Cryptology ePrint Archive: Report 2010/404

On the Insecurity of Parallel Repetition for Leakage Resilience

Allison Lewko and Brent Waters

Abstract: A fundamental question in leakage-resilient cryptography is: can leakage resilience always be amplified by parallel repetition? It is natural to expect that if we have a leakage-resilient primitive tolerating $\ell$ bits of leakage, we can take $n$ copies of it to form a system tolerating $n\ell$ bits of leakage. In this paper, we show that this is not always true. We construct a public key encryption system which is secure when at most $\ell$ bits are leaked, but if we take $n$ copies of the system and encrypt a share of the message under each using an $n$-out-of-$n$ secret-sharing scheme, leaking $n\ell$ bits renders the system insecure. Our results hold either in composite order bilinear groups under a variant of the subgroup decision assumption \emph{or} in prime order bilinear groups under the decisional linear assumption. We note that the $n$ copies of our public key systems share a common reference parameter.

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Publication Info: this is a full version of a paper appearing in FOCS 2010

Date: received 18 Jul 2010

Contact author: alewko at cs utexas edu

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Version: 20100719:223744 (All versions of this report)

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