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arXiv:cs/0607035

Resettable Zero Knowledge in the Bare Public-Key Model under Standard Assumption

Yi Deng, Dongdai Lin

Published Jul 10, 2006• 2 citations
arXivHTMLPDF

Abstract

In this paper we resolve an open problem regarding resettable zero knowledge in the bare public-key (BPK for short) model: Does there exist constant round resettable zero knowledge argument with concurrent soundness for $\mathcal{NP}$ in BPK model without assuming \emph{sub-exponential hardness}? We give a positive answer to this question by presenting such a protocol for any language in $\mathcal{NP}$ in the bare public-key model assuming only collision-resistant hash functions against \emph{polynomial-time} adversaries.

DOI
10.48550/arxiv.cs/0607035

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In this paper we resolve an open problem regarding resettable zero knowledge in the bare public-key (BPK for short) model: Does there exist constant round resettable zero knowledge argument with concurrent soundness for NP\mathcal{NP}NP in BPK model without assuming \emph{sub-exponential hardness}? We give a positive answer to this question by presenting such a protocol for any language in NP\mathcal{NP}NP in the bare public-key model assuming only collision-resistant hash functions against \emph{polynomial-time} adversaries.
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We present constant-round concurrently secure (sound) resettable zero-knowledge (rZK-CS) arguments in the bare public-key (BPK) model. Our constructions deal with generalNP ZK-arguments as well as with highly ecien t ZK-arguments for number-theoretic languages, most relevant to identication scenarios. These are the rst constant-round protocols of this type in the original real BPK model, where nothing is assured about public-keys generated by malicious veriers. As part of this work, we develop a one-round trapdoor commitment scheme that is based on any one-way permutation, which is of independent interest and, in particular, can be used to reduce the round-complexity of other cryptographic protocols involving trapdoor commitments.
A fundamental question in cryptography deals with understanding the role that randomness plays in cryptographic protocols and to what extent it is necessary. One particular line of works was initiated by Canetti, Goldreich, Goldwasser, and Micali (STOC 2000) who introduced the notion of resettable zero-knowledge, where the protocol must be zeroknowledge even if a cheating verifier can reset the prover and have several interactions in which the prover uses the same random tape. Soon afterwards, Barak, Goldreich, Goldwasser, and Lindell (FOCS 2001) studied the setting where the verifier uses a fixed random tape in multiple interactions. Subsequent to these works, a number of papers studied the notion of resettable protocols in the setting where only one of the participating parties uses a fixed random tape multiple times. The notion of resettable security has been studied in two main models: the plain model and the bare public key model (also introduced in the above paper by Canetti et. al.). In a recent work, Deng, Goyal and Sahai (FOCS 2009) gave the first construction of a simultaneous resettable zero-knowledge protocol where both participants of the protocol can reuse a fixed random tape in any (polynomial) number of executions. Their construction however required O(nɛ) rounds of interaction between the prover and the verifier. Both in the plain as well as the BPK model, this construction remain the only known simultaneous resettable zero-knowledge protocols. In this work, we study the question of round complexity of simultaneous resettable zeroknowledge in the BPK model. We present a constant round protocol in such a setting based on standard cryptographic assumptions. Our techniques are significantly different from the ones used by Deng, Goyal and Sahai. 1
Abstract. In resetting attacks against a proof system, a prover or a verifier is reset and enforced to use the same random tape on various inputs as many times as an adversary may want. Recent deployment of cloud computing gives these attacks a new importance. This paper shows that argument systems for any NP language that are both resettably-sound and resettable zero-knowledge are possible by a constant-round protocol in the BPK model. For that sake, we define and construct a resettablyextractable conditional commitment scheme.