A Parallel Repetition Theorem for Any Interactive Argument

— The question of whether or not parallel repetition reduces the soundness error is a fundamental question in the theory of protocols. While parallel repetition reduces (at an exponential rate) the error in interactive proofs and (at a weak exponential rate) in special cases of interactive arguments (e.g., 3-message protocols — Bellare, Impagliazzo and Naor [FOCS ’97], and public-coin protocols — H˚astad, Pass, Pietrzak and Wikstr¨om [Manuscript ’08]), Bellare et al. gave an example of interactive arguments for which parallel repetition does not reduce the soundness error at all. We show that by slightly modifying any interactive argument, in a way that preserves its completeness and only slightly deteriorates its soundness, we get a protocol for which parallel repetition does reduce the error at a weak exponential rate. In this modified version, the verifier flips at the beginning of each round an (1 − 1 4m , 1 4m ) biased coin (i.e., 1 is tossed with probability 1/4m...

• Type: Conference
• Year: 2009
• Where: FOCS
• Authors: Iftach Haitner
• Keywords: Exponential Rate, FOCS 2009, Interactive Arguments, Parallel Repetition, Theoretical Computer Science