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Randomized Decoding of Gabidulin Codes Beyond the Unique Decoding Radius

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12100)

Abstract

We address the problem of decoding Gabidulin codes beyond their unique error-correction radius. The complexity of this problem is of importance to assess the security of some rank-metric code-based cryptosystems. We propose an approach that introduces row or column erasures to decrease the rank of the error in order to use any proper polynomial-time Gabidulin code error-erasure decoding algorithm. The expected work factor of this new randomized decoding approach is a polynomial term times \(q^{m(n-k)-w(n+m)+w^2+\min \{2\xi (\frac{n+k}{2}-\xi ),wk\} }\), where n is the code length, q the size of the base field, m the extension degree of the field, k the code dimension, w the number of errors, and \(\xi := w-\tfrac{n-k}{2}\). It improves upon generic rank-metric decoders by an exponential factor.

Keywords

Gabidulin codes Decoding Rank metric Code-based cryptography 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Technical University of Munich (TUM)MunichGermany
  2. 2.German Aerospace Center (DLR)Oberpfaffenhofen-WesslingGermany
  3. 3.Technical University of Denmark (DTU)LyngbyDenmark
  4. 4.Univ Rennes, DGA MI, CNRS, IRMAR - UMR 6625RennesFrance

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