Cryptanalysis of Feistel Networks with Secret Round Functions

Abstract : Generic distinguishers against Feistel Network with up to 5 rounds exist in the regular setting and up to 6 rounds in a multi-key setting. We present new cryptanalyses against Feistel Networks with 5, 6 and 7 rounds which are not simply distinguishers but actually recover completely the unknown Feistel functions. When an exclusive-or is used to combine the output of the round function with the other branch, we use the so-called yoyo game which we improved using a heuristic based on particular cycle structures. The complexity of a complete recovery is equivalent to O(2 2n) encryptions where n is the branch size. This attack can be used against 6-and 7-round Feistel Networks in time respectively O(2 n2 n−1 +2n) and O(2 n2 n +2n). However when modular addition is used, this attack does not work. In this case, we use an optimized guess-and-determine strategy to attack 5 rounds with complexity O(2 n2 3n/4). Our results are, to the best of our knowledge, the first recovery attacks against generic 5-, 6-and 7-round Feistel Networks.
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Alex Biryukov, Gaëtan Leurent, Léo Perrin. Cryptanalysis of Feistel Networks with Secret Round Functions. Selected Areas in Cryptography - SAC 2015, Aug 2015, Sackville, Canada. ⟨hal-01243130⟩

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