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Trading Time for Space: Towards an Efficient IBE Scheme with Short(er) Public Parameters in the Standard Model

  • Sanjit Chatterjee
  • Palash Sarkar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3935)

Abstract

At Eurocrypt 2005, Brent Waters proposed an efficient Identity Based Encryption scheme which is secure in the standard model. One drawback of this scheme is that the number of elements in the public parameter is rather large. Here we propose a generalisation of Waters scheme. In particular, we show that there is an interesting trade-off between the tightness of the security reduction and smallness of the public parameter. For a given security level, this implies that if one reduces the number of elements in public parameter then there is a corresponding increase in the computational cost due to the increase in group size. This introduces a flexibility in choosing the public parameter size without compromising in security. In concrete terms, to achieve 80-bit security for 160-bit identities we show that compared to Waters protocol the public parameter size can be reduced by almost 90 % while increasing the computation cost by 30%. Our construction is proven secure in the standard model without random oracles. Additionally, we show that CCA security can also be achieved through the reduction to oracle decision bilinear Diffie-Hellman problem (OBDH).

Keywords

identity based encryption standard model security parameter size 

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References

  1. 1.
    Abdalla, M., Bellare, M., Rogaway, P.: DHIES: An encryption scheme based on the Diffie-Hellman problem. In: Proceedings of CT-RSA 2001. LNCS, pp. 143–158. Springer, Heidelberg (2001)Google Scholar
  2. 2.
    Boneh, D., Boyen, X.: Efficient Selective-ID Secure Identity Based Encryption Without Random Oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Boneh, D., Boyen, X.: Secure Identity Based Encryption without Random Oracles. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 443–459. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Boneh, D., Boyen, X., Goh, E.: Hierarchical Identity Based Encryption with Constant Size Ciphertext. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 440–456. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Boneh, D., Canetti, R., Halevi, S., Katz, J.: Chosen-Ciphertext Security from Identity-Based Encryption. Journal Submission. Available from D. Boneh’s websiteGoogle Scholar
  6. 6.
    Boneh, D., Franklin, M.: Identity Based Encryption from the Weil Pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Boneh, D., Franklin, M.: Identity Based Encryption from the Weil Pairing. SIAM J. of Computing 32(3), 586–615 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Boneh, D., Katz, J.: Improved Efficiency for CCA-Secure Cryptosystems Built Using Identity Based Encryption. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 87–103. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient Algorithms for Pairing-Based Cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 354–368. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Barreto P.S.L.M., Naehrig, M.: Pairing-Friendly Elliptic Curves of Prime Order. Cryptology ePrint Archive, Report 2005/133 (Accepted for presentation at SAC 2005), Available from: http://eprint.iacr.org/2005/133/
  11. 11.
    Bellare, M., Rogaway, P.: Random Oracles are Practical: A Paradigm for Designing Efficient Protocols. In: ACM Conference on Computer and Communications Security - CCS 1993, pp. 62–73 (1993)Google Scholar
  12. 12.
    Boyen, X., Mei, Q., Waters, B.: Direct Chosen Ciphertext Security from Identity-Based Techniques. In: 12th ACM Conference on Computer and Communication Security – CCS (2005) (to appear); This version is available from Cryptology ePrint Archive, Report 2005/288Google Scholar
  13. 13.
    Cocks, C.: An Identity Based Encryption Scheme Based on Quadratic Residue. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, pp. 26–28. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Canetti, R., Halevi, S., Katz, J.: A Forward-Secure Public-Key Encryption Scheme. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 255–271. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext Security from Identity Based Encryption. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 207–222. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Galindo, D.: The Exact Security of Pairing Based Encryption and Signature Schemes. In: Workshop on Provable Security, INRIA, Paris, November 3-5 (2004) (Available from author’s website)Google Scholar
  17. 17.
    Galbraith, S., Harrison, K., Soldera, D.: Implementing the Tate Pairing. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol. 2369, pp. 324–337. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Gentry, C., Silverberg, A.: Hierarchical ID-Based Cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  19. 19.
    Horwitz, J., Lynn, B.: Towards Hierarchical Identity-Based Encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 466–481. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  20. 20.
    Koblitz, N., Menezes, A.: Another look at “provable security”, Cryptology ePrint Archive, Report 2004/152, final version (to appear in Journal of Cryptology), http://eprint.iacr.org/2004/152/
  21. 21.
    Lenstra, A.K., Verheul, E.R.: Selecting Cryptographic Key Sizes. Jr. Cryptology 14(4), 255–293 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Sarkar, P.: HEAD: Hybrid Encryption with Delegated Decryption Capability. In: Canteaut, A., Viswanathan, K. (eds.) INDOCRYPT 2004. LNCS, vol. 3348, pp. 230–244. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  23. 23.
    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
  24. 24.
    Waters, B.: Efficient Identity-Based Encryption Without Random Oracles. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, Springer, Heidelberg (2005); Also available from Cryptology ePrint Archive, Report 2004/180, http://eprint.iacr.org/2004/180/ Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sanjit Chatterjee
    • 1
  • Palash Sarkar
    • 1
  1. 1.Applied Statistics Unit, Indian Statistical InstituteKolkataIndia

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