Encyclopedia of Cryptography and Security

2011 Edition
| Editors: Henk C. A. van Tilborg, Sushil Jajodia

Code-Based Cryptography

  • Nicolas Sendrier
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-5906-5_378

Related Concepts

Definition

Code-based cryptography includes all cryptosystems, symetric or asymetric, whose security relies, partially or totally, on the hardness of decoding in a linear error correcting code, possibly chosen with some particular structure or in a specific family (for instance, quasi-cyclic codes, or Goppa codes).

Applications

In the case of asymmetric primitives, the security relies, in addition to the hardness of decoding [ 1], on how well the trapdoor is concealed (typically the difficulty of obtaining a Goppa code distinguisher). The main primitives are:
  1. Public-key encryption schemes [23]

     
  2. Digital signature scheme [4]

    For other primitives, the security only depends on the hardness of decoding:

     
  3. Zero-knowledge authentification protocols [5, 6, 7]

     
  4. Pseudo-random number generator and stream cipher [89]

     
  5. Cryptographic hash function [10]

     

Recommended Reading

  1. 1.
    Berlekamp ER, McEliece RJ, van Tilborg HC (1978) On the inherent intractability of certain coding problems. IEEE Trans Inf Theory 24(3):384–386zbMATHCrossRefGoogle Scholar
  2. 2.
    McEliece RJ (1978) A public-key cryptosystem based on algebraic coding theory. DSN Progress Report, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, pp 114–116Google Scholar
  3. 3.
    Niederreiter H (1986) Knapsack-type cryptosystems and algebraic coding theory. Probl Contr Inf Theory 15(2):157–166MathSciNetGoogle Scholar
  4. 4.
    Courtois N, Finiasz M, Sendrier N (2001) How to achieve a McEliece-based digital signature scheme. In: Boyd C (ed) Advances in cryptology – ASI-ACRYPT 2001. Lecture notes in computer science, vol 2248. Springer, Berlin, pp 157–174CrossRefGoogle Scholar
  5. 5.
    Stern J (1993) A new identification scheme based on syndrome decoding. In: Stinson DR (ed) Advances in cryptology – CRYPTO’93. Lecture notes in computer science, vol 773. Springer, Berlin, pp 13–21CrossRefGoogle Scholar
  6. 6.
    Véron P (1995) A fast identification scheme. In: IEEE conference, ISIT’95, Whistler, p 359Google Scholar
  7. 7.
    Gaborit P, Girault M (2007) Lightweight code-based identification and signature. In: IEEE conference, ISIT’07, Nice. IEEE, pp 191–195Google Scholar
  8. 8.
    Fischer JB, Stern J (1996) An efficient pseudo-random generator provably as secure as syndrome decoding. In: Maurer U (ed) Advances in cryptology – EUROCRYPT’96. Lecture notes in computer science, vol 1070. Springer, Berlin, pp 245–255Google Scholar
  9. 9.
    Gaborit P, Laudaroux C, Sendrier N (2007) SYND: a very fast code-based stream cipher with a security reduction. In: IEEE conference, ISIT’07, Nice. IEEE, pp 186–190Google Scholar
  10. 10.
    Augot D, Finiasz M, Gaborit P, Manuel S, Sendrier N (2008) SHA-3 proposal: FSB. Submission to the SHA-3 NIST competitionGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Nicolas Sendrier
    • 1
  1. 1.Project-Team SECRETINRIA Paris-RocquencourtLe ChesnayFrance