Related papers: Applications of Automaton Groups in Cryptography

The discrete logarithm problem is one of the backbones in public key cryptography. In this paper we study the discrete logarithm problem in the group of circulant matrices over a finite field. This gives rise to secure and fast public key…

In this paper we present the first practical attack on the shifted conjugacy-based authentication protocol proposed by P. Dehornoy. We discuss the weaknesses of that primitive and propose ways to improve the protocol.

Public-key cryptography has become a popular way to motivate the teaching of concepts in elementary number theory, abstract algebra, and introduction to proof courses, as well as in cryptography courses. Unfortunately, many experts expect…

Recently, Aaronson et al. (arXiv:2009.07450) showed that detecting interference between two orthogonal states is as hard as swapping these states. While their original motivation was from quantum gravity, we show its applications in quantum…

One of the central themes in classical cryptography is multi-party computation, which performs joint computation on multiple participants' data while maintaining data privacy. The extension to the quantum regime was proposed in 2002, but…

Group authentication is a method of confirmation that a set of users belong to a group and of distributing a common key among them. Unlike the standard authentication schemes where one central authority authenticates users one by one, group…

More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also…

We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of…

Cryptographic group actions are a leading contender for post-quantum cryptography, and have also been used in the development of quantum cryptographic protocols. In this work, we explore quantum state group actions, which consist of a group…

We revisit the problem of designing scalable protocols for private statistics and private federated learning when each device holds its private data. Locally differentially private algorithms require little trust but are (provably) limited…

There are numerous efforts to achieve a lightweight and systematic account of what is done by a group and its individuals. The Algorithmic-Autoregulation (AA) is a special case, in which a technical community embraced the challenge of…

Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…

We consider the growth, order, and finiteness problems for automaton (semi)groups. We propose new implementations and compare them with the existing ones. As a result of extensive experimentations, we propose some conjectures on the order…

Cryptography is an art and science of secure communication. Here the sender and receiver are guaranteed the security through encryption of their data, with the help of a common key. Both the parties should agree on this key prior to…

The need of totally secure online auction has led to the invention of many auction protocols. But as new attacks are developed, auction protocols also require corresponding strengthening. We analyze the auction protocol based on the…

In previous work, we developed a single Evolutionary Algorithm (EA) to solve random instances of the Anshel-Anshel-Goldfeld (AAG) key exchange protocol over polycyclic groups. The EA consisted of six simple heuristics which manipulated…

In 1999, public key cryptography using the matrix was devised by a hish school student of 16 yesrs old girl Sarah Flannery. This cryptosystem seemed faster than RSA, and it's having the strength to surpass even the encryption to RSA.…

In this paper, we study groups of automorphisms of algebraic systems over a set of $p$-adic integers with different sets of arithmetic and coordinate-wise logical operations and congruence relations modulo $p^k,$ $k\ge 1.$ The main result…

Exchange of secret keys over public channels based on neural synchronization using a variety of learning rules offer an appealing alternative to number theory based cryptography algorithms. Though several forms of attacks are possible on…

Several of the basic cryptographic constructs have associated algebraic structures. Formal models proposed by Dolev and Yao to study the (unconditional) security of public key protocols form a group. The security of some types of protocols…