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Paper 2012/239

Zero-Knowledge for Multivariate Polynomials

Valerie Nachef and Jacques Patarin and Emmanuel Volte

Abstract

In~\cite{SSH} a Zero-Knowledge scheme $ZK(2)$ was designed from a solution of a set of multivariate quadratic equations over a finite field. In this paper we will give two methods to generalize this construction for polynomials of any degree $d$, i.e. we will design two Zero-Knowledge schemes $ZK(d)$ and $\tilde {ZK}(d)$ from a set of polynomial equations of degree $d$. We will show that $\tilde {ZK} (d)$ is optimal in term of the number of computations to be performed and that $ZK(d)$ is optimal in term of the number of bits to be send. Moreover this property is still true for all kinds of polynomials: for example if the polynomials are sparse or dense. Finally, we will present two examples of applications: with Brent equations, or with morphisms of polynomials.

Metadata
Available format(s)
PDF
Category
Cryptographic protocols
Publication info
Published elsewhere. Unknown where it was published
Keywords
Authentication schemeZero-KnowledgeMultivariate polynomials.
Contact author(s)
valerie nachef @ u-cergy fr
History
2012-04-30: received
Short URL
https://ia.cr/2012/239
License
Creative Commons Attribution
CC BY
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