Threshold and Proactive Pseudo-Random Permutations
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.