Journal:Informatica
Volume 21, Issue 2 (2010), pp. 215–228
Abstract
The asymmetric cipher protocol, based on decomposition problem in matrix semiring ℳ over semiring of natural numbers 𝒩 is presented. The security of presented cipher protocol is based on matrix decomposition problem (MDP), which is linked to the problem of solution of multivariate polynomial system of equations. Compromitation of proposed scheme relies on the solution of system of multivariate polynomial system of equations over the semiring of natural numbers 𝒩. The security parameters are defined, security analysis and implementation is presented.
Journal:Informatica
Volume 16, Issue 3 (2005), pp. 383–394
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.