Skip to main content

McEliece Cryptosystem Implementation: Theory and Practice

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5299))

Abstract

Though it is old and considered fast, the implementation of McEliece public-key encryption scheme has never been thoroughly studied. We consider that problem here and we provide an implementation with a complete description of our algorithmic choices and parameters selection, together with the state of the art in cryptanalysis. This provides a reference for measuring speed and scalability of this cryptosystem. Compared with other, number-theory based, public key scheme, we demonstrate a gain of a factor at least 5 to 10.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barg, A.: Complexity issues in coding theory. In: Pless, V.S., Huffman, W.C. (eds.) Handbook of Coding theory, ch. 7, vol. I, pp. 649–754. North-Holland, Amsterdam (1998)

    Google Scholar 

  2. Bellare, M., Rogaway, P.: Optimal asymetric encryption. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  3. Berlekamp, E.R.: Factoring polynomials over large finite fields. Mathematics of Computation 24(111), 713–715 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  4. Berlekamp, E.R., McEliece, R.J., van Tilborg, H.C.: On the inherent intractability of certain coding problems. IEEE Transactions on Information Theory 24(3) (May 1978)

    Google Scholar 

  5. Berson, T.: Failure of the McEliece public-key cryptosystem under message-resend and related-message attack. In: Kalisky, B. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 213–220. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  6. Canteaut, A., Chabaud, F.: 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 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  7. Canteaut, A., Sendrier, N.: Cryptanalysis of the original McEliece cryptosystem. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 187–199. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  8. Cover, T.: Enumerative source encoding. IEEE Transactions on Information Theory 19(1), 73–77 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  9. Finiasz, M.: Nouvelles constructions utilisant des codes correcteurs d’erreurs en cryptographie à clef publique. Thèse de doctorat, École Polytechnique (October 2004)

    Google Scholar 

  10. Ganz, J.: Factoring polynomials using binary representations of finite fields. IEEE Transactions on Information Theory 43(1), 147–153 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hall, C., Goldberg, I., Schneier, B.: Reaction attacks against several public-key cryptosystems. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 2–12. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  12. Kobara, K., Imai, H.: Semantically secure McEliece public-key cryptosystems -Conversions for McEliece PKC. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 19–35. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Pointcheval, D.: Chosen-ciphertext security for any one-way cryptosystem. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 129–146. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  17. Sendrier, N.: Cryptosystèmes à clé publique basés sur les codes correcteurs d’erreurs. Mémoire d’habilitation à diriger des recherches, Université Paris 6 (March 2002)

    Google Scholar 

  18. Sendrier, N.: Encoding information into constant weight words. In: IEEE Conference, ISIT 2005, pp. 435–438, Adelaide, Australia (September 2005)

    Google Scholar 

  19. Sun, H.M.: Further cryptanalysis of the McEliece public-key cryptosystem. IEEE Trans. on communication letters 4(1), 18–19 (2000)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Biswas, B., Sendrier, N. (2008). McEliece Cryptosystem Implementation: Theory and Practice. In: Buchmann, J., Ding, J. (eds) Post-Quantum Cryptography. PQCrypto 2008. Lecture Notes in Computer Science, vol 5299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88403-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88403-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88402-6

  • Online ISBN: 978-3-540-88403-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics