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Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More

  • Daniele Micciancio
  • Salil P. Vadhan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2729)

Abstract

We construct several new statistical zero-knowledge proofs with efficient provers, i.e. ones where the prover strategy runs in probabilistic polynomial time given an NP witness for the input string.

Our first proof systems are for approximate versions of the Shorttest Vector Problem (SVP) and Closest Vector Problem (CVP), where the witness is simply a short vector in the lattice or a lattice vector close to the target, respectively. Our proof systems are in fact proofs of knowledge, and as a result, we immediately obtain efficient lattice-based identification schemes which can be implemented with arbitrary families of lattices in which the approximate SVP or CVP are hard.

We then turn to the general question of whether all problems in SZKNP admit statistical zero-knowledge proofs with efficient provers. Towards this end, we give a statistical zero-knowledge proof system with an efficient prover for a natural restriction of Statistical Difference, a complete problem for SZK. We also suggest a plausible approach to resolving the general question in the positive.

Keywords

Proof System Commitment Scheme Vector Problem Short Vector Probabilistic Polynomial Time 
These 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Daniele Micciancio
    • 1
  • Salil P. Vadhan
    • 2
  1. 1.University of CaliforniaSan Diego, La JollaUSA
  2. 2.Harvard UniversityCambridgeUSA

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