Resettable Zero-Knowledge in the Weak Public-Key Model

Abstract

A new public-key model for resettable zero-knowledge (rZK) protocols, which is an extension and generalization of the upper-bounded public-key (UPK) model introduced by Micali and Reyzin [EuroCrypt’01, pp. 373–393], is introduced and is named weak public-key (WPK) model. The motivations and applications of the WPK model are justified in the distributed smart-card/server setting and it seems more preferable in practice, especially in E-commerce over Internet. In this WPK model a 3-round (optimal) black-box resettable zero-knowledge argument with concurrent soundness for \( \mathcal{N}\mathcal{P} \) is presented assuming the security of RSA with large exponents against subexponential-time adversaries. Our result improves Micali and Reyzin’s result of resettable zero-knowledge argument with concurrent soundness for \( \mathcal{N}\mathcal{P} \) in the UPK model. Note that although Micali and Reyzin’ protocol satisfies concurrent soundness in the UPK model, but it does not satisfy even sequential soundness in our WPK model.Our protocol works in a somewhat “parallel repetition” manner to reduce the error probability and the black-box zero-knowledge simulator works in strict polynomial time rather than expected polynomial time. The critical tools used are: verifiable random functions introduced by Micali, Rabin and Vadhan [FOCS’99, pp. 120–130], zap presented by Dwork and Naor [FOCS’00, pp. 283–293] and complexity leveraging introduced by Canetti, Goldreich, Goldwasser and Micali [STOC’00, pp. 235–244].KeywordsSmart CardSecurity ParameterCommitment SchemeCommon InputPseudorandom FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.