Ceased

Published from May 1, 2009 to November 1, 2019

Groups Complexity Cryptology

ISSN: 1869-6104

Managing Editors: Vladimir Shpilrain, Pascal Weil

Editorial Board: Laura Ciobanu, Marston Conder, Bettina Eick, Murray Elder, Benjamin Fine, Robert Gilman, Dima Grigoriev, Ki Hyoung Ko, Martin Kreuzer, Alexander V. Mikhalev, Alexei Myasnikov, Ludovic Perret, Vitalii Roman'kov, Gerhard Rosenberger, Mark Sapir, Rick M. Thomas, Boaz Tsaban, Enric Ventura Capell, Markus Lohrey

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

> Information on the submission process

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Topics

Volume 11 (2019)

Volume 10 (2018)

Volume 9 (2017)

Volume 8 (2016)

Volume 7 (2015)

Volume 6 (2014)

Volume 5 (2013)

Volume 4 (2012)

Volume 3 (2011)

Volume 2 (2010)

Volume 1 (2009)

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Submit

The Journal has been ceased. We no longer take any new submissions.

Hybrid Open Access

For complete details on hybrid open access publishing at De Gruyter please see: https://www.degruyter.com/page/560

Effective 1st January 2016, authors from an institution affiliated with either the Association of Dutch Universities (VSNU), the Consortium of Swiss Academic Libraries or some UK libraries participating in the Jisc Collections SMP may publish primary research and review articles open access in any of De Gruyter's OnlineOpen journals at a discount of 90% of the APC price. For more information and to confirm whether your institution is eligible please see the following:

The Netherlands: https://www.degruyter.com/page/1461
The UK: https://www.degruyter.com/page/1462
Switzerland: https://www.degruyter.com/page/1463

Editorial

Managing Editors

Vladimir Shpilrain
Department of Mathematics
The City College of New York
New York, NY 10031, U.S.A.
Email: shpil@groups.sci.ccny.cuny.edu

Pascal Weil
Laboratoire Bordelais de Recherche en Informatique
Université Bordeaux I
33405 Talence-Bordeaux, France
Email: pascal.weil@labri.fr

Editorial Board

Laura Ciobanu
Heriot-Watt University
Mathematical and Computer Sciences
Edinburgh EEH14 4AS, U.K.
Email: l.ciobanu@hw.ac.uk

Marston Conder
Department of Mathematics
University of Auckland
Private Bag 92019
Auckland, New Zealand
Email: m.conder@auckland.ac.nz

Bettina Eick
Institut Computational Mathematics
Technische Universität Braunschweig
Pockelsstr. 14
38106 Braunschweig, Germany
Email: beick@tu-bs.de

Murray Elder
University of Technology Sydney
Ultimo NSW 2007
Australia
Email: murray.elder@uts.edu.au

Ben Fine
Department of Mathematics and Computer Science
Fairfield University
Fairfield, CT 06430-5195, U.S.A.
Email: fine@fair1.fairfield.edu

Robert Gilman
Department of Mathematics
Stevens Institute of Technology
Hoboken, NJ 07030, U.S.A.
Email: Robert.Gilman@stevens.edu

Dima Grigoriev
Institut de Recherche Mathématique
Campus de Beaulieu
35042 Rennes, France
Email: dima@mpim-bonn.mpg.de

Markus Lohrey
Department für Elektrotechnik und Informatik
Universität Siegen
Hölderlinstr. 3
D-57076 Siegen
Email: lohrey@eti.uni-siegen.de

Ki Hyoung Ko
Department of Mathematiccal Sciences
Korea Advanced Institute of Science and Technology
Daejeon 305701, Korea
Email: knot@knot.kaist.ac.kr

Martin Kreuzer
Department of Computer Science and Mathematics
University of Passau
Innstr. 33
94032 Passau, Germany
Email: kreuzer@fim.uni-passau.de

Alexander V. Mikhalev
Department of Mechanics and Mathematics
Moscow State University
Moscow 119991, Russia
Email: mikhalev_alexander@yahoo.com

Alexei Myasnikov
Department of Mathematics and Statistics
McGill University
Montreal, Quebec H3A 2K6, Canada
Email: alexeim@math.mcgill.ca

Ludovic Perret
Université Pierre et Marie Curie
Paris, France
ludovic.perret@lip6.fr

Vitalii Romankov
Omsk State Dostoevskii University
55-a Mira Prospect
Omsk 644077, Russia
Email: romankov48@mail.ru

Gerhard Rosenberger
Department Mathematik
Universität Hamburg
Bundesstr. 55
20146 Hamburg, Germany
Email: gerhard.rosenberger@math.uni-hamburg.de

Mark Sapir
Department of Mathematics
Vanderbilt University
Nashville, TN 37240, USA
Email: m.sapir@vanderbilt.edu

Rick Thomas
Department of Informatics
University of Leicester
Leicester LE1 7RH, England
Email: rmt@mcs.le.ac.uk

Boaz Tsaban
Department of Mathematics
Bar Ilan University
Ramat Gan 52900, Israel
Email: tsaban@math.biu.ac.il

Enric Ventura Capell
Department of Applied Mathematics III
Universitat Politècnica de Catalunya
08242 Manresa-Barcelona, Spain
Email: enric.ventura@upc.edu

Volume 11 Issue 2

November 2019

Publicly Available November 1, 2019

Frontmatter

Page range: i-iv

Download PDF

October 23, 2019

Garside theory and subsurfaces: Some examples in braid groups

Saul Schleimer, Bert Wiest

Page range: 61-75

Abstract

Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid braids with a fixed number of strands, the size of this set is bounded by a polynomial in the length of the braids. In this paper we suggest a more precise bound: for rigid braids with N strands and of Garside length L , the sliding circuit set should have at most C⋅LN-2{C\cdot L^{N-2}} elements, for some constant C . We construct a family of braids which realise this potential worst case. Our example braids suggest that having a large sliding circuit set is a geometric property of braids, as our examples have multiple subsurfaces with large subsurface projection; thus they are “almost reducible” in multiple ways, and act on the curve graph with small translation distance.

October 24, 2019

Key agreement based on automaton groups

Rostislav Grigorchuk, Dima Grigoriev

Page range: 77-81

Abstract

We suggest several automaton groups as platforms for Anshel–Anshel–Goldfeld key agreement metascheme. They include Grigorchuk and universal Grigorchuk groups, Hanoi 3-towers group, the Basilica group and a subgroup of the affine group Aff4⁢(ℤ){\mathrm{Aff}_{4}(\mathbb{Z})}.

October 16, 2019

Effective construction of covers of canonical Hom-diagrams for equations over torsion-free hyperbolic groups

Olga Kharlampovich, Alexei Myasnikov, Alexander Taam

Page range: 83-101

Abstract

We show that, given a finitely generated group G as the coordinate group of a finite system of equations over a torsion-free hyperbolic group Γ, there is an algorithm which constructs a cover of a canonical solution diagram. The diagram encodes all homomorphisms from G to Γ as compositions of factorizations through Γ-NTQ groups and canonical automorphisms of the corresponding NTQ-subgroups. We also give another characterization of Γ-limit groups as iterated generalized doubles over Γ.

October 16, 2019

Ramp secret sharing with cheater identification in presence of rushing cheaters

Jyotirmoy Pramanik, Avishek Adhikari

Page range: 103-113

Abstract

Secret sharing allows one to share a piece of information among n participants in a way that only qualified subsets of participants can recover the secret whereas others cannot. Some of these participants involved may, however, want to forge their shares of the secret(s) in order to cheat other participants. Various cheater identifiable techniques have been devised in order to identify such cheaters in secret sharing schemes. On the other hand, Ramp secret sharing schemes are a practically efficient variant of usual secret sharing schemes with reduced share size and some loss in security. Ramp secret sharing schemes have many applications in secure information storage, information-theoretic private information retrieval and secret image sharing due to producing relatively smaller shares. However, to the best of our knowledge, there does not exist any cheater identifiable ramp secret sharing scheme. In this paper we define the security model for cheater identifiable ramp secret sharing schemes and provide two constructions for cheater identifiable ramp secret sharing schemes. In addition, the second construction is secure against rushing cheaters who are allowed to submit their shares during secret reconstruction after observing other participants’ responses in one round. Also, we do not make any computational assumptions for the cheaters, i.e., cheaters may be equipped with unlimited time and resources, yet, the cheating probability would be bounded above by a very small positive number.

October 24, 2019

On group automorphisms in universal algebraic geometry

Artem N. Shevlyakov

Page range: 115-121

Abstract

In this paper, we study group equations with occurrences of automorphisms. We describe equational domains in this class of equations. Moreover, we solve a number of open problem posed in universal algebraic geometry.

October 15, 2019

Randomized nonlinear software-oriented MDS diffusion layers

Mohammad Reza Mirzaee Shamsabad, Seyed Mojtaba Dehnavi, Akbar Mahmoodi Rishakani

Page range: 123-131

Abstract

MDS diffusion layers are critical components in the design of symmetric ciphers. In this paper, after introducing some new algebraic structures, we provide new MDS matrices over special types of R -modules. With the help of the proposed methodology, we have more flexibility in designing software-oriented diffusion layers. Most notably, we construct randomized and/or nonlinear MDS diffusion layers, based upon the presented theoretical results, and discuss the resistance of the presented diffusion layers against various kinds of cryptanalysis, compared with classical linear diffusion layers.

Publicly Available October 15, 2019

Constructing a pseudo-free family of finite computational groups under the general integer factoring intractability assumption

Mikhail Anokhin

Page range: 133-134

More Download PDF

Abstract

We provide a correct version of Remark 3.5 of the paper mentioned in the title. Also, we fix a typo in Remark 4.4 of that paper.

(Deutsch)

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Online ISSN: 1869-6104
Type: Journal
Language: English
Publisher: De Gruyter
First published: May 1, 2009
Last published: November 1, 2019
Publication Frequency: 2 Issues per Year
Audience: researchers and professionals in the field of cryptology