Pub. online:1 Jan 2007Type:Research ArticleOpen Access
Volume 18, Issue 1 (2007), pp. 115–124
The key agreement protocol based on infinite non-commutative group presentation and representation levels is proposed.
Two simultaneous problems in group representation level are used: the conjugator search problem (CSP) and modified discrete logarithm problem (DLP). The modified DLP in our approach is a matrix DLP and is different from that's used in other publications. The algorithm construction does not allow to perform a crypto-analysis by replacing the existing CSP solution to the decomposition problem (DP) solution.
The group presentation level serves for two commuting subgroups and invertible group's word image matrix construction. The group representation level allows reliable factors disguising in the initial word. The word equivalence problem (WEP) solution is transformed from the group presentation level to the group representation level. Hence there are not necessary to solve WEP in the group presentation level and hence there are no restrictions on the group complexity in this sense. The construction of irreducible representation of group is required. The presented protocol is a modernization of protocol declared in (Sakalauskas et al., 2005).
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.