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Encyclopedia of Cryptography and Security pp 344–347Cite as

Digital Signature Schemes from Codes

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Related Concepts

Error Correcting Codes; Signature Scheme; Syndrome Decoding Problem; Zero-Knowledge Protocols

Definition

There exist three different types of methods to obtain a signature scheme with code-based systems (like for number theory–based schemes). The first method (similar to the RSA signature) consists in being able to decode a random element of the syndrome space. This point of view is developed by Courtois-Finiasz-Sendrier [1] and necessitates to hide very large codes to obtain a reasonable probability of decoding (cf. “Digital Signature Scheme Based on McEliece”). The second method uses zero-knowledge identification algorithms together with the Fiat-Shamir paradigm [2], which permits to transform such an algorithm into a signature algorithm. It generally leads to very long signature. For coding theory, the Stern identification protocol [3] is the most efficient. The last method (similar to the El Gamal signature scheme) consists in building a special subset of the...

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Recommended Reading

  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 157–174

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  2. Fiat A, Shamir A (1987) How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko AM (ed) Advances in cryptology – CRYPTO’86. Lecture notes in computer science, vol 263. Springer, Berlin, pp 186–194

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  3. 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

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  4. Kabatianskii G, Krouk E, Smeets B (1997) A digital signature scheme based on random error-correcting codes. In: Goos G, Hartmanis J, van Leeuwen J (eds) Crytography and coding. Lecture notes in computer science, vol 1355. Springer, Berlin, pp 161–167

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  5. Pointcheval D, Stern J (1996) Security proofs for signature schemes. In: Maurer U (ed) Advances in cryptology – EUROCRYPT’96. Lecture notes in computer science, vol 1070. Springer, Berlin, pp 387–398

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  6. Véron P (1997) Improved identification schemes based on error-correcting codes. Appl Algebra Eng Commun Comput 8(1): 57–69

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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

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  8. Cayrel PL, Gaborit P, Prouff E (2008) Secure implementation of the stern authentication and signature schemes for low-resource devices. In: Grimaud G, Standaert FX (eds) CARDIS 2008. Lecture notes in computer science, vol 5189. Springer, Berlin, pp 191–205

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  10. Cayrel PL, Gaborit P, Girault M (2007) Identity-based identification and signature schemes using correcting codes. In: Augot D, Sendrier N, Tillich J-P (eds) International workshop on coding and cryptography, WCC 2007. INRIA, pp 69–78

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  11. Melchor CA, Cayrel PL, Gaborit P (2008) A new efficient threshold ring signature scheme based on coding theory. In: Buchmann J, Ding J (eds) PQCrypto. Lecture notes in computer science, vol 5299. Springer, Berlin, pp 1–16

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Author information

Authors and Affiliations

  1. XLIM-DMI, University of Limoges, Limoges, France

    Philippe Gaborit

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

    Nicolas Sendrier Dr.

Authors
  1. Philippe Gaborit
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  2. Nicolas Sendrier Dr.
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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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Gaborit, P., Sendrier, N. (2011). Digital Signature Schemes from Codes. 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_379

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