Related papers: Cryptosystems using subgroup distortion
We suggest the usage of algebraic subsets instead of subgroups in public-key cryptography. In particular, we present the subset version of two protocols introduced by Shpilrain and Ushakov with some examples in ascending HNN-extensions of…
We discuss the notion of the universal relatively hyperbolic structure on a group which is used in order to characterize relatively hyperbolic structures on the group. We also study relations between relatively hyperbolic structures on a…
In recent years, a variety of effective chaos-based image encryption schemes have been proposed. The typical structure of these schemes has the permutation and the diffusion stages performed alternatively. The confusion and diffusion effect…
Recently, interest has been emerging in the application of symbolic techniques to the specification and analysis of cryptosystems. These techniques, when accompanied by suitable proofs of soundness/completeness, can be used both to identify…
We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…
Chaotic systems have been broadly exploited through the last two decades to build encryption methods. Recently, two new image encryption schemes have been proposed, where the encryption process involves a permutation operation and an…
There is a family of hyperbolic groups known as hyperbolic hydra which contain heavily distorted free subgroups. We prove the existence of Cannon--Thurston maps (that is, maps of the boundaries induced by subgroup inclusion) for these free…
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…
This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…
Although recent advances of blockchain systems, notably in the form of cryptocurrency, have drawn tremendous interests from both researchers and practitioners, limited studies existed toward the theoretical foundation of blockchains. This…
A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…
In the following text we introduce the concept of pseudo-codecomposition of a transformation group, also we show the collection of all transformation groups pseudo-codecomposable to distal ones is a proper intermediate class of the class of…
Embedding the data in hyperbolic spaces can preserve complex relationships in very few dimensions, thus enabling compact models and improving efficiency of machine learning (ML) algorithms. The underlying idea is that hyperbolic…
It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…
A cryptographic algorithm is proposed based on fully quantum mechanical keys and ciphers. Encryption and decryption are carried out via an appropriate measurement process on entangled states as governed by a quantum mechanical, asymmetrical…
In the recent world, security is a prime important issue, and encryption is one of the best alternative way to ensure security. More over, there are many image encryption schemes have been proposed, each one of them has its own strength and…
Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in…
This article is devoted to level-1 large deviation properties in some nonuniformly hyperbolic systems via Pesin theory. In particular, our result can be applied to the nonuniformly hyperbolic diffeomorphisms described by Katok and several…
Evidence of signatures associated with cryptographic modes of operation is established. Motivated by some analogies between cryptographic and dynamical systems, in particular with chaos theory, we propose an algorithm based on Lyapunov…
Polycyclic groups are natural generalizations of cyclic groups but with more complicated algorithmic properties. They are finitely presented and the word, conjugacy, and isomorphism decision problems are all solvable in these groups.…