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 would be an argument system without perfect completeness. A natural approach to boost the gap between legitimate users and attackers would be 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. © International Association for Cryptologic Research 2007.
CITATION STYLE
Impagliazzo, R., Jaiswal, R., & Kabanets, V. (2007). Chernoff-type direct product theorems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4622 LNCS, pp. 500–516). Springer Verlag. https://doi.org/10.1007/978-3-540-74143-5_28
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