[Resource Topic] 2021/675: 3-round Feistel is Not Superpseudorandom Over Any Group

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3-round Feistel is Not Superpseudorandom Over Any Group

Authors: Hector B. Hougaard


Luby and Rackoff used a Feistel cipher over bit strings to construct a pseudorandom permutation from pseudorandom functions in 1988 and in 2002, Patel, Ramzan, and Sundaram generalized the construction to arbitrary abelian groups. They showed that the 3-round Feistel cipher is not superpseudorandom over abelian groups but left as an open problem a proof for non-abelian groups. We give this proof. Keywords: Feistel, non-abelian group, pseudorandom.

ePrint: https://eprint.iacr.org/2021/675

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