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Statistical Zero-Knowledge Proofs from Diophantine Equations (2001)
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BibTeX
@TECHREPORT{Lipmaa01statisticalzero-knowledge,
author = {Helger Lipmaa},
title = {Statistical Zero-Knowledge Proofs from Diophantine Equations},
institution = {},
year = {2001}
}
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Abstract
A family $(S_t)$ of sets is $p$-bounded Diophantine if $S_t$ has a representing $p$-bounded polynomial $R_{S,t}$, s.t.~$x\in S_t \iff (\exists y)[R_{S}(x;y)=0]$. We say that $(S_t)$ is unbounded Diophantine if additionally, $R_{S,t}$ is a fixed $t$-independent polynomial. We show that $p$-bounded (resp., unbounded) Diophantine set has a polynomial-size (resp., constant-size) statistical zero-knowledge proof system that a committed tuple $x$ belongs to $S$. We describe efficient SZK proof systems for several cryptographically interesting sets. Finally, we show how to prove in SZK that an encrypted number belongs to $S$.
