International Workshop on Post-Quantum Cryptography

PQCrypto 2011: Post-Quantum Cryptography pp 179-199

Monoidic Codes in Cryptography

  • Paulo S. L. M. Barreto
  • Richard Lindner
  • Rafael Misoczki
Conference paper

DOI: 10.1007/978-3-642-25405-5_12

Volume 7071 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Barreto P.S.L.M., Lindner R., Misoczki R. (2011) Monoidic Codes in Cryptography. In: Yang BY. (eds) Post-Quantum Cryptography. PQCrypto 2011. Lecture Notes in Computer Science, vol 7071. Springer, Berlin, Heidelberg


At SAC 2009, Misoczki and Barreto proposed a new class of codes, which have parity-check matrices that are quasi-dyadic. A special subclass of these codes were shown to coincide with Goppa codes and those were recommended for cryptosystems based on error-correcting codes. Quasi-dyadic codes have both very compact representations and allow for efficient processing, resulting in fast cryptosystems with small key sizes. In this paper, we generalize these results and introduce quasi-monoidic codes, which retain all desirable properties of quasi-dyadic codes. We show that, as before, a subclass of our codes contains only Goppa codes or, for a slightly bigger subclass, only Generalized Srivastava codes. Unlike before, we also capture codes over fields of odd characteristic. These include wild Goppa codes that were proposed at SAC 2010 by Bernstein, Lange, and Peters for their exceptional error-correction capabilities. We show how to instantiate standard code-based encryption and signature schemes with our codes and give some preliminary parameters.


post-quantum cryptography codes efficient algorithms 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Paulo S. L. M. Barreto
    • 1
  • Richard Lindner
    • 2
  • Rafael Misoczki
    • 3
  1. 1.Departmento de Engenharia de Computação e Sistemas Digitais (PCS)Escola Politécnica, Universidade de São PauloBrasil
  2. 2.Department of Computer ScienceTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Project SECRET, INRIA-RocquencourtRocquencourtFrance