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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 actiondoi:10.15388/informatica.2005.105 fatcat:q2kj4d2srjcu7nd4j3rfy23tpu