A NP-Complete Problem in Coding Theory with Application to Code Based Cryptography

  • Thierry P. Berger
  • Cheikh Thiécoumba Gueye
  • Jean Belo KlamtiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10194)


It is easy to determine if a given code \(\mathcal {C}\) is a subcode of another known code \(\mathcal {D}\). For most of occurrences, it is easy to determine if two codes \(\mathcal {C}\) and \(\mathcal {D}\) are equivalent by permutation. In this paper, we show that determining if a code \(\mathcal {C}\) is equivalent to a subcode of \(\mathcal {D}\) is a NP-complete problem. We give also some arguments to show why this problem seems much harder to solve in practice than the Equivalence Punctured Code problem or the Punctured Code problem proposed by Wieschebrink [21]. For one application of this problem we propose an improvement of the three-pass identification scheme of Girault and discuss on its performance.


Code-based cryptography Equivalence Subcode Identification scheme 



This work was carried out with financial support of CEA-MITIC for CBC project and financial support of the government of Senegal’s Ministry of Hight Education and Research for ISPQ project.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Thierry P. Berger
    • 1
  • Cheikh Thiécoumba Gueye
    • 2
  • Jean Belo Klamti
    • 2
    Email author
  1. 1.XLIM-MATHIS, UMR CNRS 6172, Université de limogesLimoges CedexFrance
  2. 2.Faculté des Sciences et Techniques, Université Cheikh Anta Diop, DMI, LACGAADakarSenegal

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