A Framework for Interactive Argument Systems using Quasigroupic Homorphic Commitment

Using a model based on probabilistic functions (PF ), it’s introduced the concept of perfect zero knowledge (PZK ) commitment scheme (CS ) allowing quasigroupic homomorphic commitment (QHC ). Using QHC of +m (modular sum in Zm), application is considered in interactive argument systems (IAS ) for several languages. In four of the examples – generalized nand ( [∧(α)]), string equality ([=(m,α,)]), string inequality ([ =(m,α,)]) and graph threecolourations (G3C) – complexity improvements are obtained, in comparison to other established results. Motivation then arises to define a general framework for PZK -IAS for membership in language with committed alphabet (MLCA), such that the properties of soundness and 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 IAS without the consideration of low level aspects of cryptographic primitives. The constructed framework is able to embrace PZK -CS allowing QHC of functions that are not themselves quasigroupic. Several theoretical considerations are made, namely recognizing a necessary requirements to demand on an eventual PZK -CS allowing QHC of some complete function in a Boolean sense. ∗(E-mail) [email protected], (Address) Estação Correios Miraflores, ap.1021, 1496-701-Algés, Portugal.