Skip to main content
SpringerLink
Log in

Construction of authentication codes with double arbiters over symplectic geometry

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

In a common authentication code with arbitration, the dishonest arbiter may make a threat to the security of authentication system. In this paper, an authentication code with double arbiters over symplectic geometry is constructed, and the relevant parameters and the probabilities of successful attacks are calculated. The model not only prevents deception from the opponent and members of the system, but also effectively limits the attacks of single arbiter. Moreover, the collusion attacks from arbiters and participators are difficult to succeed.

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. Brickell, E.F., Stinson, D.R. Authentication codes with multiple arbiters. In Advances in Cryptology-Eurocrypt’88, Lecture Notes in Computer Science, Springer-Verlag, Berlin, 1988, 330: 51–55

    Article  Google Scholar 

  2. Chen, S.D., Zhao, D.W. Two constructions of optimal cartesian authentication codes from unitary geometry over finite fields. Acta Mathematicae Applicatae Sinica, English Series, 29(4): 829–836 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen, S.D., Zhao, D.W. Construction of authentication codes with arbitration over symplectic geometry. Journal of Civil Aviation University of China, 29(1): 51–54 (2011)

    Google Scholar 

  4. Chen, S.D., Zhao, D.W. New construction of authentication codes with arbitration from pseudo-symplectic geometry over finite fields. Ars Combinatoria, 97A: 453–465 (2010)

    MATH  Google Scholar 

  5. Chen, S.D., Zhao, D.W. Construction of multi-receiver multi-fold authentication codes from singular symplectic geometry over finite fields. Algebra Colloquium, 20(04): 701–710 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chen, S.D., Zhao, D.W. Two constructions of multireceiver authentication codes from symplectic geometry over finite fields. Ars Combinatoria, 99: 193–203 (2011)

    MATH  MathSciNet  Google Scholar 

  7. Desmedt, Y., Yung, M. Arbitrated unconditionally secure authentication can be unconditionally protected against arbiter’s attacks. Advances in Cryptology. Proceedings of CRYPT’90, 1990, 537: 179–193

    Google Scholar 

  8. Gao, Y., Huo, L.Q. A new construction of the authentication codes with arbitration from singular symplectic geometry over the finite fields. Chinese Journal of Engineering Mathematics, 28(5): 629–641 (2011)

    MATH  MathSciNet  Google Scholar 

  9. Gao, Y., Huo, L.Q. New construction of the authentication codes with arbitration from singular symplectic geometry. Journal of Civil Aviation University of China, 28(1): 52–56 (2010)

    Google Scholar 

  10. Gao, Y., Shi, X.H., Wang, H.L. Construction of authentication codes with arbitration from singular symplectic geometry over finite fields. Acta Scientiarum Naturalium Universitatias Nankaiensis, 41(6): 72–77 (2008)

    MATH  Google Scholar 

  11. Johansson, T. Lower bounds on the probability of deception in authentication with arbitration. IEEE Transcations on Information Theory, 40(5): 1573–1585 (1994)

    Article  MATH  Google Scholar 

  12. Johansson, T. Further results on asymmetric authentication schemes. Information and Computation, 151: 100–133 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  13. Li, Y.X., Wang, X.M. Secret sharing schemes and linear block codes. Journal of China Institute of Communications, 14(3): 22–28 (1993)

    Google Scholar 

  14. Safavi-Naini, R., Wang, Y. A3-codes under collusion attacks. Proc. of Asiacrypt’99, LNCS 1716, Springer-Verlag, Berlin, 1999, 390–398

    Google Scholar 

  15. Shamir, A. How to share a secret. Communication of the ACM, 22(11): 612–613 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  16. Simmons, G.J. Message authentication with arbitration of transmitter receiver disputes. Proceedings of Crypto’87, Lecture Notes in Computer Science 304. Berlin, 1987, 151–165

    Google Scholar 

  17. Wan, Z.X. Geometry of Classical Groups over Finite Fields (Second Edition). Science Press, Beijing, 2002

    Google Scholar 

  18. Zhou, Z., Hu, Z.M. Authentication code with multiple arbiters. Beijing University of Posts and Telecommunications, 19(4): 75–80 (1996)

    MathSciNet  Google Scholar 

  19. Zhou, Z., Hu, Z.M. The constructions of A2-codes from conventional A-codes. Journal of Electronics, 19(4): 489–493 (1997)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Shang-di Chen & Hao Ma

Authors
  1. Shang-di Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hao Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the National Natural Science Foundation of China (No. 61179026) and the Fundamental Research Funds For the Central Universities (No. 3122013K001).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, Sd., Ma, H. Construction of authentication codes with double arbiters over symplectic geometry. Acta Math. Appl. Sin. Engl. Ser. 31, 1141–1152 (2015). https://doi.org/10.1007/s10255-015-0511-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-015-0511-3

Keywords

2000 MR Subject Classification

Search

Navigation