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The authors consider the cryptographic problem of constructing an invertible random permutation from a public random function (i.e., which can be accessed by the adversary). This goal is formalized by the notion of indifferentiability of Maurer et al. (TCC 2004). This is the natural extension to the public setting of the well-studied problem of building random permutations from random functions, which was first solved by Luby and Racko (Siam J. Comput., '88) using the so-called Feistel construction.
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