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On the Construction of Pseudorandom Permutations: Luby—Rackoff Revisited
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On the Construction of Pseudorandom Permutations: Luby—Rackoff Revisited
Moni Naor1 and Omer Reingold1
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Department of Applied Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel naor@wisdom.weizmann.ac.il,
reingold@wisdom.weizmann.ac.il, IL |
Abstract. Luby and Rackoff [26] showed a method for constructing a pseudorandom permutation from a pseudorandom 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 pseudorandom function. We reduce somewhat the complexity of the construction and simplify its proof of security by showing
that two Feistel permutations are sufficient together with initial and final pairwise 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 pseudorandom permutations with large input-length using pseudorandom functions with small input-length.
Key words. Pseudorandomness, Block ciphers, Modes of operation.
Received 2 August 1996 and revised 26 July 1997
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