On Diophantine Complexity and Statistical Zero-Knowledge Arguments

DMCA

On Diophantine Complexity and Statistical Zero-Knowledge Arguments (2003)

Cached

Download Links

Other Repositories/Bibliography

DBLP

by Helger Lipmaa

Venue:	Advances on Cryptology — ASIACRYPT 2003
Citations:	41 - 9 self

BibTeX

@INPROCEEDINGS{Lipmaa03ondiophantine,
    author = {Helger Lipmaa},
    title = {On Diophantine Complexity and Statistical Zero-Knowledge Arguments},
    booktitle = {Advances on Cryptology — ASIACRYPT 2003},
    year = {2003},
    pages = {398--415},
    publisher = {Springer-Verlag}
}

OpenURL

Abstract

Abstract. We show how to construct practical honest-verifier statistical zero-knowledge Diophantine arguments of knowledge (HVSZK AoK) that a committed tuple of integers belongs to an arbitrary language in bounded arithmetic. While doing this, we propose a new algorithm for computing the Lagrange representation of nonnegative integers and a new efficient representing polynomial for the exponential relation. We apply our results by constructing the most efficient known HVSZK AoK for non-negativity and the first constant-round practical HVSZK AoK for exponential relation. Finally, we propose the outsourcing model for cryptographic protocols and design communication-efficient versions of the Damg˚ard-Jurik multi-candidate voting scheme and of the Lipmaa-Asokan-Niemi (b + 1)st-price auction scheme that work in this model.

Keyphrases

diophantine complexity statistical zero-knowledge argument exponential relation hvszk aok design communication-efficient version lagrange representation new algorithm new efficient outsourcing model integer belongs damg ard-jurik multi-candidate voting scheme arbitrary language committed tuple nonnegative integer st-price auction scheme cryptographic protocol first constant-round practical hvszk aok

DMCA