(block_state *self, unsigned char *key,
-                int keylen);}
-  \item \code{void block_encrypt(block_state *self, unsigned char *in, 
-               unsigned char *out);}
-  \item \code{void block_decrypt(block_state *self, unsigned char *in, 
-               unsigned char *out);}
-\end{itemize}
-
-Put \code{\#include "block_template.c"} at the end of the file to
-include the actual implementation of the module.
-
-
-\subsection{Adding Stream Encryption Algorithms}
-
-The required constant definitions are as follows:
-
-\begin{verbatim}
-#define MODULE_NAME ARC4       /* Name of algorithm */
-#define BLOCK_SIZE 1           /* Will always be 1 for a stream cipher */
-#define KEY_SIZE 0             /* Size of key in bytes (0 if not fixed size) */
-\end{verbatim}
-
-The C structure must be named \ctype{stream_state}:
-
-\begin{verbatim}
-typedef struct {
-     ... whatever state variables you need ...
-} stream_state;
-\end{verbatim}
-
-There are three functions that need to be written: to initialize the
-algorithm's state, and to encrypt and decrypt a single block.
-
-\begin{itemize}
-  \item \code{void stream_init(stream_state *self, unsigned char *key,
-                int keylen);}
-  \item \code{void stream_encrypt(stream_state *self, unsigned char *block, 
-               int length);}
-  \item \code{void stream_decrypt(stream_state *self, unsigned char *block, 
-               int length);}
-\end{itemize}
-
-Put \code{\#include "stream_template.c"} at the end of the file to
-include the actual implementation of the module.
-
-
-\end{document}