A Zero-Knowledge Identification Scheme Based on the q-ary Syndrome Decoding Problem

  • Pierre-Louis Cayrel
  • Pascal Véron
  • Sidi Mohamed El Yousfi Alaoui
Conference paper

DOI: 10.1007/978-3-642-19574-7_12

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6544)
Cite this paper as:
Cayrel PL., Véron P., El Yousfi Alaoui S.M. (2011) A Zero-Knowledge Identification Scheme Based on the q-ary Syndrome Decoding Problem. In: Biryukov A., Gong G., Stinson D.R. (eds) Selected Areas in Cryptography. SAC 2010. Lecture Notes in Computer Science, vol 6544. Springer, Berlin, Heidelberg


At CRYPTO’93, Stern proposed a 3-pass code-based identification scheme with a cheating probability of 2/3. In this paper, we propose a 5-pass code-based protocol with a lower communication complexity, allowing an impersonator to succeed with only a probability of 1/2. Furthermore, we propose to use double-circulant construction in order to dramatically reduce the size of the public key.

The proposed scheme is zero-knowledge and relies on an NP-complete coding theory problem (namely the q-ary Syndrome Decoding problem). The parameters we suggest for the instantiation of this scheme take into account a recent study of (a generalization of) Stern’s information set decoding algorithm, applicable to linear codes over arbitrary fields \(\mathbb{F}_q\); the public data of our construction is then 4 Kbytes, whereas that of Stern’s scheme is 15 Kbytes for the same level of security. This provides a very practical identification scheme which is especially attractive for light-weight cryptography.


post-quantum cryptography code-based cryptography Stern’s scheme identification zero-knowledge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pierre-Louis Cayrel
    • 1
  • Pascal Véron
    • 2
  • Sidi Mohamed El Yousfi Alaoui
    • 1
  1. 1.CASED – Center for Advanced Security Research DarmstadtDarmstadtGermany
  2. 2.IMATHUniversité du Sud Toulon-VarLa Garde CedexFrance

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