Chernoff-type Direct Product Theorems

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Chernoff-type Direct Product Theorems (2007)

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by Russell Impagliazzo , Ragesh Jaiswal , Valentine Kabanets

Venue:	In Proceeding of the Twenty-Seventh Annual International Cryptology Conference (CRYPTO’07
Citations:	15 - 5 self

BibTeX

@INPROCEEDINGS{Impagliazzo07chernoff-typedirect,
    author = {Russell Impagliazzo and Ragesh Jaiswal and Valentine Kabanets},
    title = {Chernoff-type Direct Product Theorems},
    booktitle = {In Proceeding of the Twenty-Seventh Annual International Cryptology Conference (CRYPTO’07},
    year = {2007},
    pages = {500--516}
}

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Abstract

Abstract. Consider a challenge-response protocol where the probability of a correct response is at least α for a legitimate user, and at most β < α for an attacker. One example is a CAPTCHA challenge, where a human should have a significantly higher chance of answering a single challenge (e.g., uncovering a distorted letter) than an attacker; another example is an argument system without perfect completeness. A natural approach to boost the gap between legitimate users and attackers is to issue many challenges, and accept if the response is correct for more than a threshold fraction, for the threshold chosen between α and β. We give the first proof that parallel repetition with thresholds improves the security of such protocols. We do this with a very general result about an attacker’s ability to solve a large fraction of many independent instances of a hard problem, showing a Chernoff-like convergence of the fraction solved incorrectly to the probability of failure for a single instance.

Keyphrases

chernoff-type direct product theorem legitimate user first proof parallel repetition correct response many challenge attacker ability captcha challenge threshold chosen hard problem challenge-response protocol large fraction many independent instance distorted letter natural approach single challenge perfect completeness threshold fraction argument system chernoff-like convergence general result single instance

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