A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...

In this paper we define S algebras and show that every finite group can be found in some S algebra.  We define and study the S degree of a finite group and determine the S degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $D_p$.

<p style='text-indent:20px;'>In this paper, we propose to use a twisted dihedral group algebra for public-key cryptography. For this, introduce new <inline-formula><tex-math id="M1">\begin{document}$ 2 $\end{document}</tex-math></inline-formula>-cocycle id="M2">\begin{document}$ \alpha_{\lambda} $\end{document}</tex-math></inline-formula> twist the a...