[Resource Topic] 2006/472: A Framework for Interactive Argument Systems using Quasigroupic Homorphic Commitment

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A Framework for Interactive Argument Systems using Quasigroupic Homorphic Commitment

Authors: Luis Teixeira d'Aguiar Norton Brandao


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.

ePrint: https://eprint.iacr.org/2006/472

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