Efficient (Anonymous) Compact HIBE from Standard Assumptions

  • Somindu C. Ramanna
  • Palash Sarkar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8782)


We present two hierarchical identity-based encryption (HIBE) schemes, denoted as \(\mathcal{H}_{1}\) and \(\mathcal{H}_{2}\), from Type-3 pairings with constant sized ciphertexts. Scheme \(\mathcal{H}_{1}\) achieves anonymity while \(\mathcal{H}_{2}\) is non-anonymous. The constructions are obtained by extending the IBE scheme recently proposed by Jutla and Roy (Asiacrypt 2013). Security is based on the standard decisional Symmetric eXternal Diffie-Hellman (SXDH) assumption. In terms of provable security properties, previous direct constructions of constant-size ciphertext HIBE had one or more of the following drawbacks: security in the weaker model of selective-identity attacks; exponential security degradation in the depth of the HIBE; and use of non-standard assumptions. The security arguments for \(\mathcal{H}_{1}\) and \(\mathcal{H}_{2}\) avoid all of these drawbacks. Based on the current state-of-the-art, \(\mathcal{H}_{1}\) and \(\mathcal{H}_{2}\) are the schemes of choice for efficient implementation of (anonymous) HIBE constructions.


constant-size ciphertext HIBE asymmetric pairings standard assumptions dual-system encryption 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abdalla, M., et al.: Searchable encryption revisited: Consistency properties, relation to anonymous IBE, and extensions. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 205–222. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Blazy, O., Kiltz, E., Pan, J.: (Hierarchical) identity-based encryption from affine message authentication. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 408–425. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  3. 3.
    Boneh, D., Boyen, X., Goh, E.-J.: Hierarchical identity based encryption with constant size ciphertext. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 440–456. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Boneh, D., Franklin, M.K.: Identity-based encryption from the Weil pairing. SIAM J. Comput. 32(3), 586–615 (2003), Earlier version appeared in the proceedings of CRYPTO 2001Google Scholar
  5. 5.
    Boyen, X., Waters, B.: Anonymous hierarchical identity-based encryption (without random oracles). In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 290–307. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Chatterjee, S., Menezes, A.: On cryptographic protocols employing asymmetric pairings – the role of ψ revisited. Discrete Applied Mathematics 159(13), 1311–1322 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Chatterjee, S., Sarkar, P.: New constructions of constant size ciphertext HIBE without random oracle. In: Rhee, M.S., Lee, B. (eds.) ICISC 2006. LNCS, vol. 4296, pp. 310–327. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Chatterjee, S., Sarkar, P.: Constant size ciphertext HIBE in the augmented selective-id model and its extensions. J. UCS 13(10), 1367–1395 (2007)Google Scholar
  9. 9.
    Chen, J., Wee, H.: Fully, (almost) tightly secure IBE and dual system groups (2013),
  10. 10.
    Chow, S.S.M.: Removing Escrow from Identity-Based Encryption. In: Jarecki, Tsudik (eds.) [18], pp. 256–276Google Scholar
  11. 11.
    Cocks, C.: An identity based encryption scheme based on quadratic residues. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, pp. 360–363. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    De Caro, A., Iovino, V., Persiano, G.: Fully secure anonymous HIBE and secret-key anonymous IBE with short ciphertexts. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 347–366. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Ducas, L.: Anonymity from asymmetry: New constructions for anonymous HIBE. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 148–164. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Escala, A., Herold, G., Kiltz, E., Ràfols, C., Villar, J.: An algebraic framework for diffie-hellman assumptions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 129–147. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  15. 15.
    Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Applied Mathematics 156(16), 3113–3121 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    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
  17. 17.
    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
  18. 18.
    Jarecki, S., Tsudik, G. (eds.): PKC 2009. LNCS, vol. 5443. Springer, Heidelberg (2009)zbMATHGoogle Scholar
  19. 19.
    Jutla, C.S., Roy, A.: Shorter Quasi-Adaptive NIZK Proofs for Linear Subspaces. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 1–20. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. 20.
    Lee, K., Park, J., Lee, D.: Anonymous HIBE with short ciphertexts: full security in prime order groups. Designs, Codes and Cryptography, 1–31 (2013)Google Scholar
  21. 21.
    Lewko, A.B.: Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting. In: Pointcheval, Johansson [26] (eds.), pp. 318–335Google Scholar
  22. 22.
    Lewko, A., Waters, B.: New Techniques for Dual System Encryption and Fully Secure HIBE with Short Ciphertexts. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 455–479. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  23. 23.
    Okamoto, T., Takashima, K.: Achieving Short Ciphertexts or Short Secret-Keys for Adaptively Secure General Inner-Product Encryption. In: Lin, D., Tsudik, G., Wang, X. (eds.) CANS 2011. LNCS, vol. 7092, pp. 138–159. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  24. 24.
    Okamoto, T., Takashima, K.: Adaptively Attribute-Hiding (Hierarchical) Inner Product Encryption. In: Pointcheval, Johansson (eds.) [26], pp. 591–608Google Scholar
  25. 25.
    Park, J.H., Lee, D.H.: Anonymous HIBE: Compact construction over prime-order groups. IEEE Transactions on Information Theory 59(4), 2531–2541 (2013)CrossRefGoogle Scholar
  26. 26.
    Pointcheval, D., Johansson, T. (eds.): EUROCRYPT 2012. LNCS, vol. 7237. Springer, Heidelberg (2012)zbMATHGoogle Scholar
  27. 27.
    Ramanna, S.C., Chatterjee, S., Sarkar, P.: Variants of waters’ dual system primitives using asymmetric pairings - (extended abstract). In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 298–315. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  28. 28.
    Ramanna, S.C., Sarkar, P.: Anonymous constant-size ciphertext HIBE from asymmetric pairings. In: Stam, M. (ed.) IMACC 2013. LNCS, vol. 8308, pp. 344–363. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  29. 29.
    Ramanna, S.C., Sarkar, P.: Efficient (anonymous) compact hibe from standard assumptions. Cryptology ePrint Archive, Report 2013/806 (2013),
  30. 30.
    Seo, J.H., Kobayashi, T., Ohkubo, M., Suzuki, K.: Anonymous hierarchical identity-based encryption with constant size ciphertexts. In: Jarecki, Tsudik (eds.) [18], pp. 215–234Google Scholar
  31. 31.
    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
  32. 32.
    Shi, E., Waters, B.: Delegating capabilities in predicate encryption systems. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 560–578. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  33. 33.
    Smart, N.P., Vercauteren, F.: On computable isomorphisms in efficient asymmetric pairing-based systems. Discrete Applied Mathematics 155(4), 538–547 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Waters, B.: Dual System Encryption: Realizing Fully Secure IBE and HIBE under Simple Assumptions. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 619–636. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Somindu C. Ramanna
    • 1
  • Palash Sarkar
    • 1
  1. 1.Applied Statistics UnitIndian Statistical InstituteKolkataIndia

Personalised recommendations