Cryptography and Coding 2007: Cryptography and Coding pp 34-53 | Cite as

Finding Invalid Signatures in Pairing-Based Batches

  • Laurie Law
  • Brian J. Matt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4887)

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.

Keywords

Pairing-based signatures ID-based signatures Batch verification 
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References

  1. 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)CrossRefGoogle Scholar
  2. 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)CrossRefGoogle Scholar
  3. 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)CrossRefGoogle Scholar
  4. 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. 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. 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. 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. 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. 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)CrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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. 12.
    Shanks, D.: Class Number, a Theory of Factorization and Genera. Proc. Symp. Pure Math. 20, 415–440 (1969) (AMS 1971)Google Scholar
  13. 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. 14.
    Solinas, J.: Personal communicationGoogle Scholar
  15. 15.
    Stanek, M.: Attacking LCCC Batch Verification of RSA Signatures, Cryptology ePrint Archive, Report 2006/111 (2006), http://eprint.iacr.org/2006/111
  16. 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. 17.
    Yen, S., Laih, C.: Improved Digital Signature Suitable for Batch Verification. IEEE Transactions on Computers 44(7), 957–959 (1995)MATHCrossRefGoogle Scholar
  18. 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

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Laurie Law
    • 1
  • Brian J. Matt
    • 2
  1. 1.National Security Agency, Fort Meade, MD 20755USA
  2. 2.JHU Applied Physics Laboratory Laurel, MD, 21102USA

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