Cryptography Primitive II: Feistel Network

Feistel Networks are building blocks of many stream cipher notably DES, SwordFish etc, wherein one performs a fixed number of rounds of the feistel network, for both excryptopn and decrypton.

Feistel Network

The abbreviations are as follows,

F: Round function
K_i: Subkey for round i
L_i: Left half of the intermediate value at round i, L₀ would be the left half of clear text.
R_i: Right half of the intermediate value at round i, R₀ would be the right half of clear text.

Micheal Luby and Charles Rackoff proved that,

If the round function is a cryptographically secure pseudorandom function, 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.

Strong psuedorandom permutation means that it remains pseudorandom even to an adversary who gets oracle access to its inverse permutation.

Note that in one round of a feistal network, only the left half of the cleartext is encrypted, while the right half is simply exchanged position with the encrypted left half.

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