Related papers: Iterated LD-Problem in non-associative key establi…
We construct non-associative key establishment protocols for all left self-distributive (LD), multi-LD-, and other left distributive systems. Instantiations of these protocols using generalized shifted conjugacy in braid groups lead to…
We provide implementation details for non-associative key establishment protocols. In particular, we describe the implementation of non-associative key establishment protocols for all left self-distributive and all mutually left…
Conjugacy is not the only possible primitive for designing braid-based protocols. To illustrate this principle, we describe a Fiat--Shamir-style authentication protocol that be can be implemented using any binary operation that satisfies…
We introduce a generalized Anshel-Anshel-Goldfeld (AAG) key establishment protocol (KEP) for magmas. This leads to the foundation of non-associative public-key cryptography (PKC), generalizing the concept of non-commutative PKC. We show…
Due to the increasing privacy concerns and data regulations, training data have been increasingly fragmented, forming distributed databases of multiple "data silos" (e.g., within different organizations and countries). To develop effective…
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…
Traditionally, the geometric multigrid method is used with nested levels. However, the construction of a suitable hierarchy for very fine and unstructured grids is, in general, highly non-trivial. In this scenario, the non-nested multigrid…
In this paper we present a new key establishment protocol based on the decomposition problem in non-commutative groups which is: given two elements $w, w_1$ of the platform group $G$ and two subgroups $A, B \subseteq G$ (not necessarily…
There are recent cryptographic protocols that are based on Multiple Simultaneous Conjugacy Problems in braid groups. We improve an algorithm, due to Sang Jin Lee and Eonkyung Lee, to solve these problems, by applying a method developed by…
Federated Learning (FL) is a novel distributed machine learning approach to leverage data from Internet of Things (IoT) devices while maintaining data privacy. However, the current FL algorithms face the challenges of non-independent and…
Non-independent and identically distributed (non-IID) data is a key challenge in federated learning (FL), which usually hampers the optimization convergence and the performance of FL. Existing data augmentation methods based on federated…
The braid group has recently attracted much attention. This is primarily based upon the discovery of its usage in various cryptosystems [AAG],[KLCHKP]. One major focus of current research has been in solving decision problems in braid…
In a recent paper [TMP, 200:1 (2019), 966--984] by the authors, a series of integrable discrete autonomous equations on a square lattice with a non-standard structure of generalized symmetries is constructed. We build modified series by…
Artin's braid groups have been recently suggested as a new source for public-key cryptography. In this paper we propose the first group signature schemes based on the conjugacy problem, decomposition problem and root problem in the braid…
Recent advances in machine learning have highlighted Federated Learning (FL) as a promising approach that enables multiple distributed users (so-called clients) to collectively train ML models without sharing their private data. While this…
A natural problem in combinatorial rigidity theory concerns the determination of the rigidity or flexibility of bar-joint frameworks in $\mathbb{R}^d$ that admit some non-trivial symmetry. When $d=2$ there is a large literature on this…
A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite…
Federated Learning is emerging as a privacy-preserving model training approach in distributed edge applications. As such, most edge deployments are heterogeneous in nature i.e., their sensing capabilities and environments vary across…
Federated Learning (FL) on non-independently and identically distributed (non-IID) data remains a critical challenge, as existing approaches struggle with severe data heterogeneity. Current methods primarily address symptoms of non-IID by…
Artin's braid groups have been recently suggested as a new source for public-key cryptography. In this paper we propose the first undeniable signature schemes using the conjugacy problem and the decomposition problem in the braid groups…