Related papers: A note on conjugacy search and racks

Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…

Retrieval-Augmented Generation (RAG) enhances LLMs by grounding generation in query-relevant external evidence. Beyond unstructured text corpora, Graph RAG integrates knowledge graphs into the retrieval pipeline, enabling LLMs to access…

In this paper, we define the pullback crossed modules in the category of racks which mainly based on a pullback diagram of rack morphisms with extra crossed module data on some of its arrows. Furthermore we prove that the conjugation…

We consider a key exchange procedure whose security is based on the difficulty of computing discrete logarithms in a group, and where exponentiation is hidden by a conjugation. We give a platform-dependent cryptanalysis of this protocol.…

We propose a new cryptosystem based on polycyclic groups. The cryptosystem is based on the fact that the word problem can be solved effectively in polycyclic groups, while the known solutions to the conjugacy problem are far less efficient.

We examine a search on a graph among a number of different kinds of objects (vertices), one of which we want to find. In a standard graph search, all of the vertices are the same, except for one, the marked vertex, and that is the one we…

It was recently demonstrated that the Matrix Action Key Exchange (MAKE) algorithm, a new type of key exchange protocol using the semidirect product of matrix groups, is vulnerable to a linear algebraic attack if the matrices are over a…

Evaluating a Boolean conjunctive query Q against a guarded first-order theory F is equivalent to checking whether "F and not Q" is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since Q may…

Two-way Gaussian protocols have the potential to increase quantum key distribution (QKD) protocols' secret-key rates by orders of magnitudes~[Phys.~Rev.~A {\bf 94}, 012322 (2016)]. Security proofs for two-way protocols, however, are…

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…

Secure relative timestamping and secure append-only logs are two historically mostly independent lines of research, which we show to be sides of the same coin -- the authentication of prefix relations. From this more general viewpoint, we…

We present a quantum auction protocol using superpositions to represent bids and distributed search to identify the winner(s). Measuring the final quantum state gives the auction outcome while simultaneously destroying the superposition.…

LLM-powered search services have driven data integration as a significant trend. However, this trend's progress is fundamentally hindered, despite the fact that combining individual knowledge can significantly improve the relevance and…

In this paper we initiate the study of racks from the combined perspective of combinatorics and finite group theory. A rack R is a set with a self-distributive binary operation. We study the combinatorics of the partially ordered set {\cal…

We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are…

The existing cryptosystem based approaches for privacy-preserving consensus of networked systems are usually limited to those with undirected topologies. This paper proposes a new privacy-preserving algorithm for networked systems with…

A nonlocal bipartite unitary gate can sometimes be implemented using prior entanglement and only one round of classical communication in which the two parties send messages to each other simultaneously. This cuts the classical communication…

We prove the unconditional security of an entanglement-based quantum-key-distribution protocol using detectors that respond to multiple modes of light and cannot distinguish between one from two or more photons. Even with such practical…

Recently, Abdalla et al. proposed a new gateway-oriented password-based authenticated key exchange (GPAKE) protocol among a client, a gateway, and an authentication server, where each client shares a human-memorable password with a trusted…

The random oracle methodology has proven to be a powerful tool for designing and reasoning about cryptographic schemes. In this paper, we focus on the basic problem of correcting faulty or adversarially corrupted random oracles, so that…