On the Construction of Pseudo-Random Permutations: Luby-Racko Revisited

Luby and Racko [27] showed a method for constructing a pseudo-random permutation from a pseudo-random function. The method is based on composing four (or three for weakened security) so called Feistel permutations, each of which requires the evaluation of a pseudo-random function. We reduce somewhat the complexity of the construction and simplify its proof of security by showing that two Feistel permutations are su cient together with initial and nal pair-wise independent permutations. The revised construction and proof provide a framework in which similar constructions may be brought up and their security can be easily proved. We demonstrate this by presenting some additional adjustments of the construction that achieve the following: Reduce the success probability of the adversary. Provide a construction of pseudo-random permutations with large input-length using pseudorandom functions with small input-length. Incumbent of the Morris and Rose Goldman Career Development Chair, Dept. of Applied Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel. Research supported by grant no. 356/94 from the Israel Science Foundation administered by the Israeli Academy of Sciences and by BSF grant no. 94-00032. E-mail: [email protected]. y Dept. of Applied Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel. Part of this research was supported by a Clore Scholars award. E-mail: [email protected].