Adaptively Secure Efficient Lattice (H)IBE in Standard Model with Short Public Parameters

  • Kunwar Singh
  • C. Pandurangan
  • A. K. Banerjee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7644)


Independent work by Chatterjee and Sarkar [9] and Naccache [16] provided a variant of Waters’ IBE to reduce public parameters. The idea is to divide an l-bit identity into l′ blocks of l/l′ so that size of the vector \(\overrightarrow{V}\) can be reduced from l elements of G to l′ elements of G. We name this technique as blocking technique. This leads to some associated degradation in security reduction. In this paper our contribution is two fold: First we apply Waters’ [21] idea to convert Agrawal et al. [1] selective-ID secure lattice HIBE to adaptive-ID secure HIBE then using blocking technique we reduce the public parameters. Second we present efficient lattice identity based encryption in standard model with smaller public key size which is variant of [1]. Using blocking technique our scheme reduces public key size by a factor of β at the cost of increasing (β − lg (β))2 number of bits in q where q is size of field Z q . There is an interesting trade-off between reducing the public parameter size and increase in the computational cost. For 160-bit identities we show that compared to scheme [1] the public parameter size can be reduced by almost 90% while increasing the computation cost by only 8.71% for appropriate choice of β.


Lattice Hierarchical Identity Base Encryption Standard model Learning with error(LWE) 


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  1. 1.
    Agrawal, S., Boneh, D., Boyen, X.: Efficient Lattice (H)IBE in the Standard Model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Agrawal, S., Boyen, X.: Identity-based encryption from lattices in the standard model (2009) (manuscript),
  3. 3.
    Alwen, J., Peikert, C.: Generating Shorter Bases for Hard Random Lattices. In: STACS 2009, pp. 75–86 (2009)Google Scholar
  4. 4.
    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
  5. 5.
    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
  6. 6.
    Boneh, D., Franklin, M.: Identity-Based Encryption from the Weil Pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–219. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Cash, D., Hofheinz, D., Kiltz, E.: How to Delegate a Lattice Basis. IACR Cryptology ePrint Archive 2009, p. 351 (2009)Google Scholar
  9. 9.
    Chatterjee, S., Sarkar, P.: Trading Time for Space: Towards an Efficient IBE Scheme with Short(er) Public Parameters in the Standard Model. In: Won, D.H., Kim, S. (eds.) ICISC 2005. LNCS, vol. 3935, pp. 424–440. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Chatterjee, S., Sarkar, P.: HIBE With Short Public Parameters Without Random Oracle. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 145–160. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Cocks, C.: An Identity Based Encryption Scheme Based on Quadratic Residues. In: IMA Int. Conf. 2001, pp. 360–363 (2001)Google Scholar
  12. 12.
    Dodis, Y., Ostrovsky, R., Reyzin, L., Smith, A.: Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data. SIAM J. Comput. 38(1), 97–139 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    Horwitz, J., Lynn, B.: Toward Hierarchical Identity-Based Encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 466–481. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Micciancio, D., Goldwasser, S.: Complexity of Lattice Problems: A Cryptographic Perspective. In: Engineering and Computer Science. The Kluwer International Series, vol. 671. Kluwer Academic Publishers, Boston (2002)Google Scholar
  16. 16.
    Naccache, D.: Secure and Practical Identity-Based Encryption. IACR Cryptology ePrint Archive 2005, p. 369 (2005)Google Scholar
  17. 17.
    Peikert, C.: Bonsai trees (or, arboriculture in lattice-based cryptography). Cryptology ePrint Archive, Report 2009/359 (2009)Google Scholar
  18. 18.
    Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC 2008, pp. 197–206 (2008)Google Scholar
  19. 19.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC 2005, pp. 84–93 (2005)Google Scholar
  20. 20.
    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
  21. 21.
    Waters, B.: Efficient Identity-Based Encryption Without Random Oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kunwar Singh
    • 1
  • C. Pandurangan
    • 2
  • A. K. Banerjee
    • 1
  1. 1.Computer Science and Engineering DepartmentNational Institute of TechnologyTiruchirappalliIndia
  2. 2.Computer Science and Engineering DepartmentIIT MadrasChennaiIndia

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