http://dspace.nbuv.gov.ua:80/handle/123456789/150389 2026-04-05T20:46:43Z http://dspace.nbuv.gov.ua:80/handle/123456789/158006 On algebraic graph theory and non-bijectivemultivariate maps in cryptography Ustimenko, V. Special family of non-bijective multivariate maps Fn of Zmⁿ into itself is constructed for n = 2,3, ... and composite m.The map F is injective on Ωn = {x|x1+x2+: : : xn ∈ Zm*} and solution of the equation Fn(x) = b, x ∈ Ωn can be reduced to the solution of equation zr = α, z ∈ Zm*, (r, φ(m)) = 1. The “hidden RSA cryptosystem” is proposed. Similar construction is suggested for the case Ωn = Zm*ⁿ. 2015-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/158005 On the units of integral group ring of Cn × C₆ Küsmüş, Ö. There are many kind of open problems withvarying difficulty on units in a given integral group ring. In thisnote, we characterize the unit group of the integral group ring of Cn × C₆ where Cn = 〈a: aⁿ = 1〉 and C₆ = 〈x: x⁶ = 1〉. We show that U₁(Z[Cn × C₆]) can be expressed in terms of its 4 subgroups. Furthermore, forms of units in these subgroups are described by the unit group U₁(ZCn). 2015-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/158004 Lattice groups Kurdachenko, L.A.; Yashchuk, V.S.; Subbotin, I.Ya. In this paper, we introduce some algebraic struc-ture associated with groups and lattices. This structure is a semi-group and it appeared as the result of our new approach to thefuzzy groups andL-fuzzy groups whereLis a lattice. This approachallows us to employ more convenient language of algebraic structuresinstead of currently accepted language of functions. 2015-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/158003 Serial group rings of finite groups. General linear and close groups Kukharev, A.; Puninski, G. For a givenp, we determine when thepmodulargroup ring of a group from GL(n,q), SL(n,q) and PSL(n,q)-seriesis serial. 2015-01-01T00:00:00Z