International Workshop on Selected Areas in Cryptography

SAC 2009: Selected Areas in Cryptography pp 376-392

Compact McEliece Keys from Goppa Codes

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

DOI: 10.1007/978-3-642-05445-7_24

Volume 5867 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Misoczki R., Barreto P.S.L.M. (2009) Compact McEliece Keys from Goppa Codes. In: Jacobson M.J., Rijmen V., Safavi-Naini R. (eds) Selected Areas in Cryptography. SAC 2009. Lecture Notes in Computer Science, vol 5867. Springer, Berlin, Heidelberg

Abstract

The classical McEliece cryptosystem is built upon the class of Goppa codes, which remains secure to this date in contrast to many other families of codes but leads to very large public keys. Previous proposals to obtain short McEliece keys have primarily centered around replacing that class by other families of codes, most of which were shown to contain weaknesses, and at the cost of reducing in half the capability of error correction. In this paper we describe a simple way to reduce significantly the key size in McEliece and related cryptosystems using a subclass of Goppa codes, while also improving the efficiency of cryptographic operations to \(\tilde{O}(n)\) time, and keeping the capability of correcting the full designed number of errors in the binary case.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Rafael Misoczki
    • 1
  • Paulo S. L. M. Barreto
    • 1
  1. 1.Departamento de Engenharia de Computação e Sistemas Digitais (PCS), Escola PolitécnicaUniversidade de São PauloBrazil