Editing Feistel cipher (section)

==Theoretical work==
The structure and properties of Feistel ciphers have been extensively analyzed by [[cryptographer]]s.

[[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<sub>i</sub>'' used as the seed, 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 (which means that it remains pseudorandom even to an adversary who gets [[oracle machine|oracle]] access to its inverse permutation).<ref name=pseudorandom>{{Citation |first1=Michael |last1=Luby |first2=Charles |last2=Rackoff |title=How to Construct Pseudorandom Permutations from Pseudorandom Functions |journal=SIAM Journal on Computing |volume=17 |issue=2 |date=April 1988 |doi=10.1137/0217022 |pages=373–386 |issn=0097-5397}}.</ref> 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.<ref name=7-rounds>{{Citation |first=Jacques |editor1-last=Boneh |last=Patarin |title=Advances in Cryptology - CRYPTO 2003 |editor1-first=Dan |url=https://www.iacr.org/archive/crypto2003/27290510/27290510.pdf |doi=10.1007/b11817 |series=Lecture Notes in Computer Science |volume=2729 |date=October 2003 |pages=513–529 |access-date=27 July 2009|isbn=978-3-540-40674-7 |s2cid=20273458 }}</ref><ref>{{cite book |last1=Zheng |first1=Yuliang |last2=Matsumoto |first2=Tsutomu |last3=Imai |first3=Hideki |title=Advances in Cryptology — CRYPTO' 89 Proceedings |chapter=On the Construction of Block Ciphers Provably Secure and Not Relying on Any Unproved Hypotheses |volume=435 |date=20 August 1989 |pages=461–480 |doi=10.1007/0-387-34805-0_42 |language=en |series=Lecture Notes in Computer Science |isbn=978-0-387-97317-3}}</ref>