Related papers: Polycyclic groups: A new platform for cryptology?
A new 4-pass Key-Agreement Protocol is presented. The security of the protocol mainly relies on the existence of a (polynomial-computable) One-Way-Function and the supposed computational hardness of solving a specific system of equations.
The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite strings over some finite alphabet) are in the same…
Paxos is a widely used and notoriously hard to understand method for solving one type of distributed consensus problem. This note provides a quick explanation of Paxos, a novel proof of correctness that is intended to provide insight into…
We prove that centralizers of elements in [f.g. free]-by-cyclic groups are computable. As a corollary we get that, given two conjugate elements in a [f.g. free]-by-cyclic group, the set of conjugators can be computed and that the conjugacy…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
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…
Acyclic networks are a class of complex networks in which links are directed and don't have closed loops. Here we present an algorithm for transforming an ordinary undirected complex network into an acyclic one. Further analysis of an…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…
We propose an authentication scheme where forgery (a.k.a. impersonation) seems infeasible without finding the prover's long-term private key. The latter would follow from solving the conjugacy search problem in the platform (noncommutative)…
The theory of holographic algorithms, which are polynomial time algorithms for certain combinatorial counting problems, yields insight into the hierarchy of complexity classes. In particular, the theory produces algebraic tests for a…
We show that the Modified Matrix Modular Cryptosystem proposed by S.K. Rososhek is not secure against the attack based on the linear decomposition method. The security of the encryption scheme in the Rososhek's system is based on the mix of…
We propose a new approach in cryptanalysis based on an evolution of the concept of \textit{Combinatorial Equivalence}. The aim is to rewrite a cryptosystem under a combinatorially equivalent form in order to make appear new properties that…
The McEliece public-key encryption scheme has become an interesting alternative to cryptosystems based on number-theoretical problems. Differently from RSA and ElGa- mal, McEliece PKC is not known to be broken by a quantum computer.…
As the number of hacking events and cyber threats keeps going up, it is getting harder and harder to communicate securely and keep personal information safe on the Internet. Cryptography is a very important way to deal with these problems…
A new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication is proposed to reduce the number of variables in the optimization problem…
The theory of Engel groups plays an important role in group theory since these groups are closely related to the Burnside problems. In this survey we consider several classical and novel algorithmic problems for Engel groups and propose…
This paper is concerned with the problem of controlling a system of constrained dynamic subsystems in a way that balances the performance degradation of decentralized control with the practical cost of centralized control. We propose a…
In this paper, we identify many important properties and develop criteria for the existence of subquasigroups in finite quasigroups. Based on these results, we propose an effective method that concludes the nonexistence of subquasigroup of…
Rewriting systems on words are very useful in the study of monoids. In good cases, they give finite presentations of the monoids, allowing their manipulation by a computer. Even better, when the presentation is confluent and terminating,…
Ever since the link between nonlinear science and cryptography became apparent, the problem of applying chaotic dynamics to the construction of cryptographic systems has gained a broad audience and has been the subject of thousands of…