Cryptology ePrint Archive: Report 2015/031

Tight Parallel Repetition Theorems for Public-Coin Arguments using KL-divergence

Kai-Min Chung and Rafael Pass

Abstract: We present a new and conceptually simpler proof of a tight parallel-repetition theorem for public-coin arguments (Pass-Venkitasubramaniam, STOC'07, Hastad et al, TCC'10, Chung-Liu, TCC'10). We follow the same proof framework as the previous non-tight parallel-repetition theorem of Hastad et al---which relied on *statistical distance* to measure the distance between experiments---and show that it can be made tight (and further simplied) if instead relying on *KL-divergence* as the distance between the experiments.

We then show that our proof technique directly yields tight ``Chernoff-type'' parallel-repetition theorems (where one considers a ``threshold'' verifier that accepts iff the prover manages to convince a certain fraction of the parallel verifiers, as opposed to all of them) for any public-coin interactive argument; previously, tight results were only known for either constant-round protocols, or when the gap between the threshold and the original error-probability is a constant.

Category / Keywords: foundations / parallel repetition, public coin, interactive arguments, computationally sound proofs, KL divergence

Original Publication (in the same form): IACR-TCC-2015

Date: received 13 Jan 2015

Contact author: kmchung at iis sinica edu tw

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Version: 20150114:165217 (All versions of this report)

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