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Code-Based Cryptography

  • Reference work entry
Encyclopedia of Cryptography and Security

Related Concepts

Error Correcting Codes; McEliece Public Key Cryptosystem; Syndrome Decoding Problem

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 [2,  3]

  2. –

    Digital signature scheme [4]

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

  3. –

    Zero-knowledge authentification protocols [5–7]

  4. –

    Pseudo-random number generator and stream cipher [8,  9]

  5. –

    Cryptographic hash function [10]

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Recommended Reading

  1. Berlekamp ER, McEliece RJ, van Tilborg HC (1978) On the inherent intractability of certain coding problems. IEEE Trans Inf Theory 24(3):384–386

    Article  MATH  Google Scholar 

  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 114–116

    Google Scholar 

  3. Niederreiter H (1986) Knapsack-type cryptosystems and algebraic coding theory. Probl Contr Inf Theory 15(2):157–166

    MathSciNet  Google Scholar 

  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 157–174

    Chapter  Google Scholar 

  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 13–21

    Chapter  Google Scholar 

  6. Véron P (1995) A fast identification scheme. In: IEEE conference, ISIT’95, Whistler, p 359

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  7. Gaborit P, Girault M (2007) Lightweight code-based identification and signature. In: IEEE conference, ISIT’07, Nice. IEEE, pp 191–195

    Google Scholar 

  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 245–255

    Google Scholar 

  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 186–190

    Google Scholar 

  10. Augot D, Finiasz M, Gaborit P, Manuel S, Sendrier N (2008) SHA-3 proposal: FSB. Submission to the SHA-3 NIST competition

    Google Scholar 

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Author information

Authors and Affiliations

  1. Project-Team SECRET, INRIA Paris-Rocquencourt, B.P. 105, 78153, Le Chesnay, France

    Nicolas Sendrier (Dr.)

Authors
  1. Nicolas Sendrier
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

  2. Center for Secure Information Systems, George Mason University, Fairfax, VA, 22030-4422, USA

    Sushil Jajodia

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Sendrier, N. (2011). Code-Based Cryptography. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_378

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