How to construct pseudorandom permutations from pseudorandom functions
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In this paper, we describe generic attacks on unbalanced Feistel schemes with contracting functions. These schemes are used to construct pseudo-random permutations from kn bits to kn bits by using d pseudo-random functions from (k–1)n bits to n bits. We describe known plaintext attacks (KPA) and non-adaptive chosen plaintext attacks (CPA-1) against these schemes with less than 2kn plaintext/ciphertext pairs and complexity strictly less than O(2kn) for a number of rounds d ≤2k –1. Consequently at least 2k rounds are necessary to avoid generic attacks. For k=3, we found attacks up to 6 rounds, so 7 rounds are required. When d ≥2k, we also describe some attacks on schemes with generators, (i.e. schemes where the d pseudo-random functions are generated) and where more than one permutation is required.