A parallel evolutionary approach to solving systems of equations in polycyclic groups
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Matthew J. Craven
und
Daniel Robertz
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.
Acknowledgements
The Centre for Mathematical Sciences at Plymouth University is gratefully acknowledged for its generous research support and encouragement. The authors also gratefully acknowledge the kind comments of the anonymous referees.
References
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© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Computing discrete logarithms using 𝒪((log q)2) operations from {+,-,×,÷,&}
- A parallel evolutionary approach to solving systems of equations in polycyclic groups
- Authenticated commutator key agreement protocol
- On the covering number of small symmetric groups and some sporadic simple groups
- Compositions of linear functions and applications to hashing
- Hydra group doubles are not residually finite
- The status of polycyclic group-based cryptography: A survey and open problems
- On irreducible algebraic sets over linearly ordered semilattices
- A nonlinear decomposition attack
Artikel in diesem Heft
- Frontmatter
- Computing discrete logarithms using 𝒪((log q)2) operations from {+,-,×,÷,&}
- A parallel evolutionary approach to solving systems of equations in polycyclic groups
- Authenticated commutator key agreement protocol
- On the covering number of small symmetric groups and some sporadic simple groups
- Compositions of linear functions and applications to hashing
- Hydra group doubles are not residually finite
- The status of polycyclic group-based cryptography: A survey and open problems
- On irreducible algebraic sets over linearly ordered semilattices
- A nonlinear decomposition attack
