Related papers: Applications of Automaton Groups in Cryptography

This thesis deals with the conjugacy problem in groups and its twisted variants. We analyze recent results by Bogopolski, Martino, Maslakova and Ventura on the twisted conjugacy problem in free groups and its implication for the conjugacy…

Today's information society relies on cryptography to achieve security goals such as confidentiality, integrity, authentication, and non-repudiation for digital communications. Here, public-key cryptosystems play a pivotal role to share…

We design new deterministic and randomized algorithms for computational problems in free solvable groups. In particular, we prove that the word problem and the power problem can be solved in quasi-linear time and the conjugacy problem can…

Group communication is becoming a more and more popular infrastructure for efficient distributed applications. It consists in representing locally a group of remote objects as a single object accessed in a single step; communications are…

A paper presented at the ICICS 2019 conference describes what is claimed to be a `provably secure group authentication [protocol] in the asynchronous communication model'. We show here that this is far from being the case, as the protocol…

In [15], Leonardi and Ruiz-Lopez propose an additively homomorphic public key encryption scheme whose security is expected to depend on the hardness of the learning homomorphism with noise problem (LHN). Choosing parameters for their…

The conjugacy search problem in a group $G$ is the problem of recovering an $x \in G$ from given $g \in G$ and $h=x^{-1}gx$. The alleged computational hardness of this problem in some groups was used in several recently suggested public key…

The worst-case complexity of group-theoretic algorithms has been studied for a long time. Generic-case complexity, or complexity on random inputs, was introduced and studied relatively recently. In this paper, we address the average-case…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

The security of communication in everyday life becomes very important. On the other hand, all existing encryption protocols require from user additional knowledge end resources. In this paper we discuss the problem of public key…

With the evolution of the Internet, multicast communications seem particularly well adapted for large scale commercial distribution applications, for example, the pay TV channels and secure videoconferencing. Key management for multicast…

Quantum cryptography is arguably the fastest growing area in quantum information science. Novel theoretical protocols are designed on a regular basis, security proofs are constantly improving, and experiments are gradually moving from…

Cryptographic mechanisms are used in a wide range of applications, including email clients, web browsers, document and asset management systems, where typical users are not cryptography experts. A number of empirical studies have…

It has been found that many networks display community structure -- groups of vertices within which connections are dense but between which they are sparser -- and highly sensitive computer algorithms have in recent years been developed for…

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…

In this paper, we review multi-agent collective behavior algorithms in the literature and classify them according to their underlying mathematical structure. For each mathematical technique, we identify the multi-agent coordination tasks it…

Team Automata is a formalism for interacting component-based systems proposed in 1997, whereby multiple sending and receiving actions from concurrent automata can synchronise. During the past 25+ years, team automata have been studied and…

The existing algorithm to compute and verify the automata associated with an automatic group deals only with the subclass of shortlex automatic groups. This paper describes the extension of the algorithm to deal with automatic groups…

For a dataset of label-count pairs, an anonymized histogram is the multiset of counts. Anonymized histograms appear in various potentially sensitive contexts such as password-frequency lists, degree distribution in social networks, and…

We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an…