Chernoff-Type Direct Product Theorems

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Chernoff-Type Direct Product Theorems
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 instan...
Russell Impagliazzo, Ragesh Jaiswal, Valentine Kab
Added 07 Jun 2010
Updated 07 Jun 2010
Type Conference
Year 2007
Authors Russell Impagliazzo, Ragesh Jaiswal, Valentine Kabanets
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