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Cryptanalysis of the CLR-cryptosystem

Article

Abstract

In this paper we break a variant of the El-Gamal cryptosystem for a ring action of the matrix space \(E_p^{(m)}\) on \(\mathbb {Z}/p\mathbb {Z}\times \mathbb {Z}/p^2\mathbb {Z}\times \dots \times \mathbb {Z}/p^m\mathbb {Z}\). Also, we describe a general vulnerability of the protocol using tools from p-adic analysis.

Keywords

Finite fields Cryptography p-Adic numbers 

Mathematics Subject Classification

11T71 94A60 11S99 11C20 

Notes

Acknowledgements

The first author is thankful to the Swiss National Science Foundation under grant number 171248. The second author has been supported by the Swiss National Science Foundation under grant number 169510 We would also like to thank Karan Khathuria for his valuable inputs for the implementation of the attack. The authors are very grateful to the three anonymous referees whose suggestions greatly improved both the mathematics and the readability of the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.Institute of MathematicsUniversity of ZurichZurichSwitzerland

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