Cryptanalysis of Feistel Networks with Secret Round Functions

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) encryptions where n is the branch size. This attack can be used against 6and 7-round Feistel Networks in time respectively O(2 +2n) and O(2 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 3n/4 ). Our results are, to the best of our knowledge, the first recovery attacks against generic 5-, 6and 7-round Feistel Networks.