Parallel repetition theorems for interactive arguments

• Authors: Kai-Min Chung;Feng-Hao Liu
• Venue: TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
• Year: 2010

We study efficient parallel repetition theorems for several classes of interactive arguments and obtain the following results: We show a tight parallel repetition theorem for public-coin interactive arguments by giving a tight analysis for a reduction algorithm of Håstad et al. [HPPW08]. That is, n-fold parallel repetition decreases the soundness error from δ to δn. The crux of our improvement is a new analysis that avoid using Raz’s Sampling Lemma, which is the key ingredient to the previous results. We give a new security analysis to strengthen a parallel repetition theorem of Håstad et al. for a more general class of arguments. We show that n-fold parallel repetition decreases the soundness error from δ to δn/2, which is almost tight. In particular, we remove the dependency on the number of rounds in the bound, and as a consequence, extend the “concurrent” repetition theorem of Wikström [Wik09] to this model. We obtain a way to turn any interactive argument to one in the class above using fully homomorphic encryption schemes. This gives a way to amplify the soundness of any interactive argument without increasing the round complexity. We give a simple and generic transformation which shows that tight direct product theorems imply almost-tight Chernoff-type theorems. This extends our results to Chernoff-type theorems, and gives an alternative proof to the Chernoff-type theorem of Impagliazzo et al. [IJK09] for weakly-verifiable puzzles.