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Deterministic Identity Based Signature Scheme and Its Application for Aggregate Signatures

  • S. Sharmila Deva Selvi
  • S. Sree Vivek
  • C. Pandu Rangan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7372)

Abstract

Since the introduction of identity based cryptography in 1984 by Adi Shamir, several identity based signature schemes were reported. However, there are only two deterministic identity based signature schemes available in the literature and both of them use probabilistic private key generation and uses bilinear pairing. Moreover, these signatures consist of either two or more group elements and hence they are not ‘short’. Thus an interesting and challenging open question is to design a deterministic signature scheme which does not use randomness either in the key generation phase or in the signing phase, avoid bilinear pairing and having a ‘short’ signature-where the signature consists of only one element. While this problem is addressed by BLS scheme in the PKI based setting, this has been an open problem in the identity based setting since 1984. This paper settles the open problem affirmatively. Specifically, we propose a fully deterministic identity based signature scheme, without using bilinear pairing. The signature consists of just one group element of a composite order group and its security is related to strong RSA problem in the random oracle model. Our security reduction is tight as one need not use forking lemma during security reduction for fully deterministic signature schemes. The major and important consequence of our scheme is its use for aggregate signature scheme. Our scheme leads to the first full aggregate identity based signature scheme with no prior communication among different signers. Besides our aggregate signature scheme does not employ any computation that goes through several rounds.

Keywords

Identity Based Deterministic Signature Aggregate Signature Full Aggregation Random Oracle Model Provable Security 

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References

  1. 1.
    Bagherzandi, A., Jarecki, S.: Identity-Based Aggregate and Multi-Signature Schemes Based on RSA. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 480–498. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Barreto, P.S.L.M., Libert, B., McCullagh, N., Quisquater, J.-J.: Efficient and Provably-Secure Identity-Based Signatures and Signcryption from Bilinear Maps. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 515–532. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Bellare, M., Namprempre, C., Neven, G.: Unrestricted Aggregate Signatures. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 411–422. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Boldyreva, A., Gentry, C., O’Neill, A., Yum, D.H.: Ordered multisignatures and identity-based sequential aggregate signatures, with applications to secure routing. In: ACM Conference on Computer and Communications Security, CCS 2007, pp. 276–285. ACM (2007)Google Scholar
  5. 5.
    Boldyreva, A., Gentry, C., O’Neill, A., Yum, D.H.: Ordered multisignatures and identity-based sequential aggregate signatures, with applications to secure routing. Cryptology ePrint Archive, Report 2007/438 (2007), http://eprint.iacr.org/ (revised on February 21, 2010)
  6. 6.
    Boldyreva, A., Gentry, C., O’Neill, A., Yum, D.H.: New multiparty signature schemes for network routing applications. ACM Transactions on Information and System Security (TISSEC) 12(1), 1–39 (2008)CrossRefGoogle Scholar
  7. 7.
    Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and Verifiably Encrypted Signatures from Bilinear Maps. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 416–432. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Cha, J.C., 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
  9. 9.
    Cheng, X., Liu, J., Wang, X.: Identity-Based Aggregate and Verifiably Encrypted Signatures from Bilinear Pairing. In: Gervasi, O., Gavrilova, M.L., Kumar, V., Laganá, A., Lee, H.P., Mun, Y., Taniar, D., Tan, C.J.K. (eds.) ICCSA 2005, Part IV. LNCS, vol. 3483, pp. 1046–1054. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Freeman, D., Scott, M., Teske, E.: A taxonomy of pairing-friendly elliptic curves. Journal of Cryptology 23(2), 224–280 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    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
  12. 12.
    Gentry, C., Ramzan, Z.: Identity-Based Aggregate Signatures. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 257–273. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Goh, E.-J., Jarecki, S., Katz, J., Wang, N.: Efficient signature schemes with tight reductions to the diffie-hellman problems. Journal of Cryptology 20(4), 493–514 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Herranz, J.: Deterministic identity-based signatures for partial aggregation. The Computer Journal 49(3), 322–330 (2006)CrossRefGoogle Scholar
  15. 15.
    Hwang, J.Y., Lee, D.H., Yung, M.: Universal forgery of the identity-based sequential aggregate signature scheme. In: Computer and Communications Security, ASIACCS 2009, pp. 157–160. ACM (2009)Google Scholar
  16. 16.
    Lu, S., Ostrovsky, R., Sahai, A., Shacham, H., Waters, B.: Sequential Aggregate Signatures and Multisignatures Without Random Oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 465–485. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Ma, D.: Practical forward secure sequential aggregate signatures. In: Proceedings of the 2008 ACM Symposium on Information, Computer and Communications Security, ASIACCS 2008, pp. 341–352. ACM (2008)Google Scholar
  18. 18.
    Neven, G.: Efficient Sequential Aggregate Signed Data. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 52–69. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: The 2000 Symposium on Cryptography and Information Security, Okinawa, Japan, pp. 135–148 (January 2000)Google Scholar
  20. 20.
    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
  21. 21.
    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
  22. 22.
    Sree Vivek, S., Sharmila Deva Selvi, S., Shriram, J., Pandu Rangan, C.: Identity based partial aggregate signature scheme without pairing. Accepted in 35th IEEE Sarnoff Symposium (2012) full version, http://eprint.iacr.org/2010/461

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • S. Sharmila Deva Selvi
    • 1
  • S. Sree Vivek
    • 1
  • C. Pandu Rangan
    • 1
  1. 1.Theoretical Computer Science Laboratory, Department of Computer Science and EngineeringIndian Institute of Technology MadrasChennaiIndia

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