Ideals over a Non-Commutative Ring and their Application in Cryptology

  • E. M. Gabidulin
  • A. V. Paramonov
  • O. V. Tretjakov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 547)


A new modification of the McEliece public-key cryptosystem is proposed that employs the so-called maximum-rank-distance (MRD) codes in place of Goppa codes and that hides the generator matrix of the MRD code by addition of a randomly-chosen matrix. A short review of the mathematical background required for the construction of MRD codes is given. The cryptanalytic work function for the modified McEliece system is shown to be much greater than that of the original system. Extensions of the rank metric are also considered.


Generator Matrix Left Ideal Cyclic Shift Rank Distance Goppa Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • E. M. Gabidulin
    • 1
  • A. V. Paramonov
    • 1
  • O. V. Tretjakov
    • 1
  1. 1.Moscow Institute of Physics and TechnologyDolgoprudnii, Moscow RegionUSSR

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