相关论文: Undeniable Signature Schemes Using Braid Groups

We describe a series of complexes that relate to the braid groups as the matching complexes relate to the symmetric groups. A modified construction applies as well to other complexes based on edge sets in graphs. We show that our…

We show that a non-trivial, non-central normal subgroup of the braid groups contains a braid whose closure is a hyperbolic knot with arbitrary large genus. This shows that non-faithfulness of a quantum representation implies that the…

The mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base points. We prove that the centralizer of any braid can be expressed in terms of semidirect and direct products of mixed…

A (t,n)-threshold secret sharing scheme is a method to distribute a secret among n participants in such a way that any t participants can recover the secret, but no t-1 participants can. In this paper, we propose two secret sharing schemes…

In 2019 G\'omez described a new public key cryptography scheme based on ideas from multivariate public key cryptography using hidden irreducible polynomials. We show that the scheme's design has a flaw which lets an attacker recover the…

In the recently emerging field of nonabelian group-based cryptography, a prominently used one-way function is the Conjugacy Search Problem (CSP), and two important classes of platform groups are polycyclic and matrix groups. In this paper,…

The Rabin public-key cryptosystem is revisited with a focus on the problem of identifying the encrypted message unambiguously for any pair of primes. In particular, a deterministic scheme using quartic reciprocity is described that works…

In this paper we discuss the Hidden Subgroup Problem (HSP) in relation to post-quantum group-based cryptography. We review the relationship between HSP and other computational problems discuss an optimal solution method, and review the…

In this article, we consider the problem of community detection in signed networks. We propose SignedLouvain, an adaptation of the Louvain method to maximise signed modularity, efficiently taking advantage of the structure induced by signed…

Dehn twists around simple closed curves in oriented surfaces satisfy the braid relations. This gives rise to a group theoretic from the braid group to the mapping class group. We prove here that this map is trivial in stable homology with…

A directly public verifiable signcryption scheme is introduced in this paper that provides the security attributes of message confidentiality, authentication, integrity, non-repudiation, unforgeability, and forward secrecy of message…

Let $G$ be one of the Artin groups of finite type ${\mathbf B}_n={\mathbf C}_n$, and affine type $\tilde{\mathbf A}_{n-1}$ and $\tilde{\mathbf C}_{n-1}$. In this paper, we show that if $\alpha$ and $\beta$ are elements of $G$ such that…

We give new combinatorial constructions for codes providing authentication and secrecy for equiprobable source probability distributions. In particular, we construct an infinite class of optimal authentication codes which are multiple-fold…

An extension of the Artin Braid Group with new operators that generate double and triple intersections is considered. The extended Alexander theorem, relating intersecting closed braids and intersecting knots is proved for double and triple…

Two recently published papers propose some very simple key distribution schemes designed to enable two or more parties to establish a shared secret key with the aid of a third party. Unfortunately, as we show, most of the schemes are…

A special type of conjugacy classes in symmetric groups is studied and used to answer a question about odd-degree irreducible characters

We initiate the study of computational problems on elliptic curve isogeny graphs defined over RSA moduli. We conjecture that several variants of the neighbor-search problem over these graphs are hard, and provide a comprehensive list of…

We give a public key encryption scheme with plausible quasi-exponential security based on the conjectured intractability of two constraint satisfaction problems (CSPs), both of which are instantiated with a corruption rate of $1 - o(1)$.…

Community detection in graphs is crucial for understanding the organization of nodes into densely connected clusters. While numerous strategies have been developed to identify these clusters, the success of community detection can lead to…

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…