Interactive zero-knowledge with restricted random oracles

  • Authors:
  • Moti Yung;Yunlei Zhao

  • Affiliations:
  • RSA Laboratories and Department of Computer Science, Columbia University, New York, NY;Software School, School of Information Science and Engineering, Fudan University, Shanghai, China

  • Venue:
  • TCC'06 Proceedings of the Third conference on Theory of Cryptography
  • Year:
  • 2006

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Abstract

We investigate the design and proofs of zero-knowledge (ZK) interactive systems under what we call the “restricted random oracle model” which restrains the usage of the oracle in the protocol design to that of collapsing protocol rounds a la Fiat-Shamir heuristics, and limits the oracle programmability in the security proofs. We analyze subtleties resulting from the involvement of random oracles in the interactive setting and derive our methodology. Then we investigate the Feige-Shamir 4-round ZK argument for $\mathcal{NP}$ in this model: First we show that a 2-round protocol is possible for a very interesting set of languages; we then show that while the original protocol is not concurrently secure in the public-key model, a modified protocol in our model is, in fact, concurrently secure in the bare public-key model. We point at applications and implications of this fact. Of possible independent interest is a concurrent attack against the Feige-Shamir ZK in the public-key model (for which it was not originally designed).