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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}