Related papers: Cryptosystems using subgroup distortion
Chebyshev polynomials have been recently proposed for designing public-key systems. Indeed, they enjoy some nice chaotic properties, which seem to be suitable for use in Cryptography. Moreover, they satisfy a semi-group property, which…
The interleaving of chaos and cryptography has been the aim of a large set of works since the beginning of the nineties. Many encryption proposals have been introduced to improve conventional cryptography. However, many proposals possess…
The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modelling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian…
Hierarchical clustering is a fundamental machine-learning technique for grouping data points into dendrograms. However, existing hierarchical clustering methods encounter two primary challenges: 1) Most methods specify dendrograms without a…
A position-multiplexing based cryptosystem is proposed to enhance the information security with an ultra-broadband illumination. The simplified optical encryption system only contains one diffuser acting as the random phase mask (RPM).…
Hyperbolic metamaterials (HMMs) offer unconventional properties in the field of optics, enabling opportunities for confinement and propagation of light at the nanoscale. In-plane orientation of the optical axis, in the direction coinciding…
We present a quantum-classical hybrid algorithm that simulates electronic structures of periodic systems such as ground states and quasiparticle band structures. By extending the unitary coupled cluster (UCC) theory to describe crystals in…
Vinberg's algorithm is the main method for finding fundamental domains for reflection groups acting on hyperbolic space. Experience shows that it can be slow. We explain why this should be expected, and prove this slowness in some cases.…
We consider a group-theoretic analogue of the classic subset sum problem. It is known that every virtually nilpotent group has polynomial time decidable subset sum problem. In this paper we use subgroup distortion to show that every…
In this work, we propose a general protocol for distributed quantum computing that accommodates arbitrary unknown subroutines. It can be applied to scale up quantum computing through multi-chip interconnection, as well as to tasks such as…
Recently, an image encryption scheme based on chaotic standard and logistic maps was proposed. This paper studies the security of the scheme and shows that it can be broken with only one chosen-plaintext. Some other security defects of the…
Cryptocurrency refers to a type of digital asset that uses distributed ledger, or blockchain, technology to enable a secure transaction. Although the technology is widely misunderstood, many central banks are considering launching their own…
We build quasi--isometry invariants of relatively hyperbolic groups which detect the hyperbolic parts of the group; these are variations of the stable dimension constructions previously introduced by the authors. We prove that, given any…
The goal of this article is to survey some recent developments in the study of groups acting on hyperbolic spaces. We focus on the class of acylindrically hyperbolic groups; it is broad enough to include many examples of interest, yet a…
The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new…
We present novel homomorphic encryption schemes for integer arithmetic, intended for use in secure single-party computation in the cloud. These schemes are capable of securely computing only low degree polynomials homomorphically, but this…
We generalize the classical knapsack and subset sum problems to arbitrary groups and study the computational complexity of these new problems. We show that these problems, as well as the bounded submonoid membership problem, are P-time…
We use the classical construction of Schottky groups in hyperbolic geometry to produce non-Schottky subgroups of the mapping class group.
Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient.…
Hyperbolic embeddings are a class of representation learning methods that offer competitive performances when data can be abstracted as a tree-like graph. However, in practice, learning hyperbolic embeddings of hierarchical data is…