Encyclopedia of Cryptography and Security

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

Digital Signature Scheme Based on McEliece

  • Matthieu Finiasz
  • Nicolas Sendrier
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-5906-5_380

Related Concepts


In the CFS scheme [1], the digital signature is obtained by applying the decoding procedure of some public error correcting code on a digest of the message to be signed, obtained by a cryptographic hash function. Only the legal user, who knows the hidden algebraic structure of the code, can produce the signature, while anyone can check that the signature is a valid answer to the decoding problem.


The construction for the McEliece-based signature scheme was proposed by Courtois, Finiasz, and Sendrier in 2001 [1]. Despite its name, this construction is based on Niederreiter’s encryption scheme rather than the original McEliece cryptosystem. It was the first practical code-based digital signature scheme with a security reduction to the Syndrome Decoding Problem.

General Idea

The public key is a binary r ×n matrix H, which is an arbitrary parity check matrix of some t-e...

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Recommended Reading

  1. 1.
    Courtois N, Finiasz M, Sendrier N (2001) How to achieve a McEliece-based digital signature scheme. In: Boyd C (ed) Advances in cryptology – ASIACRYPT 2001. Lecture notes in computer science, vol 2248. Springer, Berlin, pp 157–174Google Scholar
  2. 2.
    Wagner D (2002) A generalized birthday problem. In: Yung M (ed) Advances in cryptology – CRYPTO’02. Lecture notes in computer science, vol 2442. Springer, Berlin, pp 288–303Google Scholar
  3. 3.
    Coron JS, Joux A (2004) Cryptanalysis of a provably secure cryptographic hash function. Cryptology ePrint Archive. http://eprint.iacr.org/2004/013/
  4. 4.
    Finiasz M, Sendrier N (2009) Security bounds for the design of code-based cryptosystems. In: Matsui M (ed) Advances in cryptology – ASIACRYPT 2009. Lecture notes in computer science, vol 5912. Springer, Berlin, pp 88–105Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Matthieu Finiasz
    • 1
  • Nicolas Sendrier
    • 2
  1. 1.ENSTAENSTAFrance
  2. 2.Project-Team SECRETINRIA Paris-RocquencourtLe ChesnayFrance