Threshold and proactive pseudo-random permutations

Authors:
Yevgeniy Dodis;Aleksandr Yampolskiy;Moti Yung
Affiliations:
Department of Computer Science, New York University, New York, NY;Department of Computer Science, Yale University, New Haven, CT;Department of Computer Science, RSA Laboratories and Columbia University, New York, NY
Venue:
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Year:
2006

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Abstract

We construct a reasonably efficient threshold and proactive pseudo-random permutation (PRP). Our protocol needs only O(1) communication rounds. It tolerates up to (n – 1)/2 of n dishonest servers in the semi-honest environment. Many protocols that use PRPs (e.g., a CBC block cipher mode) can now be translated into the distributed setting. Our main technique for constructing invertible threshold PRPs is a distributed Luby-Rackoff construction where both the secret keys and the input are shared among the servers. We also present protocols for obliviously computing pseudo-random functions by Naor-Reingold [41] and Dodis-Yampolskiy [25] with shared input and keys.