This paper proposes the t-class of SOBER stream ciphers: t8, t16 and t32. t8, t16 and t32 offer 64-, 128and 256-bit key strength respectively. The t-class ciphers are based on the same principles as the original SOBER family: SOBER [17], SOBER-II [18], S16 and S32 [19], utilising the structure SOBER-II and S16 are based. The t-class ciphers are software stream ciphers designed for software impl...

We obtain the further characterizations and properties of weakly open functions in bitopological spaces due to Jelić [5]. AMS Mathematics Subject Classification (2000): 54C10, 54E55

We study the topological spectrum of a seminormed ring $R$ which we define as space prime ideals $\mathfrak{p}$ such that equals kernel some bounded power-multiplicative seminorm. For any show is quasi-compact sober space. When perfectoid Tate construct natural homeomorphism between and its tilt $R^{\flat}$. As an application, prove integral domain if only domain.

Two ways of mounting distinguishing attacks on two similar stream ciphers, SOBER-t16 and SOBER-t32, are proposed. It results in distinguishing attacks faster than exhaustive key search on full SOBERt16 and on SOBER-t32 without stuttering.

In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.

Abstract We give two concrete examples of continuous valuations on dcpo’s to separate minimal valuations, point-continuous and valuations: (1) Let ${\mathcal J}$ be the Johnstone’s non-sober dcpo, μ valuation with ( U )=1 for nonempty Scott opens )=0 $U=\emptyset$ . Then, is a that not minimal. (2) Lebesgue measure extends Sorgenfrey line $\mathbb{R}_\ell$ Its restriction open subsets λ. its im...

Given a poset P , the set Γ(P ) of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Posd (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P ) ∼= Γ(Q) implies P ∼= Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Posd is not....