Parallel Repetition of Computationally Sound Protocols Revisited

Abstract. Parallel repetition is well known to reduce the error probability at an exponential rate for single- and multi-prover interactive proofs. Bellare, Impagliazzo and Naor (1997) show that this is also true for protocols where the soundness only holds against computationally bounded provers (e.g. interactive arguments) if the protocol has at most three rounds. On the other hand, for four rounds they give a protocol where this is no longer the case: the error probability does not decrease below some constant even if the protocol is repeated a polynomial number of times. Unfortunately, this protocol is not very convincing as the communication complexity of each instance of the protocol grows linearly with the number of repetitions, and for such protocols the error does not even decrease for some types of interactive proofs. Noticing this, Bellare et al. construct (a quite artificial) oracle relative to which a four round protocol exists whose communication complexity does not depe...

• Type: Conference
• Year: 2007
• Where: TCC
• Authors: Krzysztof Pietrzak, Douglas Wikström
• Keywords: Communication Complexity, Cryptography, Error Probability, Parallel Repetition, TCC 2007