We consider the 4D Martínez Alonso–Shabat equation E uty=uzuxy−uyuxz (also referred to as universal hierarchy equation) and using its known Lax pair construct two infinite-dimensional differential coverings over E. In these coverings, we give a complete description of Lie algebras nonlocal symmetries. particular, our results generalize ones obtained in Morozov Sergyeyev (2014) contain construct...

We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of Stein manifolds.

In this paper, we present a classification of elliptic curves defined over a cubic extension of a finite field with odd characteristic which have coverings over the finite field therefore subjected to the GHS attack. The densities of these weak curves, with hyperelliptic and non-hyperelliptic coverings, are then analyzed respectively. In particular, we show, for elliptic curves defined by Legen...

A group is said to have a finite covering by subgroups if it is the set theoretic union of finitely many subgroups. A theorem of B. H. Neumann [11] characterizes groups with finite coverings by proper subgroups as precisely those groups with finite non-cyclic homomorphic images. R. Baer (see [13, Theorem 4.16]) proved that a group has a finite covering by abelian subgroups if and only if it is ...

The shares in a (k; n) Shamir threshold scheme consist of n points on some polynomial of degree at most k ?1. If one or more of the shares are faulty, then the secret may not be reconstructed correctly. Supposing that at most t of the n shares are faulty, we show how a suitably chosen covering design can be used to compute the correct secret. We review known results on coverings of the desired ...