Encyclopedia of Cryptography and Security

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

Digital Signature Schemes from Codes

  • Philippe Gaborit
  • Nicolas Sendrier
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-5906-5_379

Related Concepts

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. 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
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    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 186–194Google Scholar
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    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 13–21Google Scholar
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    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 161–167Google Scholar
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    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 387–398Google Scholar
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    Véron P (1997) Improved identification schemes based on error-correcting codes. Appl Algebra Eng Commun Comput 8(1): 57–69zbMATHGoogle Scholar
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    Gaborit P, Girault M (2007) Lightweight code-based identification and signature. In: IEEE conference, ISIT’07, Nice. IEEE, pp 191–195Google Scholar
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    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 191–205Google Scholar
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    Cayrel PL, Otmani A, Vergnaud D (2007) On kabatianskii-krouk-smeets signatures. In: First international workshop, WAIFI 2007, Madrid. Lecture notes in computer science, vol 4547. Springer, Berlin, pp 237–251Google Scholar
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    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 69–78Google Scholar
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    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 1–16Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Philippe Gaborit
    • 1
  • Nicolas Sendrier
    • 2
  1. 1.XLIM-DMIUniversity of LimogesLimogesFrance
  2. 2.Project-Team SECRETINRIA Paris-RocquencourtLe ChesnayFrance