Déchène has proposed generalized Jacobians as a source of groups for public-key cryptosystems based on the hardness of the Discrete Logarithm Problem (DLP). Her specific proposal gives rise to a group isomorphic to the semidirect product of an elliptic curve and a multiplicative group of a finite field. We explain why her proposal has no advantages over simply taking the direct product of group...

The minimal faithful permutation degree μ(G) of a finite group G is the least nonnegative integer n such that G embeds in the symmetric group Sym(n). We make observations in varying degrees of generality about μ(G) when G decomposes as a semidirect product, and provide exact formulae in the case that the base group is an elementary abelian p-group and the extending group a cyclic group of prime...

Following standard methods we explore the construction of the discrete Poincaré group, the semidirect product of discrete translations and integral Lorentz transformations, using the Wigner-Mackey construction restricted to the momentum and position space on the lattice. The orbit condition, irreducibility and assimptotic limit are discussed.

Every semidirect product of groups K oH has size |K| · |H|, yet the size of such a group’s automorphism group varies with the chosen action of H on K. This paper will explore groups of the form Aut(K oH), considering especially the case where H and K are cyclic. Only finite groups will be considered.

In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider variational wavelet approach for loops, invariant bases on semidirect product, KAM calculation via FWT.

for nonnegative integers nβα. Each root β corresponds to a unipotent subgroup Uβ of G, whose Lie algebra is gβ. There is an isomorphism of the additive Lie groupGa ∼= C with Uβ; this is T -equivariant, with multiplication by β(t) on C corresponding to conjugation by t on Uβ (u 7→ tut −1). The product of the groups Uβ for β ∈ R+ forms a unipotent group U , isomorphic to C , with N = #R+, and B =...

We study the bigraded vector space structure of Landau–Ginzburg orbifolds with permutation symmetries variables. calculate formula Poincaré polynomial for a certain loop orbifoldized by semidirect product diagonal symmetry group and cyclic check that generalization Berglund–Hübsch transpose gives mirror symmetric pairs these cases.

Motivated by the search for new examples of “noncommutative manifolds”, we study the noncommutative geometry of the group C*-algebras of various discrete groups. The examples we consider are the infinite dihedral group Z×σZ2 and the semidirect product group Z×σZ. We present a unified treatment of the K-homology and cyclic cohomology of these algebras.

2 Groups 3 2.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Homomoprphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Direct and Semidirect Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Normal Subgroups . . . . . . . . . . . . . . . . . . . . . ....

In this paper, we present a new diverse class of post-quantum group-based Digital Signature Schemes (DSS). The approach is significantly different from previous examples digital signatures and adopts the framework group action-based cryptography: show that each finite defines action relative to semidirect product by its automorphism group, give security bounds on resulting signature scheme in t...