A characterization of non-interactive instance-dependent commitment-schemes (NIC)

  • Authors:
  • Bruce Kapron;Lior Malka;Venkatesh Srinivasan

  • Affiliations:
  • Department of Computer Science, University of Victoria, BC, Canada;Department of Computer Science, University of Victoria, BC, Canada;Department of Computer Science, University of Victoria, BC, Canada

  • Venue:
  • ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
  • Year:
  • 2007

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Abstract

We provide a new characterization of certain zero-knowledge protocols as non-interactive instance-dependent commitment-schemes (NIC). To obtain this result we consider the notion of V-bit protocols, which are very common, and found many applications in zero-knowledge. Our characterization result states that a protocol has a V-bit zero-knowledge protocol if and only if it has a NIC. The NIC inherits its hiding property from the zero-knowledge property of the protocol, and vice versa. Our characterization result yields a framework that strengthens and simplifies many zero-knowledge protocols in various settings. For example, applying this framework to the result of Micciancio et al. [18] (who showed that some problems, including GRAPH-NONISOMORPHISM and QUADRATIC-RESIDUOUSITY, unconditionally have a concurrent zero-knowledge proof) we easily get that arbitrary, monotone boolean formulae over a large class of problems (which contains, e.g., the complement of any random self-reducible problem) unconditionally have a concurrent zero-knowledge proof.