Known-Key Distinguishers on 11-Round Feistel and Collision Attacks on Its Hashing Modes

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Abstract

We present new attacks on the Feistel network, where each round function consists of a subkey XOR, S-boxes, and then a linear transformation (i.e., an SP round function). Our techniques are based largely on what they call the rebound attacks. As a result, our attacks work most effectively when the S-boxes have a “good” differential property (like the inverse function xx − 1 in the finite field) and when the linear transformation has an “optimal” branch number (i.e., a maximum distance separable matrix). We first describe known-key distinguishers on such Feistel block ciphers of up to 11 rounds, increasing significantly the number of rounds from previous work. We then apply our distinguishers to the Matyas-Meyer-Oseas and Miyaguchi-Preneel modes in which the Feistel ciphers are used, obtaining collision and half-collision attacks on these hash functions.