相关论文: Polycyclic groups: A new platform for cryptology?

Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular,…

We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conugacy problem given by the authors in a previous paper, are two…

This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent…

In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm.…

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…

In this paper homomorphic cryptosystems are designed for the first time over any finite group. Applying Barrington's construction we produce for any boolean circuit of the logarithmic depth its encrypted simulation of a polynomial size over…

Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate…

The discrete logarithm problem in a finite group is the basis for many protocols in cryptography. The best general algorithms which solve this problem have time complexity of $\mathcal{O}(\sqrt{N}\log N)$, and a space complexity of…

In this short note, we develop a novel idea of a bilinear cryptosystem using the discrete logarithm problem in matrices. These matrices come from a linear representation of a finite $p$-group of class 2. We discuss an example at the end.

We consider operation of blockchain-based cryptocurrency in case of partitioning. We define the Partitionable Blockchain Consensus Problem. The problem may have an interesting solution if the partitions proceed independently by splitting…

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…

Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use…

Code-based cryptography is an interesting alternative to classic number-theory PKC since it is conjectured to be secure against quantum computer attacks. Many families of codes have been proposed for these cryptosystems, one of the main…

Weanalyzethecomputationalcomplexityofanalgorithmtosolve the conjugacy search problem in a certain family of metabelian groups. We prove that in general the time complexity of the conjugacy search problem for these groups is at most…

Theoretical computer science has found fertile ground in many areas of mathematics. The approach has been to consider classical problems through the prism of computational complexity, where the number of basic computational steps taken to…

Propose a new cryptographic information concept. It allows : - to create absolutely algorithmic unbreakable ciphers for communication through open digital channels; - to create new code-breaking methods. They will be the most efficient…

Cryptographic Protocols (CP) are distributed algorithms intended for secure communication in an insecure environment. They are used, for example, in electronic payments, electronic voting procedures, systems of confidential data processing,…

Here is a more detailed description of the algorithm proposed in [1]. This algorithm simultaneously uses two cryptographic procedures: encryption using a generalization of the Markovski algorithm [2] and encryption using a system of…

By combining the one-way coupled chaotic map lattice system with a bit-reverse operation, we construct a new cryptosystem which is extremely sensitive to the system parameters even for low-dimensional systems. The security of this new…

Bogopolski, Martino and Ventura in [BMV10] introduced a general criteria to construct groups extensions with unsolvable conjugacy problem using short exact sequences. We prove that such extensions have always solvable word problem. This…