Related papers: Quasigroups in cryptology

The paper explains that post-quantum cryptography is necessary due to the introduction of quantum computing causing certain algorithms to be broken. We analyze the different types of post-quantum cryptography, quantum cryptography and…

We address a cryptanalysis of two protocols based on the supposed difficulty of discrete logarithm problem on (semi) groups of matrices over a group ring. We can find the secret key and break entirely the protocols.

We present an overview of the theory of self-distributive quasigroups, both in the two-sided and one-sided cases, and relate the older results to the modern theory of quandles, to which self-distributive quasigroups are a special case. Most…

Let G be a group which is hyperbolic relative to a collection of subgroups A, and it is also hyperbolic relative to a collection of subgroups B. Suppose that the collection A contains B. We characterize, for subgroups of G, when…

In 1991 the first public key protocol involving automaton groups has been proposed. In this paper we give a survey about algorithmic problems around automaton groups which may have potential applications in cryptography. We then present a…

In this paper we investigate graph inverse semigroups which are subsemigroups of compact-like topological semigroups. More precisely, we characterise graph inverse semigroups which admit a compact semigroup topology and describe graph…

We generalize a recently discovered example of a private quantum subsystem to find private subsystems for Abelian subgroups of the $n$-qubit Pauli group, which exist in the absence of private subspaces. In doing so, we also connect these…

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.

For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two quasiconvex subgroups $Q$ and $R$ is quasiconvex and isomorphic to $Q \ast_{Q\cap R} R$. Our results generalized known combination…

A random group contains many quasiconvex surface subgroups.

A symmetric encryption method based on properties of quasicrystals is proposed. The advantages of the cipher are strict aperiodicity and everywhere discontinuous property as well as the speed of computation, simplicity of implementation and…

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…

We review the plethora of uncertainty relations that appear in quantum mechanics and their nuances. We present both foundational applications, e.g. in understanding and defining complementarity, and practical applications, e.g. in quantum…

We describe some new univariate spline quasi-interpolants on uniform partitions of bounded intervals. Then we give some applications to numerical analysis: integration, differentiation and approximation of zeros.

We propose a generalization of the quantum hashing technique based on the notion of the small-bias sets. These sets have proved useful in different areas of computer science, and here their properties give an optimal construction for…

In this paper we define a new algebraic object: the disguised-groups. We show the main properties of the disguised-groups and, as a consequence, we will see that disguised-groups coincide with regular semigroups. We prove many of the…

Motivated by appearance of multisemigroups in the study of additive $2$-categories, we define and investigate the notion of a multisemigroup with multiplicities. This notion seems to be better suitable for applications in higher…

We discuss twisted cohomology, not just for ordinary cohomology but also for $K$-theory and other exceptional cohomology theories, and discuss several of the applications of these in mathematical physics. Our list of applications is by no…

The advantages of post-quantum cryptography over classical cryptography are covered in this survey. We address several post-quantum cryptography techniques. We conclude that the deployment of quantum-safe cryptographic systems is…

In this article we provide evidence for a well-known conjecture which states that quasi-isometric simply-connected nilpotent Lie groups are isomorphic. We do so by constructing new examples which are rigid in the sense that whenever they…