Feistel cipher
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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 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.
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History
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.
Theoretical Work
Many modern symmetric block ciphers are based on 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 [1], and proved that if the round function is a cryptographically secure pseudorandom number generator, with Ki used as the seed, then 3 rounds is sufficient to make the block cipher secure, while 4 rounds is sufficient to make the block cipher "strongly" secure, meaning that it is secure against chosen-ciphertext attacks. Because of this very important result of Luby and Rackoff, Feistel ciphers are sometimes inaccurately called Luby-Rackoff block ciphers. Further theoretical work has generalized the construction somewhat, and given more precise bounds for security [3].
Construction Details
The basic operation is as follows:
Split the plaintext block into two equal pieces, (<math>L_0</math>, <math>R_0</math>)
For each round <math>i =1,2,\dots,n</math>, compute
- <math>L_i = R_{i-1}</math>
- <math>R_i = L_{i-1} \oplus f(R_{i-1}, K_{i})</math>
where <math>f</math> is the round function and <math>K_i</math> is the sub-key.
Then the ciphertext is (<math>L_n</math>, <math>R_n</math>).
Regardless of the function <math>f</math>, decryption is accomplished via
- <math>R_{i-1} = L_i</math>
- <math>L_{i-1} = R_i \oplus f(L_i, K_i)</math>
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. The Texas Instruments Digital Signature Transponder [2] uses a proprietary unbalanced Feistel cipher to perform challenge-response authentication.
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.
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
References
[1] M. Luby and C. Rackoff. "How to Construct Pseudorandom Permutations and Pseudorandom Functions." In SIAM J. Comput.," vol. 17, 1988, pp. 373-386.
[2] S. Bono, M. Green, A. Stubblefield, A. Rubin, A. Juels, M. Szydlo. "Security Analysis of a Cryptographically-Enabled RFID Device". In Proceedings of the USENIX Security Symposium, August 2005. (pdf)
[3] Jacques Patarin, Luby-Rackoff: 7 Rounds Are Enough for Security, Lecture Notes in Computer Science, Volume 2729, Oct 2003, Pages 513 - 529
See also
| Block ciphers edit |
| Algorithms: 3-Way | AES | Akelarre | Anubis | Blowfish | Camellia | CAST-128 | CAST-256 | CMEA | CS-Cipher | DEAL | DES | DES-X | FEAL | FOX | FROG | G-DES | GOST | ICE | IDEA | Iraqi | KASUMI | KHAZAD | Khufu and Khafre | Libelle | LOKI89/91 | LOKI97 | Lucifer | MacGuffin | Madryga | MAGENTA | MARS | MISTY1 | MMB | NewDES | Noekeon | RC2 | RC5 | RC6 | REDOC | Red Pike | S-1 | SAFER | SEED | Serpent | SHACAL | SHARK | Skipjack | SMS4 | Square | TEA | Triple DES | Twofish | XTEA |
| Design: Feistel network | Key schedule | Product cipher | S-box | SPN Attacks: Brute force | Linear / Differential cryptanalysis | Mod n | Related key | XSL Standardization: AES process | CRYPTREC | NESSIE Misc: Avalanche effect | Block size | IV | Key size | Modes of operation | Piling-up lemma | Weak key |