In this paper, we investigate the existence and invariant of algebraic attacks, which have been recently shown as an important cryptanalysis method for symmetric-key cryptographical systems. For a given boolean function f in n variables and two positive integers d and e, we observe that the sufficient condition d + e ≥ n, shown in [8] or [9], cannot guarantee the existence of a function g with ...

For a ring R, denote by SpecΓ(κ,R) the κ-spectrum of the Γ-invariant of strongly uniform right R-modules. Recent realization techniques of Goodearl and Wehrung show that SpecΓ(א1 , R) is full for a suitable von Neumann regular algebra R, but the techniques do not extend to cardinals κ > א1. By a direct construction, we prove that for any field F and any regular uncountable cardinal κ there is a...

In this paper, by considering the notion of $Sigma$-hyperalgebras for an arbitrary signature $Sigma$, we study the notions of regular and strongly regular relations on a $Sigma$-hyperalgebra, $mathfrak{A}$. We show that each regular relation which contains a strongly regular relation is a strongly regular relation. Then we concentrate on the connection between the fundamental relation of $mathf...

Nuclear pore complexes (NPCs) form gateways for material transfer across the nuclear envelope of eukaryotic cells. Disordered proteins, rich in phenylalanine-glycine repeat motifs (FG-nups), form the central transport channel. Understanding how nups are arranged in the interior of the NPC may explain how NPC functions as a selectivity filter for transport of large molecules and a sieve-like fil...