Encyclopedia of Cryptography and Security

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

Niederreiter Encryption Scheme

  • Nicolas Sendrier
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-5906-5_385

Related Concepts


The Niederreiter PKC is a public-key encryption scheme based on error correcting codes. The cryptogram is a syndrome of an error pattern relatively to a parity check matrix of some linear code. Only the legal user, who knows the hidden algebraic structure of this code, can recover the error pattern, the cleartext, from the syndrome.


The system was introduced by Harald Niederreiter in 1986 [1]. Its security is, as for the McEliece public-key cryptosystem, related to difficult algorithmic problems of algebraic coding theory. It has the same advantages (efficient encryption and decryption) and drawbacks (public-key size, information rate) as the McEliece system. The block size, however, is smaller.

General idea

The cryptogram is a linear combination of t columns of a parity check matrix \(H\in {F}^{r\times n}_{q}\)

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Recommended Reading

  1. 1.
    Niederreiter H (1986) Knapsack-type cryptosystems and algebraic coding theory. Probl Contr Inf Theory 15(2):157–166MathSciNetGoogle Scholar
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    Sidel’nikov VM, Shestakov SO (1992) On cryptosystem based on generalized Reed-Solomon codes. Discret Math (in russian) 4(3):57–63MathSciNetGoogle Scholar
  3. 3.
    Sendrier N (1998) On the concatenated structure of a linear code. Appl Algebra Eng Commun Comput 9(3):221–242zbMATHMathSciNetGoogle Scholar
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    Li YX, Deng RH, Wang XM (1994) On the equivalence of McEliece’s and Niederreiter’s public-key cryptosystems. IEEE Trans Inf Theory 40(1):271–273zbMATHMathSciNetGoogle Scholar
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    Sendrier N (2005) Encoding information into constant weight words. In: IEEE conference, ISIT 2005, Adelaide, pp 435–438Google Scholar
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    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

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