Pub. online:1 Jan 2010Type:Research ArticleOpen Access
Volume 21, Issue 2 (2010), pp. 215–228
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.
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).