Related papers: Group Signature Schemes Using Braid Groups
This paper is a survey of some properties of the braid groups and related groups that lead to questions on mapping class groups.
In this paper we provide an alternative solution to a result by Juh\'{a}sz that the twisted conjugacy problem for odd dihedral Artin groups is solvable, that is, groups with presentation $G(m) = \langle a,b \; | \; _{m}(a,b) = {}_{m}(b,a)…
In this work, we address a question posed by Dehornoy et al. in the book "Foundations of Garside Theory" that asks for a theory of groups of $\mathrm{I}_G$-type when $G$ is a Garside group. In this article, we introduce a broader notion…
Group ring NTRU (GR-NTRU) provides a general structure to design different variants of NTRU-like schemes by employing different groups. Although, most of the schemes in literature are built over cyclic groups, nonabelian groups can also be…
We characterize twisted right-angled Artin groups whose finitely generated subgroups are also twisted right-angled Artin groups. Additionally, we give a classification of coherence within this class of groups in terms of the defining graph.…
The n-string braid group of a graph X is defined as the fundamental group of the n-point configuration space of the space X. This configuration space is a finite dimensional aspherical space. A. Abrams and R. Ghrist have conjectured that…
In his initial paper on braids E.Artin gave a presentation with two generators for an arbitrary braid group. We give analogues of this Artin's presentation for various generalizations of braids.
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…
There are several public key establishment protocols as well as complete public key cryptosystems based on allegedly hard problems from combinatorial (semi)group theory known by now. Most of these problems are search problems, i.e., they…
We present and discuss some open problems formulated by participants of the International Workshop "Knots, Braids, and Auto\-mor\-phism Groups" held in Novosibirsk, 2014. Problems are related to palindromic and commutator widths of groups;…
We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption…
We propose modifications of known quasigroup based stream ciphers. Systems of orthogonal n-ary groupoids are used.
The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptography. There are however recent discoveries of faster algorithms…
The notion of aggregate signature has been motivated by applications and it enables any user to compress different signatures signed by different signers on different messages into a short signature. Sequential aggregate signature, in turn,…
This paper proposes a signature scheme where the signatures are generated by the cooperation of a number of people from a given group of senders and the signatures are verified by a certain number of people from the group of recipients.…
Blockchain's decentralization, transparency, and tamper-resistance properties have facilitated the system's use in various application fields. However, the low throughput and high confirmation latency hinder the widespread adoption of…
We prove a conjecture due to Makanin: if a and b are elements of the Artin braid group B_n such that a^k=b^k for some nonzero integer k, then a and b are conjugate. The proof involves the Nielsen-Thurston classification of braids.
In this paper,we propose a modified Anshel-Anshel-Goldfeld(AAG) key exchange scheme. The hardness assumption underlying this modified construction is based on the membership problem for Mihailova subgroups of the braid group, a problem that…
Group authentication is a method of confirmation that a set of users belong to a group and of distributing a common key among them. Unlike the standard authentication schemes where one central authority authenticates users one by one, group…
In this paper we solve the isomorphism problem for all large-type Artin groups. Our strategy involves reconstructing the Coxeter groups associated with large-type Artin groups in a purely algebraic way. This answers several questions raised…