Related papers: Non-associative key establishment for left distrib…
In this paper we propose right-angled Artin groups as a platform for secret sharing schemes based on the efficiency (linear time) of the word problem. Inspired by previous work of Grigoriev-Shpilrain in the context of graphs, we define two…
We begin with a review of the notion of a braid group. We then discuss some known solutions to decision problems in braid groups. We then move on to proving new results in braid group algorithmics. We offer a quick solution to the…
We introduce natural language processing into the study of knot theory, as made natural by the braid word representation of knots. We study the UNKNOT problem of determining whether or not a given knot is the unknot. After describing an…
Any Quantum Key Distribution (QKD) protocol consists first of sequences of measurements that produce some correlation between classical data. We show that these correlation data must violate some Bell inequality in order to contain…
Secret key establishment leveraging the physical layer as a source of common randomness has been investigated in a range of settings. We investigate the problem of establishing, in an information-theoretic sense, a secret key between a user…
In this paper, we consider continuous-variable quantum key distribution (QKD) protocols which use non-Gaussian modulations. These specific modulation schemes are compatible with very efficient error correction procedures, hence allowing the…
Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the $(d,m,l)$-generalized Yang-Baxter equation, for $m/2\leq l \leq m$, which allows to systematically…
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…
We consider in this paper the information-theoretic secure key distribution problem over main and wire-tap noise channels with a public discussion in presence of an active adversary. In contrast to the solution proposed by ourselves for a…
In this paper, a new key-agreement scheme is proposed and analyzed. In addition to being provably secure in shared secret key indistinguishability model, the scheme has an interesting feature: while using exponentiation over a cyclic…
We give a new method to construct isolated left orderings of groups whose positive cones are finitely generated. Our construction uses an amalgamated free product of two groups having an isolated ordering. We construct a lot of new examples…
This paper considers secret-key generation between several agents and a base station that observe independent and identically distributed realizations of correlated random variables. Each agent wishes to generate the longest possible…
Machine learning and pattern recognition techniques have been successfully applied to algorithmic problems in free groups. In this paper, we seek to extend these techniques to finitely presented non-free groups, with a particular emphasis…
In the recently emerging field of group-based cryptography, the Conjugacy Search Problem (CSP) has gained traction as a non-commutative replacement of the Discrete Log Problem (DLP). The problem of finding a secure class of nonabelian…
Consensus strategies find a variety of applications in distributed coordination and decision making in multi-agent systems. In particular, average consensus plays a key role in a number of applications and is closely associated with two…
Given a system of equations in a "random" finitely generated subgroup of the braid group, we show how to find a small ordered list of elements in the subgroup, which contains a solution to the equations with a significant probability.…
In this paper we consider distributed allocation problems with memory constraint limits. Firstly, we propose a tractable relaxation to the problem of optimal symmetric allocations from [1]. The approximated problem is based on the Q-error…
We present a general framework encompassing a number of continuous-variable quantum key distribution protocols, including standard one-way protocols, measurement-device-independent protocols as well as some two-way protocols, or any other…
Let $G$ be a finite group, $N$ a normal subgroup of $G$ and $x\in G-N$. We discuss when the coset $Nx$ is contained in the union of two conjugacy classes, $K$ and $D$, of $G$. We show that $N$ need not be solvable, and can even be…
In this paper, we discuss distributed adaptive algorithms for synchronization of complex networks, consensus of multi-agents with or without pinning controller. The dynamics of individual node is governed by generalized QUAD condition. We…