Theoretical Work
Many modern and also some old symmetric block ciphers are based on Feistel networks (e.g. GOST 28147-89 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 Ki 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).
Because of this very important result of Luby and Rackoff, Feistel ciphers are sometimes called Luby-Rackoff block ciphers. Further theoretical work has generalized the construction somewhat, and given more precise bounds for security.
Read more about this topic: Feistel Cipher
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