Pub. online:1 Jan 2005Type:Research ArticleOpen Access
Volume 16, Issue 3 (2005), pp. 383–394
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.
Pub. online:1 Jan 2004Type:Research ArticleOpen Access
Volume 15, Issue 2 (2004), pp. 251–270
A new digital signature scheme in non‐commutative Gaussian monoid is presented. Two algebraic structures are employed: Gaussian monoid and a certain module being compatible with a monoid. For both monoid and module, presentation and action level attributes are defined. Monoid action level is defined as monoid element (word) action on module element as an operator. A module is a set of functions (elements) with special properties and could be treated as some generalization of vector space.
Signature scheme is based on the one‐way functions (OWF) design using: three recognized hard problems in monoid presentation level, one postulated hard problem in monoid action level and one provable hard problem in module action level.
For signature creation and verification the word equivalence problem is solved in monoid action level thus avoiding solving it in monoid presentation level. Then the three recognized hard problems in monoid presentation level can be essentially as hard as possible to increase signature security. Thus they do not influence on the word problem complexity and, consequently, on the complexity of signature realization.
The investigation of signature scheme security against four kind of attacks is presented. It is shown that the signature has a provable security property with respect to the list of attacks presented here, which are postulated to be complete.