Parallel repetition for leakage resilience amplification revisited Conference Paper

Author(s): Jain, Abhishek; Pietrzak, Krzysztof
Title: Parallel repetition for leakage resilience amplification revisited
Title Series: LNCS
Abstract: If a cryptographic primitive remains secure even if ℓ bits about the secret key are leaked to the adversary, one would expect that at least one of n independent instantiations of the scheme remains secure given n·ℓ bits of leakage. This intuition has been proven true for schemes satisfying some special information-theoretic properties by Alwen et al. [Eurocrypt'10]. On the negative side, Lewko and Waters [FOCS'10] construct a CPA secure public-key encryption scheme for which this intuition fails. The counterexample of Lewko and Waters leaves open the interesting possibility that for any scheme there exists a constant c>0, such that n fold repetition remains secure against c·n·ℓ bits of leakage. Furthermore, their counterexample requires the n copies of the encryption scheme to share a common reference parameter, leaving open the possibility that the intuition is true for all schemes without common setup. In this work we give a stronger counterexample ruling out these possibilities. We construct a signature scheme such that: 1. a single instantiation remains secure given ℓ = log(k) bits of leakage where k is a security parameter. 2. any polynomial number of independent instantiations can be broken (in the strongest sense of key-recovery) given ℓ′ = poly(k) bits of leakage. Note that ℓ does not depend on the number of instances. The computational assumption underlying our counterexample is that non-interactive computationally sound proofs exist. Moreover, under a stronger (non-standard) assumption about such proofs, our counterexample does not require a common reference parameter. The underlying idea of our counterexample is rather generic and can be applied to other primitives like encryption schemes. © 2011 International Association for Cryptologic Research.
Keywords: Cryptographic primitives; Parallel repetition; Computational assumptions; Encryption schemes; Key-recovery; Leakage-resilience; Non-interactive; Polynomial number; Public-key encryption scheme; Reference parameters; Secret key; Security parameters; Signature Scheme
Conference Title: TCC: Theory of Cryptography Conference
Volume: 6597
Publisher: Springer  
Date Published: 2011-01-01
Start Page: 58
End Page: 69
DOI: 10.1007/978-3-642-19571-6_5
Open access: no
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