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Statistical zero-knowledge proofs with efficient provers: Lattice problems and more (2003)
| Venue: | In CRYPTO |
| Citations: | 50 - 10 self |
BibTeX
@INPROCEEDINGS{Micciancio03statisticalzero-knowledge,
author = {Daniele Micciancio and Salil Vadhan},
title = {Statistical zero-knowledge proofs with efficient provers: Lattice problems and more},
booktitle = {In CRYPTO},
year = {2003},
pages = {282--298},
publisher = {Springer-Verlag}
}
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Abstract
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 Shortest 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. 1
Keyphrases
efficient provers statistical zero-knowledge proof lattice problem general question efficient lattice-based identification scheme plausible approach shortest vector problem approximate svp natural restriction szk np short vector probabilistic polynomial time closest vector problem lattice vector several new statistical zero-knowledge proof statistical difference statistical zero-knowledge proof system input string first proof system fact proof approximate version arbitrary family np witness efficient prover complete problem prover strategy proof system
