LNCS 2729 Statistical Zero Knowledge Proofs with Efficient Provers Lattice Problems and More 1st Edition by Daniele Micciancio, Salil Vadhan  ISBN 3540451463 9783540451464

LNCS 2729 – Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More 1st Edition by Daniele Micciancio, Salil P. Vadhan  – Ebook PDF Instant Download/Delivery. 3540451463, 9783540451464

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Product details:

ISBN 10: 3540451463

ISBN 13: 9783540451464

Author:  Daniele Micciancio, Salil P. Vadhan  

LNCS 2729 – Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More 1st Edition: 

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 SZK∩NP 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.

 

LNCS 2729 – Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More 1st Edition Table of contents:

1 Introduction
1.1 Statistical Zero Knowledge
1.2 Lattice Problems
1.3 Our Results
1.4 Related Work

2 Preliminaries
2.1 Statistical Difference
2.2 Lattice Problems and Technical Tools

3 The Closest Vector Problem

4 The Shortest Vector Problem

5 Identification Schemes

6 Statistical Difference
6.1 Efficient Provers for All of SZK?

 

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