Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Finding Invalid Signatures in Pairing-Based Batches

  • Conference paper
Cryptography and Coding (Cryptography and Coding 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4887))

Included in the following conference series:

Abstract

This paper describes efficient methods for finding invalid digital signatures after a batch verification has failed. We present an improvement to the basic binary “divide-and-conquer” method, which can identify an invalid signature in half the time. We also present new, efficient methods for finding invalid signatures in some pairing-based batches with low numbers of invalid signatures. We specify these methods for the Cha-Cheon signature scheme of [5]. These new methods offer significant speedups for Cha-Cheon batches as well as other pairing-based signature schemes.

The views and conclusions contained in this presentation are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the National Security Agency, the Army Research Laboratory, or the U. S. Government.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bellare, M., Garay, J., Rabin, T.: Fast Batch Verification for Modular Exponentiation and Digital Signatures. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 236–250. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  2. Boneh, D., Lynn, B., Shacham, H.: Short Signatures from the Weil Pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  3. Boyd, C., Pavlovski, C.: Attacking and Repairing Batch Verification Schemes. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 58–71. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  4. Camenisch, J., Hohenberger, S., Pedersen, M.: Batch Verification of Short Signatures. In: EUROCRYPT 2007. LNCS, vol. 4515, pp. 246–263. Springer, Heidelberg (2007), See also Cryptology ePrint Archive, Report 2007/172 (2007), http://eprint.iacr.org/2007/172

  5. Cha, J., Cheon, J.: An Identity-Based Signature from Gap Diffie-Hellman Groups. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 18–30. Springer, Heidelberg (2002)

    Google Scholar 

  6. Cheon, J., Kim, Y., Yoon, H.: A New ID-based Signature with Batch Verification, Cryptology ePrint Archive, Report 2004/131 (2004), http://eprint.iacr.org/2004/131

  7. Granger, R., Page, D., Smart, N.P.: High Security Pairing-Based Cryptography Revisited. In: Hess, F., Pauli, S., Pohst, M. (eds.) ANTS VII. LNCS, vol. 4076, pp. 480–494. Springer, Heidelberg (2006)

    Google Scholar 

  8. Granger, R., Smart, N.P.: On Computing Products of Pairings, Cryptology ePrint Archive, Report 2006/172 (2006), http://eprint.iacr.org/2006/172

  9. Lee, S., Cho, S., Choi, J., Cho, Y.: Efficient Identification of Bad Signatures in RSA-Type Batch Signature. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E89-A(1), 74–80 (2006)

    Article  Google Scholar 

  10. Naccache, D., M’Raihi, D., Vaudenay, S., Raphaeli, D.: Can D.S.A. be improved? Complexity Trade-offs with the Digital Signature Standard. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 77–85. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  11. Pastuszak, J., Michalek, D., Pieprzyk, J., Seberry, J.: Identification of Bad Signatures in Batches. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 28–45. Springer, Heidelberg (2000)

    Google Scholar 

  12. Shanks, D.: Class Number, a Theory of Factorization and Genera. Proc. Symp. Pure Math. 20, 415–440 (1969) (AMS 1971)

    Google Scholar 

  13. Solinas, J.: Low-Weight Binary Representations for Pairs of Integers, Technical Report CORR 2001-41, Centre for Applied Cryptographic Research (2001)

    Google Scholar 

  14. Solinas, J.: Personal communication

    Google Scholar 

  15. Stanek, M.: Attacking LCCC Batch Verification of RSA Signatures, Cryptology ePrint Archive, Report 2006/111 (2006), http://eprint.iacr.org/2006/111

  16. Sury, B., Wang, T., Zhao, F.: Identities Involving Reciprocals of Binomial Coefficients. Journal of Integer Sequences 7, Article 04.2.8 (2004)

    Google Scholar 

  17. Yen, S., Laih, C.: Improved Digital Signature Suitable for Batch Verification. IEEE Transactions on Computers 44(7), 957–959 (1995)

    Article  MATH  Google Scholar 

  18. Yoon, H., Cheon, J.H., Kim, Y.: Batch verifications with ID-based signatures. In: Park, C., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 223–248. Springer, Heidelberg (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Security Agency, Fort Meade, MD 20755, USA

    Laurie Law

  2. JHU Applied Physics Laboratory Laurel, MD, 21102, USA

    Brian J. Matt

Authors
  1. Laurie Law
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brian J. Matt
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Steven D. Galbraith

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Law, L., Matt, B.J. (2007). Finding Invalid Signatures in Pairing-Based Batches. In: Galbraith, S.D. (eds) Cryptography and Coding. Cryptography and Coding 2007. Lecture Notes in Computer Science, vol 4887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77272-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-77272-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77271-2

  • Online ISBN: 978-3-540-77272-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation