arXiv subjects
Publications and source records attributed to Alvaro Otero Sanchez.
We compute the Wedderburn decomposition of a finite twisted skew group algebra over a finite abelian group $G$ and a finite field $K$. To do so, we prove that this twisted skew group algebra is a homomorphic image of a finite group algebra. We then characterise its Shoda pairs, as well as propose an algorithm for computing a complete set of them.
In this paper we solve an open question formulated in the original paper of twisted skew group codes regarding when a twisted skew group code is checkable. Also, we prove that all ideals of dimension 3 over a twisted group algebra are abelian group codes, generalising another previous result over group algebras. Finally, we prove a bound on the dimension and distance of a twisted group code, as well as when such bound is reached.
This paper classifies the derivations of twisted group algebras in terms of the generators and defining relations of the group. In particular, we generalize some know results over group algebras to the case of twisted group algebras. We will give necessary and sufficient condition for a map defined over the generators to be extended to a derivation over a twisted group ring. We present how this results can be use in case of an abelian group or dihedral group. We also present how this results can be use to compute the first Hochschild cohomology group of twisted group algebras.
We present a new key exchange protocol based on circulant matrices acting on matrices over a congruence-simple semiring. We describe how to compute matrices with the necessary properties for the implementation of the protocol. Additionally, we provide an analysis of its computational cost and its security against known attacks.
We present a cryptanalysis of a key exchange protocol based on the digital semiring. For this purpose, we find the maximal solution of a linear system over such semiring, and use the properties of circulant matrix to demonstrate that the protocol is vulnerable. Specifically, we provide an efficient attack that recovers the shared secret key from publicly exchanged information for any instance of the digital semiring in polynomial time.
This article analyzes a key exchange protocol based on the triad tropical semiring, recently proposed by Jackson, J. and Perumal, R. We demonstrate that the triad tropical semiring is isomorphic to a circulant matrix over tropical numbers. Consequently, matrices in this semiring can be represented as tropical matrices. As a result, we conduct a cryptanalysis of the key exchange protocol using an algorithm introduced by Sulaiman Alhussaini, Craig Collett, and Sergei Sergeev to solve the double discrete logarithm problem over tropical matrices