
It is known that a super-pseudorandom permutation on 2n bits can be obtained from a random function f on n bits and two bisymmetric and AXU hash functions h1 and h2 on n bits. It has a Feistel type structure which is usually denoted by φ(h1, f, f, h2). Bisymmetric and AXU hash functions h1, h2 are much weaker primitives than a random function f and they can be computed much faster than random functions. This paper shows that we can further weaken the condition on h1.
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