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Statistical Zero-Knowledge Proofs from Diophantine Equations
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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 $S$. |
BibTeX
@misc{eprint-2001-11498,
title={Statistical Zero-Knowledge Proofs from Diophantine Equations},
booktitle={IACR Eprint archive},
keywords={foundations/Diophantine equations, integer commitment scheme, statistical zero-knowledge},
url={http://eprint.iacr.org/2001/086},
note={Submitted? Preliminary version, Nov 5 2001 helger@tcs.hut.fi 11646 received 25 Oct 2001, last revised 20 Nov 2001},
author={Helger Lipmaa},
year=2001
}