Python Cryptography Modules

# The Python Cryptography Modules

## Release 1.1.0

## Manual Edition 1.1.0

# Introduction

This document describes a package containing various cryptographic modules available for the Python programming language. It assumes you have some basic knowledge about the Python language and about cryptography in general.

## Design Goals

The Python cryptography modules are 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. Individual modules also define variables to help you write Python code that doesn't depend on the algorithms used; for example, each block cipher module defines a variable that gives the algorithm's block size. 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 IDEA instead by simply changing `from Crypto.Cipher import DES` to `from Crypto.Cipher import idea`, and changing all references to `DES.new()` to `IDEA.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 AMD K6/200 running Linux. The exact speeds will obviously vary with different machines and different compilers, but they provide a basis for comparing algorithms. Currently the cryptographic implementations are acceptably fast, but not spectacularly good. I welcome any suggestions or patches for faster code.

If you live outside of Canada or the US, please do not attempt to download it from a North American FTP site; you may get the site's maintainer in trouble. Documentation is not covered by the ITAR regulations, and can be freely sent anywhere in the world.

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 at akuchling@acm.org.

## 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. The individuals are credited in the relevant chapters of this documentation. Bruce Schneier's book Applied Cryptography was also very useful in writing this toolkit; I highly recommend it if you're interested in learning more about cryptography. Mr. Schneier also has a Web site at http://www.counterpane.com.

Good luck with your cryptography hacking!

A.M.K.

akuchling@acm.org

Washington, DC, USA

January 1998

# `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; the hash functions described below do not. Examples of cryptographically secure hash functions include MD2, MD5, SHA, and HAVAL.

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 listed in the following table:

Hash function
  Digest length
MD2
  128 bits
MD4
  128 bits
MD5
  128 bits
SHA
  160 bits
HAVAL
  Variable size: 128, 160, 192, 224, or 256 bits.

All hashing modules share the same interface. After importing a given hashing module, call the `new()` function to create a new hashing object. (In older versions of the Python interpreter, the `md5()` function was used to perform this task. If you're modifying an old script, you should change any calls to `md5()` to use `new()` instead.) You can now feed arbitrary strings into the object, and can ask for the hash value at any time. The `new()` function can also be passed an optional string parameter, which will be hashed immediately.

Hash function modules define one variable:

Variable: hashing modules digestsize
  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 `digestsize` is faster.

The methods for hashing objects are always the following:

Method: hashing objects copy ()
  Return a separate copy of this hashing object. An `update` to this copy won't affect the original object.

Method: hashing objects 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.

Method: hashing objects digest ()
  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 `digest()`. The object is not altered in any way by this function; you can continue updating the object after calling this function.

Method: hashing objects update (arg)
  Update this hashing object with the string arg.

Here's an example, using RSA Data Security's MD5 algorithm:

    >>> from Crypto.Hash import MD5
    >>> m = MD5.new()
    >>> m.update('abc')
    >>> m.digest()
    '\220\001P\230<\322O\260\326\226?}(\341\177r'

Or, more compactly:

    >>> MD5.new('abc').digest()
    '\220\001P\230<\322O\260\326\226?}(\341\177r'

## Algorithm-specific Notes for Hash Functions

HAVAL provides a variable-size digest, and allows for a variable number of rounds. It's believed that increasing the number of rounds increases the security; at least, I don't know of any results to the contrary. The `HAVAL.new()` accordingly has two keyword arguments, `rounds` and `digestsize`. `rounds` can be 3, 4, or 5, and has a default value of 5. `digestsize` can be 128, 160, 192, 224, or 256 bits, and has a default value of 256.

## Security Notes

Hashing algorithms are broken when it's easy 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 it. Bob could then compute a different contract that has the same hash value, and it would appear that Alice has signed that bogus contract; she'd have no way to prove otherwise. Finding such a message by brute force takes `pow(2, b-1)` operations, where the hash function produces 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 `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 424 K/sec. MD4 is faster at 11710 K/sec but there have been some partial attacks on it. MD4 operates in 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 Dobbertin's attack. Because MD5 is more commonly used, the implementation is better optimized and thus faster on x86 processors (19303 K/sec). MD4 may be faster than MD5 when other processors and compilers are used.

All the MD algorithms produce 128-bit hashes; SHA 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 7192 K/sec.

HAVAL is a variable-size hash function; it can generate hash values that are 128, 160, 192, 224, or 256 bits in size, and can use 3, 4, or 5 rounds. 5-round HAVAL runs at 2381 K/sec.

## Credits

The MD2, MD4, and HAVAL implementations were written by A.M. Kuchling, and the MD5 code was implemented by Colin Plumb. The SHA code was originally written by Peter Gutmann.

# `Crypto.Cipher`: Encryption Algorithms

Encryption algorithms transform their input data (called plaintext) in some way that is dependent on a variable key, producing 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, 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.

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, where the plaintext is combined with the previous ciphertext before encrypting; this eliminates any such structure. 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 `new()` function.

There is also a special PGP mode, which is a 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 available in the `Crypto.Cipher` package:

Cipher
  Key Size/Block Size
ARC2
  Variable/8 bytes
Blowfish
  Variable/8 bytes
CAST
  Variable/8 bytes
DES
  8 bytes/8 bytes
DES3 (Triple DES)
  16 bytes/8 bytes
Diamond
  Variable/16 bytes
IDEA
  16 bytes/8 bytes
RC5
  Variable/8 bytes

In a strict formal sense, 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:

Cipher
Key Size
ARC4
Variable
Sapphire
Variable

ARC4 is short for `Alleged RC4'. The real RC4 algorithm is proprietary to RSA Data Security Inc. In September of 1994, someone posted C code to both the Cypherpunks mailing list and to the Usenet newsgroup `sci.crypt`, claiming that it implemented the RC4 algorithm. This posted code is what I'm calling Alleged RC4, or ARC4 for short. I don't know if ARC4 is in fact RC4, but ARC4 has been subjected to scrutiny on the Cypherpunks mailing list and elsewhere, and does not seem to be easily breakable. The legal issues surrounding the use of ARC4 are unclear, but be aware that it hasn't been subject to much scrutiny, and may have some critical flaw that hasn't yet been discovered. The same is true of ARC2, which was posted in January, 1996.

An example usage of the DES module:

    >>> from Crypto.Cipher import DES
    >>> obj=DES.new('abcdefgh', DES.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'

All cipher algorithms share a common interface. After importing a given module, there is exactly one function and two variables available.

Function: encryption modules new (key, mode [,IV])
  Returns a ciphering object, using key and feedback mode mode. If mode is CBC or CFB, 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.

Variable: encryption modules blocksize
  An integer value; the size of the blocks encrypted by this module. Strings passed to the `encrypt` and `decrypt` functions must be a multiple of this length. For stream ciphers, `blocksize` will be 1.

Variable: encryption modules keysize
  An integer value; the size of the keys required by this module. If `keysize` is zero, then the algorithm accepts arbitrary-length keys. You cannot pass a key of length 0 (that is, the null string `"` as such a variable-length key.

All cipher objects have one attribute:

Attribute: encryption objects 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.

All ciphering objects have the following methods:

Method: encryption objects decrypt (string)
  Decrypts 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.

Method: encryption objects encrypt (string)
  Encrypts a non-null 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.

## Algorithm-specific Notes for Encryption Algorithms

The Diamond block cipher allows you to select the number of rounds to apply, ranging from 5 to 15 (inclusive.) This is set via the `rounds` keyword argument to the `new()` function; the default value is 8 rounds.

RC5 has even more parameters; see Ronald Rivest's paper for the implementation details. The keyword parameters are:

- `version`: The version of the RC5 algorithm to use; currently the only legal value is `0x10` for RC5 1.0.
- `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.)
- `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.

## 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 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 chosen-plaintext attack, which is particularly effective if it's possible to choose plaintexts that reveal something about the key when encrypted.

DES (1455 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 linear cryptanalysis can break DES in `pow(2, 43)` steps. However, unless you're encrypting data that you want to be safe from major governments, DES will be fine. DES3 (509 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 (809 K/sec), and it's been around long enough to have been examined. There are no known attacks against ARC2 (1112 K/sec), ARC4 (2852 K/sec), Blowfish (2229 K/sec), CAST (1053 K/sec), Diamond (777 K/sec), RC5 (1365 K/sec), or Sapphire (1468 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.

## 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 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 `sci.crypt` newsgroup by an unknown party, and re-implemented by A.M. Kuchling. The Sapphire stream cipher was developed by Michael P. Johnson, and is in the public domain; the implementation used here was written by A.M. Kuchling and is based on Johnson's code.

# `Crypto.PublicKey`: Public Key Algorithms

So far, the encryption algorithms described have all been private key ciphers. That is, 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 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:

Algorithm
  Capabilities
RSA
  Encryption, authentication/signatures
ElGamal
  Encryption, authentication/signatures
DSA
  Authentication/signatures
qNEW
  Authentication/signatures

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:

    >>> 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

Public key modules make the following functions available:

Function: public-key modules 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.)

Function: public-key modules generate (size, randfunc, progress_func=None)
  Generate a fresh public/private key pair. size is a algorithm-dependent size parameter; 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. `randfunc` is a random number generation function; it should accept a single integer N and return a string of random data N bytes long. You should always use a cryptographically secure random number generator, such as the one defined in the `randpool` module; don't just use the current time and the `whrandom` module.

  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.

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 `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.

Method: public-key objects canencrypt ()
  Returns true if the algorithm is capable of encrypting and decrypting data; returns false otherwise. To test if a given key object can sign data, use `key.canencrypt() and key.hasprivate()`.

Method: public-key objects cansign ()
  Returns true if the algorithm is capable of signing data; returns false otherwise. To test if a given key object can sign data, use `key.cansign() and key.hasprivate()`.

Method: public-key objects decrypt (tuple)
  Decrypts 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 string is too long.

Method: public-key objects encrypt (string, K)
  Encrypts string with the private key, returning a tuple of strings; the length of the tuple varies from algorithm to algorithm. 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 string is too long. For ElGamal objects, the value of K expressed as a big-endian integer must be relatively prime to `self.p-1`; an exception is raised if it is not.

Method: public-key objects hasprivate ()
  Returns true if the key object contains the private key data, which will allow decrypting data and generating signatures. Otherwise this returns false.

Method: public-key objects publickey ()
  Returns a new public key object that doesn't contain the private key data.

Method: public-key objects sign (string, K)
  Sign 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. K should be a string of random data that is as long as possible. Different algorithms will return tuples of different sizes. `sign()` raises an exception if string is too long. For ElGamal objects, the value of K expressed as a big-endian integer must be relatively prime to `self.p-1`; an exception is raised if it is not.

Method: public-key objects 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 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.

Method: public-key objects verify (string, signature)
  Returns true if the signature is valid, and false otherwise. string is not processed in any way; `verify` does not run a hash function over the data, but you can easily do that yourself.

## The ElGamal and DSA algorithms

For RSA, the K parameters are unused; if you like, you can just pass empty strings. The ElGamal and DSA algorithms require a real 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. K is never derived or needed by others; theoretically, it can be thrown away once the encryption or signing operation is performed. However, revealing K for a given message would enable others to derive the secret key data; worse, reusing the same value of 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 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 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 cannot choose and enforce one policy for this, so I've added the K parameter to the `encrypt` and `sign` functions. You must choose 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), K must be relatively prime to `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 `Crypto.Util.number` module.

## Security Notes for Public-key Algorithms

Any of these algorithms can be trivially broken; for example, RSA can be broken by factoring the modulus n into its two prime factors. This is easily done by the following code:

    for i in range(2, n):
        if (n%i)==0: print i, 'is a factor' ; break

However, 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 computer science and 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 512, 768, and 1024 bit-keys. For ElGamal and DSA, the key sizes should be somewhat larger for the same level of security, around 768, 1024, and 1536 bits.

# `Crypto.Util`: Odds and Ends

This chapter contains all the modules that don't fit into any of the other chapters.

## `Crypto.Util.number`

This module contains various functions of number-theoretic functions.

Function: GCD (x,y)
  Return the greatest common divisor of x and y.

Function: getPrime (N, randfunc)
  Return an N-bit random prime number, using random data obtained from the function randfunc. randfunc must take a single integer argument, and return a string of random data of the corresponding length; the `getBytes()` method of a `RandomPool` object will serve the purpose nicely, as will the `read()` method of an opened file such as ``/dev/random'`.

Function: getRandomNumber (N, randfunc)
  Return an N-bit random number, using random data obtained from the function randfunc. As usual, randfunc must take a single integer argument, and return a string of random data of the corresponding length.

Function: inverse (u, v)
  Return the inverse of u modulo v.

Function: isPrime (N)
  Returns true if the number N is prime, as determined by a Rabin-Miller test.

## `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. This is obviously a Bad Thing; 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 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 ``M'` or ``F'`. What's the entropy of this field? Since there are only two possible values, it's not 8 bits, but two; if you were trying to guess the value, you wouldn't have to bother trying ``Q'` or ``@'`.

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. ``Guido'` is a possible string, as is ``In th'`; ``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 easily 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 `randpool` module implements a strong random number generator in the `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.

Class: `randpool` RandomPool ([numbytes, cipher, hash])
  An object of the `RandomPool` class can be created without parameters if desired. numbytes sets the number of bytes of random data in the pool. cipher and hash are strings containing the module name of the encryption algorithm and the hash function to use in stirring the random data. The default values of these parameters are 128 bytes (or 1024 bits), `'IDEA'`, and `'MD5'`.

`RandomPool` objects define the following variables and methods:

Method: `RandomPool` objects addEvent (time, [string])
  Adds an event to the random pool. time should be set to the current system time, measured at the highest resolution available. 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.

The return value is the value of `self.entropy` after the data has been added. The function works in the following manner: the time between successive calls to the `addEvent` 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 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 `addEvent()` be called as frequently as possible, with whatever random data can be found.

Variable: `RandomPool` objects bits
  A constant integer value containing the number of bits of data in the pool, equal to the `bytes` variable multiplied by 8.

Variable: `RandomPool` objects bytes
  A constant integer value containing the number of bytes of data in the pool.

Variable: `RandomPool` objects entropy
  An integer value containing the number of bits of entropy currently in the pool. The value is incremented by the `addEvent()` method, and decreased by the `getBytes` method.

Method: `RandomPool` objects getBytes (num)
  Returns a string containing 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.

Method: `RandomPool` objects 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 `stir()` be called before and after using the `RandomPool` object. Even better, several calls to `stir()` can be interleaved with calls to `addEvent()`.

The `KeyboardRandomPool` class is a subclass of `RandomPool` that adds the capability to save and load the pool from a disk file, and provides a method to obtain random data from the keyboard.

Class: `randpool` RandomPool ([filename, numbytes, cipher, hash])
  The path given in 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. The other arguments are identical to those for the `RandomPool` constructor.

Method: `RandomPool` objects 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.

Method: `RandomPool` objects save ()
  Opens the file named by the `filename` attribute, and saves the random data into the file using the `pickle` module.

## `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".

Function: Key2English (key)
  Accepts a string of arbitrary data key, and returns a string containing uppercase English words separated by spaces. key's length must be a multiple of 8.

Function: English2Key (string)
  Accepts 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 string must be a multiple of 6.

# The Demonstration Programs

The Python cryptography modules comes with various demonstration programs, located in the ``Demo/'` directory. None of them is particularly well-finished, or suitable for serious use. Rather, they're intended to illustrate how the toolkit is used, and to provide some interesting possible uses. Feel free to incorporate the code (or modifications of it) into your own programs.

## Demo 1: ``cipher'`

``cipher'` encrypts and decrypts files. On most Unix systems, the ``crypt'` program uses a variant of the Enigma cipher. This is not secure, and there exists a freely available program called "Crypt Breaker's Workbench" which helps in breaking the cipher if you have some knowledge of the encrypted data.

``cipher'` is a more secure file encryption program. Simply list the names of the files to be encrypted on the command line. ``cipher'` will go through the list and encrypt or decrypt them; ``cipher'` can recognize files it has previously encrypted. The ciphertext of a file is placed in a file of the same name with '``.cip'`' appended; the original file is not deleted, since I'm not sure that all errors during operation are caught, and I don't want people to accidentally erase important files.

There are two command-line options: `-c` and `-k`. Both of them require an argument. `-c ciphername` uses the given encryption algorithm ciphername; for example, `-c des` will use the DES algorithm. The name should be the same as an available module name; thus it should be in lowercase letters. The default cipher is IDEA.

`-k key` can be used to set the encryption key to be used. Note that on a multiuser Unix system, the `ps` command can be used to view the arguments of commands executed by other users, so this is insecure; if you're the only user (say, on your home computer running Linux) you don't have to worry about this. If no key is set on the command line, ``cipher'` will prompt the user to input a key on standard input.

### Technical Details

The encrypted file is not pure ciphertext. First comes a magic string; this is currently the sequence ``ctx'` and a byte containing 1 (the version number of ``cipher'`). This is followed by the null-terminated name of the encryption algorithm, and the rest of the file contains the ciphertext.

The plaintext is encrypted in CBC mode. The initial value for the feedback is always set to a block filled with the letter 'A', and then a block of random data is encrypted. This garbage block will be discarded on decryption. Note that the random data is not generated in a cryptographically secure way, and this may provide a tiny foothold for an attacker.

After the random block is generated, the magic string, length of the original file, and original filename are all encrypted before the file data is finally processed. Some extra characters of padding may be added to obtain an integer number of blocks. This padding will also be discarded on decryption. Note that the plaintext file will be completely read into memory before encryption is performed; no buffering is done. Therefore, don't encrypt 20-megabyte files unless you're willing to face the consequences of a 20-megabyte process.

Areas for improvements to ``cipher'` are: cryptographically secure generation of random data for padding, key entry, and buffering of file input.

## Demo 2: `secimp` and `sign`

``secimp'` demonstrates an application of the Toolkit that may be useful if Python is being used as an extension language for mail and Web clients: secure importing of Python modules. To use it, run ``sign.py'` in a directory with several compiled Python files present. It will use the key in ``testkey.py'` to generate digital signatures for the compiled Python code, and save both the signature and the code in a file ending in ``.pys'`. Then run `python -i secimp.py`, and import a file by using `secimport`.

For example, if ``foo.pys'` was constructed, do `secimport('foo')`. The import should succeed. Now fire up Emacs or some other editor, and change a string in the code in ``foo.pys'`; you might try changing a letter in the name of a variable. When you run `secimport('foo')`, it should raise an exception reporting the failed signature. If you execute the statement `__import__ = secimport`, the secure import will be used by default for all future module imports. Alternatively, if you were creating a restricted execution environment using ``rexec.py'`, you could place `secimport()` in the restricted environment's namespace as the default import function.

# Extending the cryptography modules

Preserving the a common interface for cryptographic routines is a good idea. This chapter explains how to interface your own routines to the Toolkit.

The basic process is as follows:

1. Modify the default definition of a C structure to include whatever instance data your algorithm requires.
2. Write 3 or 4 standard routines. Their names and parameters are specified in the following subsections.
3. Modify ``buildkit'` to contain an entry for your new algorithm. Then run ``buildkit'` to rebuild all the source files.
4. Send a copy of the code to me, if you like; code for new algorithms will be gratefully accepted.

## Creating a Custom Object

In the C code for the interpreter, Python objects are defined as a structure. The default structure is the following:

    typedef struct
    {
     PCTObject_HEAD
    } ALGobject;

`PCTObject_HEAD` is a preprocessor macro which will contain various internal variables used by the interpreter; it must always be the first item in the structure definition, and must not be followed by a semicolon. Following it, you can put whatever instance variables you require. Data that does not depend on the instance or key, such as a static lookup table, need not be encapsulated inside objects; instead, it can be defined as a variable interior to the module.

As an example, for IDEA encryption, a schedule of encryption and decryption data has to be maintained, resulting in the following definition:

    typedef struct
    {
     PCTObject_HEAD
     int EK[6][9], DK[6][9];
    } IDEAobject;

## Standard Routines

The interface to Python is implemented in the files ending in ``.in'`, so ``hash.in'` contains the basic code for modules containing hash functions, for example. ``buildkit'`, a Python script, reads the configuration file and generates source code by interweaving the interface files and the implementation file.

If your algorithm is called ALG, the implementation should be in the file ``ALG.c'`. This is case-sensitive, as are the following function names.

### Hash functions

`void ALGinit(ALGobject *self);`
`void ALGupdate(ALGobject *self, char *buffer, int length);`
`PyObject *ALGdigest(ALGobject *self);`
`void ALGcopy(ALGobject *source, ALGobject *dest);`

Hashing function: void ALGinit (ALGobject *self)
  This function should initialize the hashing object, setting state variables to their expected initial state.

Hashing function: void ALGupdate (ALGobject *self,
  char *buffer, int length) This function should perform a hash on the region pointed to by buffer, which will contain length bytes. The contents of the object pointed to by self should be updated appropriately.

Hashing function: void ALGdigest (ALGobject *self)
  This function returns a string containing the value of the hash function. The object should not be changed in any way by this function. Some hash functions require some computation to be performed before returning a value; for example, the number of bytes may be hashed into the final value. If this is the case for your hash function, you must make a copy of the object's data, perform the final computation on that copy, and return the result.

Results are returned by calling a Python function, `PyString_FromStringAndSize(char *string, int length)`. This function returns a string object which should be returned to the caller. So, the last line of the `ALGdigest` function might be:

      return PyString_FromStringAndSize(digest, 16);

Hashing function: void ALGcopy ALGobject *source, ALGobject *dest)
  Given the source and destination objects, the state variables of the source object should be copied to the dest object; the source object should not be altered in any way by the operation.

### Block ciphers

`void ALGinit(ALGobject *self, unsigned char *key, int length);`
`PyObject *ALGencrypt(ALGobject *self, unsigned char *block);`
`PyObject *ALGdecrypt(ALGobject *self, unsigned char *block);`

Block encryption function: void ALGinit (ALGobject *self, unsigned char *key, int length)
  This function initializes a block cipher object to encrypt and decrypt with key. If the cipher requires a fixed-length key, then the buffer pointed to by key will always of that length, and the value of length will be a random value that should be ignored. If the algorithm accepts a variable-length key, then length will be nonzero, and will contain the size of the key.

Block encryption function: void ALGencrypt (ALGobject *self, unsigned char *block)
  This function should encrypt the data pointed to by block, using the key-dependent data contained in self. Only ECB mode needs to be implemented; `block.in` takes care of the other ciphering modes.

Block encryption function: void ALGdecrypt (ALGobject *self, unsigned char *block)
  This function should decrypt the data pointed to by block, using the key-dependent data contained in self.

## Portability macros

Implementation code must be carefully written to produce the same results with any machine or compiler, without having to set any compile-time definitions. Code that is simply portable by nature is preferable, but it is possible to detect features of the host machine when new objects are created, and then execute special code to convert data to a preferred form.

While portability macros are written for speed, there's no need to execute them on every encryption or updating operation. Instead, add variables to your object to hold the values of the portability macros, and execute the macros only once per object, in your `ALGinit` function. Then the code can simply check the results of the macros and act appropriately.

Currently there is only one portability macro defined:

Macro: void TestEndianness (variable)
  Determines the endianness of the current machine, and sets variable to a constant representing the value for this machine. Possible constants are `PCT_BIG_ENDIAN` and `PCT_LITTLE_ENDIAN`; they are defined along with the `TestEndianness` macro.

## Informing the author

Code for additional cryptographic algorithms can be mailed to me at akuchling@acm.org. You can make things much easier for me by doing the following:

- If you wrote the code, please release it into the public domain or under the MIT license . If you didn't write it, please tell me where to find the original author or source code, so that I can check the licensing conditions.
- Include some test data. It is not sufficient to check that encryption and decryption cancel out properly. An implementation might work fine on a single platform, but two machines with different endianness might produce different results. This would be fatal for portability and interoperating programs. So, please include test data; you can either send me patches to ``test.py'`, or simply send me documents describing the data.

# Concept Index

Jump to: a - b - c - d - e - f - g - h - i - j - k - l - m - n - o - p - r - s - t - u - v - y

## a

- addEvent on `RandomPool` objects
- ALGcopy, ALGcopy
- ALGdecrypt, ALGdecrypt
- ALGdigest, ALGdigest
- ALGencrypt, ALGencrypt
- ALGinit, ALGinit, ALGinit, ALGinit
- ALGupdate, ALGupdate
- ARC2 (block cipher)
- ARC4 (stream cipher), ARC4 (stream cipher), ARC4 (stream cipher)

## b

- bits
- blocksize
- Blowfish (block cipher), Blowfish (block cipher)
- Brown, Lawrence
- buildkit, buildkit
- bytes

## c

- C language
- canencrypt on public-key objects
- cansign on public-key objects
- CAST (block cipher)
- cipher
- cipher (demo program)
- construct
- copy on hashing objects
- crypt
- Crypt Breaker's Workbench
- Cyphers, Graven

## d

- decrypt on encryption objects
- decrypt on public-key objects
- DES (block cipher), DES (block cipher)
- DES3 (block cipher)
- Diamond (block cipher)
- digest on hashing objects, digest on hashing objects
- digestsize

## e

- encrypt on encryption objects
- encrypt on public-key objects
- English2Key
- Enigma
- entropy, entropy

## f

- feedback mode, CBC, feedback mode, CBC
- feedback mode, CFB
- feedback mode, ECB

## g

- GCD
- generate
- getBytes on `RandomPool` objects
- getPrime
- getRandomNumber
- Gutmann, Peter

## h

- hasprivate on public-key objects
- HAVAL (hash function)

## i

- IDEA (block cipher), IDEA (block cipher)
- Intel
- inverse
- isPrime
- ITAR, regulations
- IV

## j

- Johnson, Michael Paul

## k

- Key2English
- keysize
- Kuchling, Andrew
- Kwan, Matthew

## l

- language, C
- licensing terms
- Linux

## m

- MD2 (hash function)
- MD5 (hash function), MD5 (hash function)

## n

- new

## o

- Olson, Bryan
- Outerbridge, Richard

## p

- Plumb, Colin
- publickey on public-key objects

## r

- random numbers
- randomize on `RandomPool` objects
- RandomPool, RandomPool
- RC4 (stream cipher)
- RC5 (block cipher)
- regulations, ITAR
- RSA Data Security, Inc., RSA Data Security, Inc.

## s

- Sapphire (stream cipher), Sapphire (stream cipher)
- save on `RandomPool` objects
- Schneier, Bruce, Schneier, Bruce
- sci.crypt, sci.crypt
- SHA (hash function)
- sign on public-key objects
- size on public-key objects
- stir on `RandomPool` objects
- stream cipher

## t

- TestEndianness
- Triple DES (block cipher)

## u

- update on hashing objects

## v

- verify on public-key objects

## y

- Young, Eric

This document was generated on 6 January 1998 using the texi2html translator version 1.52.