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# Feistel cipher

(Redirected from Feistel network)

In cryptography, a Feistel cipher is a block cipher with a particular structure, named after IBM cryptographer Horst Feistel; it is also commonly known as a Feistel network. A large proportion of block ciphers use the scheme, including the Data Encryption Standard (DES). The Feistel structure has the advantage that 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.

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 diffusion".

Bit shuffling creates the diffusion effect, while substitution is used for confusion.

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, (L0, R0)

For each round $i =1,2,\dots,n$, compute

Li = Ri - 1
$R_i = L_{i-1} \oplus f(R_{i-1}, K_i)$

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

Then the ciphertext is (Ln, Rn).

Regardless of the function f, decryption is accomplished via

Ri - 1 = Li
$L_{i-1} = R_i \oplus f(L_i, K_i)$

One advantage of this model is that the function used does not have to be invertible, and can be very complex.

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:

Unbalanced Feistel ciphers use a modified structure where L0 and R0 are not of equal lengths. The Skipjack encryption algorithm is an example of such a cipher.

## List of Feistel ciphers

Feistel or modified Feistel: Blowfish, Camellia, CAST-128, DES, FEAL, KASUMI, LOKI97, Lucifer, MAGENTA, MISTY1, RC5, TEA, Triple DES, Twofish, XTEA

Generalised Feistel: CAST-256, MacGuffin, RC2, RC6, Skipjack