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Feistel networks were first seen commercially in IBM's Lucifer cipher, designed by Feistel and Don Coppersmith. Feistel networks gained respectability when the US Federal Government adopted the DES (a cipher based on Lucifer, with changes made by the NSA). 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' design). Things have changed in the decades since as hardware has become more capable.

Feistel networks and similar constructions are product ciphers, and so combine multiple rounds of repeated operations, such as:

• Bit-shuffling (often called permutation boxes or P-boxes)
• Simple non-linear functions (often called substitution boxes or S-boxes)
• Linear mixing (in the sense of modular algebra) using XOR

to produce a function with large amounts of what Claude Shannon described as " confusion and diffusionIn cryptography, confusion and diffusion are two properties of the operation of a secure cipher which were identified by Shannon in his paper, " Communication Theory of Secrecy Systems" published in 1949. In Shannon's original definitions, confusion refer".

Many modern symmetric block ciphers are based on Feistel networks, and the structure and properties of Feistel ciphers have been extensively explored by cryptographers.

The basic operation is as follows:

Split the plaintext block into two equal pieces, (, )

For each round , compute

where is the round function and is the sub-key.

Then the ciphertext is (, ).

Regardless of the function , decryption is accomplished via

This diagram illustrates both encryption and decryption. Note the reversal of the subkey order for decryption; this is the only difference between encryption and decryption:

1 List of Feistel ciphers

Feistel or modified Feistel:

Generalised Feistel: