Making Classical Honest Verifier Zero Knowledge Protocols Secure against Quantum Attacks

  • Sean Hallgren
  • Alexandra Kolla
  • Pranab Sen
  • Shengyu Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5126)

Abstract

We show that any problem that has a classical zero-knowledge protocol against the honest verifier also has, under a reasonable condition, a classical zero-knowledge protocol which is secure against all classical and quantum polynomial time verifiers, even cheating ones. Here we refer to the generalized notion of zero-knowledge with classical and quantum auxiliary inputs respectively.

Our condition on the original protocol is that, for positive instances of the problem, the simulated message transcript should be quantum computationally indistinguishable from the actual message transcript. This is a natural strengthening of the notion of honest verifier computational zero-knowledge, and includes in particular, the complexity class of honest verifier statistical zero-knowledge. Our result answers an open question of Watrous [Wat06], and generalizes classical results by Goldreich, Sahai and Vadhan [GSV98], and Vadhan [Vad06] who showed that honest verifier statistical, respectively computational, zero knowledge is equal to general statistical, respectively computational, zero knowledge.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sean Hallgren
    • 1
  • Alexandra Kolla
    • 2
  • Pranab Sen
    • 3
  • Shengyu Zhang
    • 4
  1. 1.Pennsylvania State UniversityUniversity ParkU.S.A.
  2. 2.U C BerkeleyBerkeleyU.S.A.
  3. 3.Tata Institute of Fundamental ResearchMumbaiIndia
  4. 4.California Institute of TechnologyPasadenaU.S.A.

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