Related papers: A Cryptosystem Using Cluster Algebras
In this paper, we propose to use a twisted dihedral group algebra for public-key cryptography. For this, we introduce a new $2$-cocycle $\alpha_{\lambda}$ to twist the dihedral group algebra. Using the ambient space…
The article concerns the existence and uniqueness of quantisations of cluster algebras. We prove that cluster algebras with an initial exchange matrix of full rank admit a quantisation in the sense of Berenstein-Zelevinsky and give an…
In this paper, we introduce and study the quantum deformations of the cluster superalgebra. Then we prove the quantum version of the Laurent phenomenon for the super-case.
Encryption schemes attempt to provide a means for entities to communicate confidentially over a public channel. Such schemes have been studied for centuries, and their use has become widespread. However, developments in the area of quantum…
We review how the (quantum) cluster algebra naturally emerges in the study of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories.
Cloud computing is the broad and diverse phenomenon. Users are allowed to store huge amount of data on cloud storage for future use. Most of the cloud service providers store data in plain text format or in secured manner but client will…
Outsourcing data in the cloud has become nowadays very common. Since -- generally speaking -- cloud data storage and management providers cannot be fully trusted, mechanisms providing the confidentiality of the stored data are necessary. A…
Subspace clustering algorithms are used for understanding the cluster structure that explains the dataset well. These methods are extensively used for data-exploration tasks in various areas of Natural Sciences. However, most of these…
Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for…
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…
This paper investigates the finite generation of cluster automorphism groups. By applying the pseudo $\mathbb{N}$-grading introduced in our previous work, we establish a sufficient condition for a cluster automorphism group to be finitely…
We theoretically propose a symmetric encryption scheme based on Restricted Boltzmann Machines that functions as a probabilistic Enigma device, encoding information in the marginal distributions of visible states while utilizing bias…
Cryptography is the discipline that allows securing of the exchange of information. In this internship, we will focus on a certain branch of this discipline, secure computation in a network. The main goal of this internship, illustrated in…
Clustering data objects into homogeneous groups is one of the most important tasks in data mining. Spectral clustering is arguably one of the most important algorithms for clustering, as it is appealing for its theoretical soundness and is…
Encryption and Decryption is the process of sending a message in a ciphered way that appears meaningless and could be deciphered using a key for security purposes to avoid data breaches. This paper expands on the previous work on…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…
The present paper proposes a new and systematic approach to the so-called black box group methods in computational group theory. Instead of a single black box, we consider categories of black boxes and their morphisms. This makes new…
In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.
Cluster analysis is the distribution of objects into different groups or more precisely the partitioning of a data set into subsets (clusters) so that the data in subsets share some common trait according to some distance measure. Unlike…