Skip to main content
SpringerLink
Log in

Improved identification schemes based on error-correcting codes

  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

As it is often the case in public-key cryptography, the first practical identification schemes were based on hard problems from number theory (factoring, discrete logarithms). The security of the proposed scheme depends on an NP-complete problem from the theory of error correcting codes: the syndrome decoding problem which relies on the hardness of decoding a binary word of given weight and given syndrome. Starting from Stern’s scheme [18], we define a dual version which, unlike the other schemes based on the SD problem, uses a generator matrix of a random linear binary code. This allows, among other things, an improvement of the transmission rate with regards to the other schemes. Finally, by using techniques of computation in a finite field, we show how it is possible to considerably reduce:

  • - the complexity of the computations done by the prover (which is usually a portable device with a limited computing power).

  • - the size of the data stored by the latter.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. Proceedings of the 1st ACM Conference Comput. Commun. Security, 62–73 (1993)

  2. Berlekamp, E. R.: Algebraic Coding Theory, McGraw-Hill Book Company, 1968

  3. Berlekamp, E. R., Mc Eliece, R. J., Van Tilborg, H. C. A.: On the inherent intractability of certain coding problems. IEEE Trans. Inform. Theory, 384–386 (1978)

  4. Berlekamp, E. R.: Bit-Serial Reed-Solomon Encoders. IEEE Trans. Inform. Theory, vol IT-28, 6, 869–874 (1982)

    Article  Google Scholar 

  5. Canteaut, A., Chabanne, H.: A further improvement of the workfactor in an attempt at breaking Mc Eliece’s cryptosystem. Proceedings of Eurocode’94, 163–167

  6. Chabaud, F.: On the Security of Some Cryptosystems Based On Error-Correcting Codes, Eurocrypt’94. Lecture Notes in Computer Science Vol. 950, pp. 131–139. Berlin, Heidelberg, New York: Springer 1995

    Google Scholar 

  7. Fiat, A., Shamir, A.: How To Prove Yourself: Practical Solutions to Identification and Signatures Problems. Advances in Cryptology, Crypto’86, Lecture Notes in Computer Science Vol. 263, pp. 186–194. Berlin, Hiedelberg, New York: Springer

  8. Feige, U., Fiat, A., Shamir, A.: Zero-knowledge proofs of identify. Proc. 19th ACM Symp. Theory of Computing, 210–217 (1987)

  9. Girault, M.: A (non-practical) three-pass identification protocol using coding theory, Advances in Cryptology, Auscrypt’90, Lecture Notes in Computer Science Vol. 453, pp. 265–272. Berlin, Heidelberg, New York: Springer

  10. Girault, M., Stern, J.: On the length of cryptographic hash-values used in identification schemes. Crypto’94, Lecture Notes in Computer Science Vol. 839, pp. 202–215 Berlin, Heidelberg, New York: Springer 1994

    Google Scholar 

  11. Goldwasser, S., Micali S., Rackoff, C.: The knowledge complexity of interactive proof systems. Proc. 17th ACM Symp. Theory Computing, 291–304 (1985)

  12. Harari, S. A New Authentication Algorithm, Proceedings of Coding Theory and Applications, Lecture Notes in Computer Science Vol. 388, pp. 91–105, Berlin, Heidelberg, New York: Springer 1988

    Google Scholar 

  13. Leon, J. S.: A probabilistic algorithm for computing minimum weights of large error-correcting codes, IEEE Trans. Inform. Theory, IT-34(5): 1354–1359

  14. MacWilliams, F. J., Sloane, N. J. A.: The Theory of error-correcting codes, North-Holland, Amsterdam-New-York-Oxford, 1977

    MATH  Google Scholar 

  15. Pointcheval, D.: Neural Networks and their cryptographic applications. Proc. Eurocode’94, 183–193

  16. Shamir, A.: An efficient identification scheme based on permuted kernels. Proc. Crypto’89, Lecture Notes in Computer Science Vol. 435, pp. 606–609, Berlin, Heidelberg, New York: Springer

  17. Stern, J.: A method for finding codewords of small weight. Coding Theory and Applications. Lecture Notes in Computer Science Vol. 434, pp. 173–180. Berlin, Heidelberg, New York: Springer

  18. Stern, J.: A new identification scheme based on syndrome decoding, Crypto’93, Lecture Notes in Computer Science Vol. 773, pp. 13–21, Berlin, Heidelberg, New York: Springer 1994

    Google Scholar 

  19. Stern, J.: Designing identification schemes with keys of short size. Crypto’94, Lecture Notes in Computer Science Vol. 839, pp. 164–173, Berlin, Heidelberg, New York: Springer 1994

    Google Scholar 

  20. Zierler, N.: On the Theorem of Gleason and Marsh. Proc. Am. Math. Soc., 9: 236–237, Math. Rev., 20: 851, 1958

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. G.E.C.T., Université de Toulon et du Var, B.P. 132, F-83957, La Garde Cedex, France

    Pascal Véron

Authors
  1. Pascal Véron
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pascal Véron.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Véron, P. Improved identification schemes based on error-correcting codes. AAECC 8, 57–69 (1997). https://doi.org/10.1007/s002000050053

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002000050053

Keywords

Search

Navigation