TY - GEN

T1 - A parallel repetition theorem for any interactive argument

AU - Haitner, Iftach

PY - 2009

Y1 - 2009

N2 - 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 - Håstad, Pass, Pietrzak and Wikström [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), where m is the round complexity of the (original) protocol. If the coin is one, the verifier halts the interaction and accepts, otherwise it sends the same message that the original verifier would. At the end of the protocol (if reached), the verifier accepts if and only if the original verifier would.

AB - 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 - Håstad, Pass, Pietrzak and Wikström [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), where m is the round complexity of the (original) protocol. If the coin is one, the verifier halts the interaction and accepts, otherwise it sends the same message that the original verifier would. At the end of the protocol (if reached), the verifier accepts if and only if the original verifier would.

KW - Computationally sound proofs

KW - Hardness amplification

KW - Interactive arguments

KW - Parallel repetition

UR - http://www.scopus.com/inward/record.url?scp=77952397401&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2009.50

DO - 10.1109/FOCS.2009.50

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:77952397401

SN - 9780769538501

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 241

EP - 250

BT - Proceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009

T2 - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009

Y2 - 25 October 2009 through 27 October 2009

ER -