Related papers: Cryptosystems using subgroup distortion
Hyperbolic metamaterials were originally introduced to overcome the diffraction limit of optical imaging. Soon thereafter it was realized that hyperbolic metamaterials demonstrate a number of novel phenomena resulting from the broadband…
We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear…
The article explores the creation of a cryptosystem using a halidon group ring of a dihedral group. Due to the non-abelian nature of the group, constructing the cryptosystem is more challenging compared to an abelian group. The logic used…
We develop a generalized framework for invariant-based cryptography by extending the use of structural identities as core cryptographic mechanisms. Starting from a previously introduced scheme where a secret is encoded via a four-point…
We show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic groups, we use this to study translation lengths for actions…
In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. Under the assumption that the rarefaction curve of…
This paper introduces the idea of pseudo-group. Applications of pseudo-groups in Group Theory and Symmetry Breaking in Particle Physics and Cosmology are considered.
We discuss how non-commutative fundamental groups could eventually contribute to algorithms for finding rational points on hyperbolic curves.
Cryptographic Protocols (CP) are distributed algorithms intended for secure communication in an insecure environment. They are used, for example, in electronic payments, electronic voting procedures, systems of confidential data processing,…
Here is a more detailed description of the algorithm proposed in [1]. This algorithm simultaneously uses two cryptographic procedures: encryption using a generalization of the Markovski algorithm [2] and encryption using a system of…
We give solutions to several decision problems in word hyperbolic groups
In the last decade, a number of public key cryptosystems based on com- binatorial group theoretic problems in braid groups have been proposed. We survey these cryptosystems and some known attacks on them. This survey includes: Basic facts…
Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a…
Hyperbolic deep learning leverages the metric properties of hyperbolic spaces to develop efficient and informative embeddings of hierarchical data. Here, we focus on the solvable group structure of hyperbolic spaces, which follows naturally…
In this work, we present new constructions for topological subsystem codes using semi-regular Euclidean and hyperbolic tessellations. They give us new families of codes, and we also provide a new family of codes obtained through an already…
We give examples of hyperbolic groups with finite-rank free subgroups of huge (Ackermannian) distortion.
We establish an algorithm to encrypt and decrypt messages, where messages can be seen as elements of a finite field, using of mutations in a cluster algebra finite type.
We study those group rings whose group of units is hyperbolic.
We introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the later one…
We present a large scale hyperbolic recommender system. We discuss why hyperbolic geometry is a more suitable underlying geometry for many recommendation systems and cover the fundamental milestones and insights that we have gained from its…