Published by De Gruyter

Volume 5 Issue 2

Issue of Groups Complexity Cryptology

Contents
Journal Overview

Publicly Available November 1, 2013

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Page range: i-iv

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October 8, 2013

Another look at non-uniformity

Neal Koblitz, Alfred Menezes

Page range: 117-139

Abstract

Abstract. We argue that it is unnatural and undesirable to use the non-uniform model of complexity for practice-oriented security reductions in cryptography.

November 1, 2013

An asymmetric generalisation of Artin monoids

Daan Krammer

Page range: 141-167

Abstract

Abstract. We propose a slight weakening of the definitions of Artin monoids and Coxeter monoids. We study one `infinite series' in detail.

October 15, 2013

Non-associative key establishment for left distributive systems

Arkadius Kalka, Mina Teicher

Page range: 169-191

Abstract

Abstract. 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 instances of a natural and apparently new group-theoretic problem, which we call the (subgroup) conjugacy coset problem.

October 16, 2013

On the dimension of matrix representations of finitely generated torsion free nilpotent groups

Maggie Habeeb, Delaram Kahrobaei

Page range: 193-209

Abstract

Abstract. It is well known that any polycyclic group, and hence any finitely generated nilpotent group, can be embedded into for an appropriate ; that is, each element in the group has a unique matrix representation. An algorithm to determine this embedding was presented in [J. Algebra 300 (2006), 376–383]. In this paper, we determine the complexity of the crux of the algorithm and the dimension of the matrices produced as well as provide a modification of the algorithm presented in [J. Algebra 300 (2006), 376–383].

October 11, 2013

On the intersection of subgroups in free groups: Echelon subgroups are inert

Amnon Rosenmann

Page range: 211-221

Abstract

Abstract. A subgroup H of a free group F is called inert in F if for every . In this paper we expand the known families of inert subgroups. We show that the inertia property holds for 1-generator endomorphisms. Equivalently, echelon subgroups in free groups are inert. An echelon subgroup is defined through a set of generators that are in echelon form with respect to some ordered basis of the free group, and may be seen as a generalization of a free factor. For example, the fixed subgroups of automorphisms of finitely generated free groups are echelon subgroups. The proofs follow mostly a graph-theoretic or combinatorial approach.

October 9, 2013

A secret sharing scheme based on the Closest Vector Theorem and a modification to a private key cryptosystem

Benjamin Fine, Anja I. S. Moldenhauer, Gerhard Rosenberger

Page range: 223-238

Abstract

Abstract. We explain and perform the steps for an ( n , t ) secret sharing scheme based on the closest vector theorem. We then compare this scheme and its complexity to the secret sharing schemes of both Shamir and Panagopoulos. Finally we modify the ( n , t ) secret sharing scheme to a private key cryptosystem.

About this journal

Objective
Groups – Complexity – Cryptology is a journal for speedy publication of articles in the areas of combinatorial and computational group theory, computer algebra, complexity theory, and cryptology. Preference is given to papers that touch upon at least two of these areas, but strong papers representing just one of the areas are considered, too. Groups – Complexity – Cryptology primarily publishes research papers, but comprehensive and timely survey articles on a topic inside the scope of the journal are also welcome. All submitted papers are peer-reviewed before publication.

Topics

Cryptology
Combinatorial and computational group theory
Computer algebra
Complexity theory

Article formats
Editorials, Research Papers, Survey Articles

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