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Lecture notes in computer science

Simultaneously Resettable Arguments of Knowledge

Chongwon Cho, Rafail Ostrovsky, Alessandra Scafuro, Ivan Visconti

Published Jan 1, 2012• 23 citations
Publisher
DOI
10.1007/978-3-642-28914-9_30

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Resettable-security, introduced by Canetti, Goldreich, Goldwasser and Micali (STOC'00), considers the security of cryptographic two-party protocols (in particular zero-knowledge arguments) in a setting where the attacker may “reset” or “rewind” one of the players. The strongest notion of resettable security, simultaneous resettability, introduced by Barak, Goldreich, Goldwasser and Lindell (FOCS'01), requires resettable security to hold for both parties: in the context of zero-knowledge, both the soundness and the zero-knowledge conditions remain robust to resetting attacks. To date, all known constructions of protocols satisfying simultaneous resettable security rely on the existence of ZAPs; constructions of ZAPs are only known based on the existence of trapdoor permutations or number-theoretic assumptions. In this paper, we provide a new method for constructing protocols satisfying simultaneous resettable security while relying only on the minimal assumption of one-way functions. Our key results establish, assuming only one-way functions: Every language in NP has an ω(1)-round simultaneously resettable witness indistinguishable argument system; Every language in NP has a (polynomial-round) simultaneously resettable zero-knowledge argument system. The key conceptual insight in our technique is relying on black-box impossibility results for concurrent zero-knowledge to achieve resettable-security.

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Concurrent non-malleable zero-knowledge and simultaneous resettable non-malleable zero-knowledge in constant rounds

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Concurrent non-malleable zero-knowledge ( CNMZK ) considers the concurrent execution of zero-knowledge protocols in a setting even when adversaries can simultaneously corrupt multiple provers and verifiers. As far as we know, the round complexity of all the constructions of CNMZK arguments for NP is at least ω (log n ). In this paper, we provide the first construction of a constant-round concurrent non-malleable zero-knowledge argument for every language in NP . Our protocol relies on the existence of families of collision-resistant hash functions , one-way permutations and indistinguishability obfuscators . As an additional contribution, we study the composition of two central notions in zero knowledge, the simultaneously resettable zero-knowledge and non-malleable zero-knowledge , which seemingly have stronger proved security guarantees. We give the first construction of a constant-round simultaneously-resettable non-malleable zero-knowledge . To the best of our knowledge, this is the first study to combine the two security concepts described above together in the zero-knowledge protocols.

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Direct Minimum-Knowledge Computations

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Resettable-security, introduced by Canetti, Goldreich, Goldwasser and Micali (STOC'00), considers the security of cryptographic two-party protocols (in particular zero-knowledge arguments) in a setting where the attacker may “reset” or “rewind” one of the players. The strongest notion of resettable security, simultaneous resettability, introduced by Barak, Goldreich, Goldwasser and Lindell (FOCS'01), requires resettable security to hold for both parties: in the context of zero-knowledge, both the soundness and the zero-knowledge conditions remain robust to resetting attacks. To date, all known constructions of protocols satisfying simultaneous resettable security rely on the existence of ZAPs; constructions of ZAPs are only known based on the existence of trapdoor permutations or number-theoretic assumptions. In this paper, we provide a new method for constructing protocols satisfying simultaneous resettable security while relying only on the minimal assumption of one-way functions. Our key results establish, assuming only one-way functions: Every language in NP has an ω(1)-round simultaneously resettable witness indistinguishable argument system; Every language in NP has a (polynomial-round) simultaneously resettable zero-knowledge argument system. The key conceptual insight in our technique is relying on black-box impossibility results for concurrent zero-knowledge to achieve resettable-security.
Concurrent non-malleable zero-knowledge ( CNMZK ) considers the concurrent execution of zero-knowledge protocols in a setting even when adversaries can simultaneously corrupt multiple provers and verifiers. As far as we know, the round complexity of all the constructions of CNMZK arguments for NP is at least ω (log n ). In this paper, we provide the first construction of a constant-round concurrent non-malleable zero-knowledge argument for every language in NP . Our protocol relies on the existence of families of collision-resistant hash functions , one-way permutations and indistinguishability obfuscators . As an additional contribution, we study the composition of two central notions in zero knowledge, the simultaneously resettable zero-knowledge and non-malleable zero-knowledge , which seemingly have stronger proved security guarantees. We give the first construction of a constant-round simultaneously-resettable non-malleable zero-knowledge . To the best of our knowledge, this is the first study to combine the two security concepts described above together in the zero-knowledge protocols.