In cryptography, a Feistel cipher is a symmetric structure used in the construction of block ciphers, named after the Germanborn physicist and cryptographer Horst Feistel who did pioneering research while working for IBM (USA); 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.
A Feistel network is an iterated cipher with an internal function called a round function.^{[1]}
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Feistel networks were first seen commercially in IBM's Lucifer cipher, designed by Horst Feistel and Don Coppersmith. Feistel networks gained respectability when the U.S. 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).
Many modern and also some old symmetric block ciphers are based on Feistel networks (eg GOST_2814789 block cipher), and the structure and properties of Feistel ciphers have been extensively explored by cryptographers. Specifically, Michael Luby and Charles Rackoff analyzed the Feistel cipher construction, and proved that if the round function is a cryptographically secure pseudorandom function, with K_{i} used as the seed, then 3 rounds is sufficient to make the block cipher a pseudorandom permutation, while 4 rounds is 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).^{[2]}
Because of this very important result of Luby and Rackoff, Feistel ciphers are sometimes called LubyRackoff block ciphers. Further theoretical work has generalized the construction somewhat, and given more precise bounds for security.^{[3]}
Let F be the round function and let be the subkeys for the rounds respectively.
Then the basic operation is as follows:
Split the plaintext block into two equal pieces, (L_{0}, R_{0})
For each round , compute
Then the ciphertext is (R_{n + 1},L_{n + 1}).
Decryption of a ciphertext (R_{n + 1},L_{n + 1}) is accomplished by computing for
Then (L_{0},R_{0}) is the plaintext again.
One advantage of the Feistel model compared to a substitutionpermutation network is that the round function F does not have to be invertible, and can be very complex.
The 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 L_{0} and R_{0} are not of equal lengths.^{[4]} The Skipjack encryption algorithm is an example of such a cipher. The Texas Instruments Digital Signature Transponder uses a proprietary unbalanced Feistel cipher to perform challengeresponse authentication.^{[5]}
The Feistel construction is also used in cryptographic algorithms other than block ciphers. For example, the Optimal Asymmetric Encryption Padding (OAEP) scheme uses a simple Feistel network to randomize ciphertexts in certain asymmetric key encryption schemes.
Feistel or modified Feistel: Blowfish, Camellia, CAST128, DES, FEAL, ICE, KASUMI, LOKI97, Lucifer, MARS, MAGENTA, MISTY1, RC5, TEA, Triple DES, Twofish, XTEA, GOST_2814789
Generalised Feistel: CAST256, MacGuffin, RC2, RC6, Skipjack, SMS4
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In cryptography, a Feistel cipher is a symmetric structure used in the construction of block ciphers, named after the German IBM cryptographer Horst Feistel; it is also commonly known as a Feistel network. A large set 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 construction is iterative in nature which makes implementing the cryptosystem in hardware easier.
Feistel networks and similar constructions are product ciphers, and so combine multiple rounds of repeated operations, such as:
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.
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Many modern symmetric block ciphers uses Feistel networks, and the structure and properties of Feistel ciphers have been extensively explored by cryptographers. Specifically, Michael Luby and Charles Rackoff analyzed the Feistel block cipher construction, and proved that if the round function is a cryptographically secure pseudorandom function, with K_{i} used as the seed, then 3 rounds is sufficient to make the block cipher a pseudorandom permutation, while 4 rounds is 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).^{[1]} Because of this very important result of Luby and Rackoff, Feistel ciphers are sometimes called LubyRackoff block ciphers. Further theoretical studies generalized the construction, and defined more precise limits for security.^{[2]}
[[File:thumbrightFeistel network operation on block cipher, where P is the plaintext and C is the ciphertext]]
Let $\{\backslash rm\; F\}$ be the round function and let $K\_1,K\_2,\backslash ldots,K\_\{n\}$ be the subkeys for the rounds $1,2,\backslash ldots,n$ respectively.
Then the basic operation is as follows:
Split the plaintext block into two equal pieces, ($L\_1$, $R\_1$)
For each round $i\; =1,2,\backslash dots,n$, compute (calculate)
Then the ciphertext is $(R\_n,\; L\_n)$. (Commonly the two pieces $R\_n$ and $L\_n$ are not switched after the last round.)
Decryption of a ciphertext $(R\_n,\; L\_n)$ is accomplished by computing for $i=n,n1,\backslash ldots,1$
Then $(L\_1,R\_1)$ is the plaintext again.
One advantage of this model is that the round function $\{\backslash rm\; F\}$ does not have to be invertible, and can be very complex.
The diagram illustrates the encryption process. Decryption requires only reversing the order of the subkey $K\_\{n\},K\_\{n1\},\backslash ldots,K\_1$ using the same process; this is the only difference between encryption and decryption:
Unbalanced Feistel ciphers use a modified structure where $L\_1$ and $R\_1$ are not of equal lengths. The MacGuffin cipher is an experimental example of such a cipher.
The Feistel construction is also used in cryptographic algorithms other than block ciphers. For example, the Optimal Asymmetric Encryption Padding (OAEP) scheme uses a simple Feistel network to randomize ciphertexts in certain asymmetrickey encryption schemes.
Feistel or modified Feistel: Blowfish, Camellia, CAST128, DES, FEAL, ICE, KASUMI, LOKI97, Lucifer, MARS, MAGENTA, MISTY1, RC5, TEA, Triple DES, Twofish, XTEA, GOST 2814789
Generalised Feistel: CAST256, MacGuffin, RC2, RC6, Skipjack
