CryptoDB
A Framework for Interactive Argument Systems using Quasigroupic Homorphic Commitment
| Authors: | |
|---|---|
| Download: | |
| Abstract: | Using a model based on \textit{probabilistic functions} (\textit{PF}), it's introduced the concept of \textit{perfect zero knowledge} (\textit{PZK}) \textit{commitment scheme} (\textit{CS}) allowing \textit{quasigroupic} \textit{homomorphic commitment} (\textit{QHC}). Using \textit{QHC} of $+_m$ (modular sum in $\mathbb{Z}_m$), application is considered in interactive argument systems (\textit{IAS}) for several languages. In four of the examples -- generalized nand ($\Lnandalpha$), string equality ($\left[=_{\left(m,\alpha,\right)}\right]$), string inequality ($\left[\neq_{\left(m,\alpha,\right)}\right]$) and graph three-colourations ($G3C$) -- complexity improvements are obtained, in comparison to other established results. Motivation then arises to define a general framework for \textit{PZK}-\textit{IAS} for membership in language with committed alphabet (\textit{MLCA}), such that the properties of soundness and \textit{PZK} result from high-level parametrizable aspects. A general simulator is constructed for sequential and (most interestingly) for parallel versions of execution. It therefore becomes easier to conceptualize functionalities of this kind of \textit{IAS} without the consideration of low level aspects of cryptographic primitives. The constructed framework is able to embrace \AcroCS\; allowing \textit{QHC} of functions that are not themselves quasigroupic. Several theoretical considerations are made, namely recognizing a necessary requirements to demand on an eventual \AcroCS \;allowing \textit{QHC} of some complete function in a Boolean sense. |
BibTeX
@misc{eprint-2006-21963,
title={A Framework for Interactive Argument Systems using Quasigroupic Homorphic Commitment},
booktitle={IACR Eprint archive},
keywords={cryptographic protocols / zero knowledge, commitment scheme},
url={http://eprint.iacr.org/2006/472},
note={Submitted to a Conference criptog@criptog.com 13488 received 5 Dec 2006},
author={Luis Teixeira d'Aguiar Norton Brandao},
year=2006
}