One Digital Signature Scheme in Semimodule over Semiring

Article type: Research Article

Authors: Sakalauskas, Eligijus

Affiliations: Kaunas University of Technology, Department of Applied Mathematics, Studentų 50, 51368 Kaunas, Lithuania, e-mail: esakal@asi.lt

Abstract: A modernization of signature scheme published in (Sakalauskas, 2004) is presented. This scheme differs from the prototype by its structure and uses a more general algebraic systems. It has a higher security and shorter key length and is also more computationally effective. The introduced new algebraic structures, semiring and semimodule, are mutually compatible algebraic systems. The semiring is a set of operators acting in a semimodule as endomorphisms. There is postulated that action operation has a one-way function (OWF) property. The compatibility of both algebraic structures' means that the action operation has right and left distributivity property with respect to the additive operation defined in semimodule and semiring. Two other essential OWFs are defined. The latter are based on known constructions and have a greater complexity than other recognized hard problems such as conjugator search problem in noncommutative groups, for example.

Keywords: digital signature scheme, one-way function, Gaussian group, semiring action problem

Journal: Informatica, vol. 16, no. 3, pp. 383-394, 2005