Related papers: Multilinear Cryptography using Nilpotent Groups
The structure of a group which is not nilpotent but all of whose proper subgroups are nilpotent has interested the researches of several authors both in the finite case and in the infinite case. The present paper generalizes some classic…
In the paper, we introduce the terminology equivariant pointwise clutching map. By using this, we give details on how to glue an equivariant vector bundle over a finite set so as to obtain a new Lie group representation such that the…
We calculate the higher homotopy groups of the Deligne-Getzler infinity-groupoid associated to a nilpotent L-infinity algebra. As an application, we present a new approach to the rational homotopy theory of mapping spaces.
Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate…
On the transversals of a subgroup of a group, using the binary operation of the group, structural mappings are defined. Based on these mappings, the notion of the hypergroup over the group is introduced, which generalizes the notion of the…
Clustering is a popular unsupervised learning tool often used to discover groups within a larger population such as customer segments, or patient subtypes. However, despite its use as a tool for subgroup discovery and description - few…
We present a new characterization of Lusztig's canonical quotient group. We also define a duality map: to a pair consisting of a nilpotent orbit and a conjugacy class in its fundamental group, the map assigns a nilpotent orbit in the…
Homomorphic encryption is a method used in cryptopgraphy to create programs that can interact with encrypted data without ever leaving the data in the clear. This has many potential applications in cybersecurity. This paper uses…
The nonlinear concepts of mixed summable families and maps for the spaces that only non-void sets are developed. Several characterizations of the corresponding concepts are achieved and the proof for a general Pietsch Domination-type…
We delineate the image of multilinear Lie polynomial of degree $2$ evaluated on $L$ where $L$ is a finite-dimensional nilpotent Lie algebra over field $k$ with $\dim L' \leq 4$.
This article shows how box dimension of the unit-time map can be used in studying the multiplicity of nilpotent singularities of planar vector fields. Using unit-time map on the characteristic curve of nilpotent singularity we define…
We find a short equational basis for the variety of $3$-supernilpotent loops. We also present a conceptually simple proof that $k$-nilpotence and $k$-supernilpotence are equivalent for groups. Connections between $3$-supernilpotent loops,…
We develop a structure theory for nilpotent symplectic alternating algebras.
We discuss a matrix public key cryptosystem and its numerical implementation.
We prove that the lamplighter group admits an injective Lipschitz map to any finitely generated metabelian group which is not virtually nilpotent. This implies that finitely generated metabelian groups satisfy the ``analytically…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm.…
In our earlier article~\cite{CanSakran} we initiated a study of the complement-finite submonoids of the group of integer points of a unipotent linear algebraic group. In the present article, we continue to develop tools and techniques for…
Unclonable cryptography leverages the quantum no-cloning principle to copy-protect cryptographic functionalities. While most existing works address the basic single-copy security, the stronger notion of multi-copy security remains largely…
We formalize the simulation paradigm of cryptography in terms of category theory and show that protocols secure against abstract attacks form a symmetric monoidal category, thus giving an abstract model of composable security definitions in…