Advertisement

Galindo-Garcia Identity-Based Signature Revisited

  • Sanjit Chatterjee
  • Chethan Kamath
  • Vikas Kumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7839)

Abstract

In Africacrypt 2009, Galindo-Garcia [12] proposed a lightweight identity-based signature (IBS) scheme based on the Schnorr signature. The construction is simple and claimed to be the most efficient IBS till date. The security is based on the discrete-log assumption and the security argument consists of two reductions: \(\mathcal{B}_{1}\) and \(\mathcal{B}_{2}\), both of which use the multiple-forking lemma [4] to solve the discrete-log problem (DLP).

In this work, we revisit the security argument given in [12]. Our contributions are two fold: (i) we identify several problems in the original argument and (ii) we provide a detailed new security argument which allows significantly tighter reductions. In particular, we show that the reduction \(\mathcal{B}_{1}\) in [12] fails in the standard security model for IBS [1], while the reduction \(\mathcal{B}_{2}\) is incomplete. To remedy these problems, we adopt a two-pronged approach. First, we sketch ways to fill the gaps by making minimal changes to the structure of the original security argument; then, we provide a new security argument. The new argument consists of three reductions: \(\mathcal{R}_{1}\), \(\mathcal{R}_{2}\) and \(\mathcal{R}_{3}\) and in each of them, solving the DLP is reduced to breaking the IBS. \(\mathcal{R}_{1}\) uses the general forking lemma [2] together with the programming of the random oracles and Coron’s technique [8]. Reductions \(\mathcal{R}_{2}\) and \(\mathcal{R}_{3}\), on the other hand, use the multiple-forking lemma along with the programming of the random oracles. We show that the reductions \(\mathcal{R}_{1}\) and \(\mathcal{R}_{2}\) are significantly tighter than their original counterparts.

Keywords

Identity-based signatures Galindo-Garcia identity-based signature Schnorr signatures Forking lemma Discrete-log assumption 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bellare, M., Namprempre, C., Neven, G.: Security proofs for identity-based identification and signature schemes. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 268–286. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Bellare, M., Neven, G.: Multi-signatures in the plain public-key model and a general forking lemma. In: Proceedings of the 13th ACM Conference on Computer and Communications Security, CCS 2006, pp. 390–399. ACM, New York (2006)Google Scholar
  3. 3.
    Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Proceedings of the 1st ACM Conference on Computer and Communications Security, CCS 1993, pp. 62–73. ACM, New York (1993)Google Scholar
  4. 4.
    Boldyreva, A., Palacio, A., Warinschi, B.: Secure proxy signature schemes for delegation of signing rights. Journal of Cryptology 25, 57–115 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Boneh, D., Boyen, X.: Efficient selective-id secure identity-based encryption without random oracles. In: Cachin, C., Camenisch, J. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Chatterjee, S., Kamath, C., Kumar, V.: Galindo-Garcia identity-based signature revisited. Cryptology ePrint Archive, Report 2012/646 (2012)Google Scholar
  7. 7.
    Choon, J., Cheon, J.H.: 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)CrossRefGoogle Scholar
  8. 8.
    Coron, J.-S.: On the exact security of full domain hash. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 229–235. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Sharmila Deva Selvi, S., Sree Vivek, S., Pandu Rangan, C.: Identity-based deterministic signature scheme without forking-lemma. In: Iwata, T., Nishigaki, M. (eds.) IWSEC 2011. LNCS, vol. 7038, pp. 79–95. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Fiat, A., Shamir, A.: How to prove yourself: Practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)CrossRefGoogle Scholar
  11. 11.
    Galindo, D.: Boneh-franklin identity based encryption revisited. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 791–802. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Galindo, D., Garcia, F.D.: A Schnorr-like lightweight identity-based signature scheme. In: Preneel, B. (ed.) AFRICACRYPT 2009. LNCS, vol. 5580, pp. 135–148. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Guillou, L.C., Quisquater, J.-J.: A “paradoxical” identity-based signature scheme resulting from zero-knowledge. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 216–231. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  14. 14.
    Herranz, J.: Deterministic identity-based signatures for partial aggregation. The Computer Journal 49(3), 322–330 (2005)CrossRefGoogle Scholar
  15. 15.
    Hess, F.: Efficient identity based signature schemes based on pairings. In: Nyberg, K., Heys, H. (eds.) SAC 2002. LNCS, vol. 2595, pp. 310–324. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. Journal of Cryptology 13, 361–396 (2000)CrossRefzbMATHGoogle Scholar
  17. 17.
    Radhakishan, V., Selvakumar, S.: Prevention of man-in-the-middle attacks using id-based signatures. In: Second International Conference on Networking and Distributed Computing - ICNDC 2011, pp. 165–169 (2011)Google Scholar
  18. 18.
    Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  19. 19.
    Shoup, V.: OAEP reconsidered. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 239–259. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  20. 20.
    Xie, M., Wang, L.: One-round identity-based key exchange with perfect forward security. Information Processing Letters 112(14-15), 587–591 (2012)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sanjit Chatterjee
    • 1
  • Chethan Kamath
    • 1
  • Vikas Kumar
    • 1
  1. 1.Dept. of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia

Personalised recommendations