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McEliece Public Key Cryptosystem

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Encyclopedia of Cryptography and Security

The Cryptosystem

This system was introduced by McEliece in 1978 [7] and is among the oldest public-key cryptography schemes. It's security is related to hard algorithmic problems of algebraic coding theory whereas for most other public-key systems it is connected to algorithmic number theory (see RSA public key encryption, Elliptic Curve Cryptography, etc.). Its main advantages are very efficient encryption and decryption procedures and a good practical and theoretical security. On the other hand, its main drawbacks are a public key of large size and a ciphertext which is larger than the cleartext.

General Idea

The cleartext of k binary digits is encoded into a codeword of \(n>k\) binary digits by means of some public encoder of a linear code of length n and dimension k (for the standard terminology of coding theory, we refer the reader to cyclic codes). Then the ciphertext is obtained by flipping t randomly chosen bits in this codeword.

If t is less than half the minimum Hamming...

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Notes

  1. 1.

    The cost for flipping t bits is negligible, it requires a random number generator though.

  2. 2.

    Ker(H) denotes the linear code of parity check matrix H.

  3. 3.

    For parameters suitable with the McEliece system, the equality always holds.

References

  1. Barg. A. (1998). “Complexity issues in coding theory.” Handbook of Coding Theory, vol. 1, chapter 7, eds. V.S. Pless and W.C. Huffman. North-Holland, Amsterdam, 649–754.

    Google Scholar 

  2. Berlekamp, E.R., R.J. McEliece, and H.C. van Tilborg (1978). “On the inherent intractability of certain coding problems.” IEEE Transactions on Information Theory, 24 (3), 384–386.

    Article  MATH  Google Scholar 

  3. Canteaut A. and F. Chabaud (1998). “A new algorithm for finding minimum-weight words in a linear code: Application to McEliece's cryptosystem and to narrow-sense BCH codes of length 511.” IEEE Transactions on Information Theory, 44 (1), 367–378.

    Article  MATH  MathSciNet  Google Scholar 

  4. Courtois. N., M. Finiasz, and N. Sendrier (2001). “How to achieve a McEliece-based digital signature scheme.” Advances in Cryptology—ASIACRYPT 2001, Lecture Notes in Computer Science, vol. 2248, ed. C. Boyd. Springer-Verlag, Berlin, 157–174.

    Google Scholar 

  5. Gabidulin, E., A. Paramonov, and O. Tretjakov (1991). “Ideals over a non-commutative ring and their application to cryptology.” Advances in Cryptology—EUROCRYPT'91, Lecture Notes in Computer Science, vol. 547, ed. D.W. Davies. Springer-Verlag, Berlin, 482–489.

    Google Scholar 

  6. Li, Y.X., R.H. Deng, and X.M. Wang (1994). “On the equivalence of McEliece's and Niederreiter's public-key cryptosystems.” IEEE Transactions on Information Theory, 40 (1), 271–273.

    Article  MATH  MathSciNet  Google Scholar 

  7. McEliece, R.J. (1978). “A public-key cryptosystem based on algebraic coding theory.” DSN Prog. Rep., Jet Prop. Lab., California Inst. Technol., Pasadena, CA, 114–116.

    Google Scholar 

  8. MacWilliams, F.J. and N.J.A. Sloane. (1977). The Theory of Error-Correcting Codes, chapter 12. Alternant, Goppa and other generalized BCH codes. North-Holland, Amsterdam.

    Google Scholar 

  9. Niederreiter, H. (1986). “Knapsack-type crytosystems and algebraic coding theory.” Prob. Contr. Inform. Theory, 15 (2), 157–166.

    MathSciNet  Google Scholar 

  10. Patterson, N.J. (1975). “The algebraic decoding of Goppa codes.” IEEE Transactions on Information Theory, 21 (2), 203–207.

    Article  MATH  MathSciNet  Google Scholar 

  11. Sendrier, N. (1998). “On the concatenated structure of a linear code.” AAECC, 9 (3), 221–242.

    Article  MATH  MathSciNet  Google Scholar 

  12. Sendrier, N. (2000). “Finding the permutation between equivalent codes: The support splitting algorithm.” IEEE Transactions on Information Theory, 46 (4), 1193–1203.

    Article  MATH  MathSciNet  Google Scholar 

  13. Sendrier, N. (2002). Cryptosystemes cl publique bass sur les codes correcteurs d'erreurs. Mmoire d'habilitation diriger des recherches, Universit Paris 6.

    Google Scholar 

  14. Sendrier, N. (2002). “On the security of the McEliece public-key cryptosystem.” Information, Coding and Mathematics, eds. M. Blaum, P.G. Farrell, and H. van Tilborg. Kluwer, 141–163. Proceedings of Workshop honoring Prof. Bob McEliece on his 60th birthday.

    Google Scholar 

  15. Sidel'nikov, V.M. (1994). “A public-key cryptosystem based on Reed-Muller codes.” Discrete Mathematics and Applications, 4 (3), 191–207.

    Article  MATH  MathSciNet  Google Scholar 

  16. Sidel'nikov, V.M. and S.O. Shestakov (1992). “On cryptosystem based on generalized Reed–Solomon codes.” Discrete Mathematics, 4 (3), 57–63 (in Russian).

    MATH  MathSciNet  Google Scholar 

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Authors
  1. Nicolas Sendrier
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Editors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

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© 2005 International Federation for Information Processing

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Sendrier, N. (2005). McEliece Public Key Cryptosystem. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_248

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