Feistel cipher

In a Feistel cipher, encryption and decryption are very similar operations, and both consist of iteratively running a function called a "round function" a fixed number of times.

Many modern symmetric block ciphers are based on Feistel networks.

Feistel networks gained respectability when the U.S. Federal Government adopted the DES (a cipher based on Lucifer, with changes made by the NSA) in 1976.

Like other components of the DES, the iterative nature of the Feistel construction makes implementing the cryptosystem in hardware easier (particularly on the hardware available at the time of DES's design).

A Feistel network uses a round function, a function which takes two inputs – a data block and a subkey – and returns one output of the same size as the data block.

This is repeated a fixed number of times, and the final output is the encrypted data.

An important advantage of Feistel networks compared to other cipher designs such as substitution–permutation networks is that the entire operation is guaranteed to be invertible (that is, encrypted data can be decrypted), even if the round function is not itself invertible.

The round function can be made arbitrarily complicated, since it does not need to be designed to be invertible.

[2]: 465  [3]: 347  Furthermore, the encryption and decryption operations are very similar, even identical in some cases, requiring only a reversal of the key schedule.

Therefore, the size of the code or circuitry required to implement such a cipher is nearly halved.

The structure and properties of Feistel ciphers have been extensively analyzed by cryptographers.

Michael Luby and Charles Rackoff analyzed the Feistel cipher construction and proved that if the round function is a cryptographically secure pseudorandom function, with Ki used as the seed, then 3 rounds are sufficient to make the block cipher a pseudorandom permutation, while 4 rounds are sufficient to make it a "strong" pseudorandom permutation (which means that it remains pseudorandom even to an adversary who gets oracle access to its inverse permutation).

Further theoretical work has generalized the construction somewhat and given more precise bounds for security.

Then the basic operation is as follows: Split the plaintext block into two equal pieces: (

The Texas Instruments digital signature transponder uses a proprietary unbalanced Feistel cipher to perform challenge–response authentication.

[8] The Thorp shuffle is an extreme case of an unbalanced Feistel cipher in which one side is a single bit.

This has better provable security than a balanced Feistel cipher but requires more rounds.

A generalized Feistel algorithm can be used to create strong permutations on small domains of size not a power of two (see format-preserving encryption).