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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board Member: Blackburn, Simon R. / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Schäge, Sven / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

2 Issues per year


SCImago Journal Rank (SJR) 2015: 1.208
Source Normalized Impact per Paper (SNIP) 2015: 2.294
Impact per Publication (IPP) 2015: 1.103

Mathematical Citation Quotient (MCQ) 2015: 0.48

Online
ISSN
1869-6104
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A parallel evolutionary approach to solving systems of equations in polycyclic groups

Matthew J. Craven
  • Centre for Mathematical Sciences, Plymouth University, Drake Circus, Plymouth, PL4 8AA, United Kingdom of Great Britain and Northern Ireland
  • :
/ Daniel Robertz
  • Centre for Mathematical Sciences, Plymouth University, Drake Circus, Plymouth, PL4 8AA, United Kingdom of Great Britain and Northern Ireland
  • :
Published Online: 2016-10-11 | DOI: https://doi.org/10.1515/gcc-2016-0012

Abstract

The Anshel–Anshel–Goldfeld (AAG) key exchange protocol is based upon the multiple conjugacy problem for a finitely-presented group. The hardness in breaking this protocol relies on the supposed difficulty in solving the corresponding equations for the conjugating element in the group. Two such protocols based on polycyclic groups as a platform were recently proposed and were shown to be resistant to length-based attack. In this article we propose a parallel evolutionary approach which runs on multicore high-performance architectures. The approach is shown to be more efficient than previous attempts to break these protocols, and also more successful. Comprehensive data of experiments run with a GAP implementation are provided and compared to the results of earlier length-based attacks. These demonstrate that the proposed platform is not as secure as first thought and also show that existing measures of cryptographic complexity are not optimal. A more accurate alternative measure is suggested. Finally, a linear algebra attack for one of the protocols is introduced.

Keywords: Evolutionary algorithms; polycyclic groups; cryptography; Anshel–Anshel–Goldfeld keyagreement protocol; high performance computing; parallel

MSC 2010: 20P05; 68W30; 90C27; 94A60


Received: 2016-03-14

Published Online: 2016-10-11

Published in Print: 2016-11-01


Citation Information: Groups Complexity Cryptology. Volume 8, Issue 2, Pages 109–125, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2016-0012, October 2016

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