International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: On the Insecurity of Parallel Repetition for Leakage Resilience

Allison B. Lewko
Brent Waters
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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.
  title={On the Insecurity of Parallel Repetition for Leakage Resilience},
  booktitle={IACR Eprint archive},
  note={this is a full version of  a paper appearing in FOCS 2010 14808 received 18 Jul 2010},
  author={Allison B. Lewko and Brent Waters},