Compact Hierarchical IBE from Lattices in the Standard Model

  • Daode Zhang
  • Fuyang Fang
  • Bao Li
  • Haiyang Xue
  • Bei Liang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10631)


At Crypto’10, Agrawal et al. proposed a lattice-based selectively secure Hierarchical Identity-based Encryption (HIBE) scheme (ABB10b) with small ciphertext on the condition that \(\lambda \) (the length of identity at each level) is small in the standard model. In this paper, we present another lattice-based selectively secure HIBE scheme with depth d, using a gadget matrix \(\mathbf {G}'\in \mathbb {Z}_q^{n\times n\lceil \log _bq\rceil }\) with enough large \(b=2^d\) to replace the matrix \(\mathbf {B} \in \mathbb {Z}_q^{n\times m}\) in the HIBE scheme proposed by Agrawal et al. at Eurocrypt’10. In our HIBE scheme, not only the size of ciphertext at level \(\ell \) is \(O(\frac{d+\ell }{\lambda d})\) larger than the size in ABB10b and at least \(O(\ell )\) smaller than the sizes in the previous HIBE schemes except ABB10b, but also the size of the master public key is at least O(d) times smaller than the previous schemes.


Lattices Hierarchical identity-based encryption Selectively secure Compact public parameters 



We thank the anonymous ICICS’2017 reviewers for their helpful comments. This work is supported by the National Cryptography Development Fund MMJJ20170116 and the National Nature Science Foundation of China (No. 61602473, No. 61502480, No. 61672019, No. 61772522, No. 61379137, No. 61572495) and National Basic Research Programm of China (973 project, No. 2014CB340603).


  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). Scholar
  2. 2.
    Agrawal, S., Boneh, D., Boyen, X.: Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 98–115. Springer, Heidelberg (2010). Scholar
  3. 3.
    Banerjee, A., Peikert, C., Rosen, A.: Pseudorandom functions and lattices. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 719–737. Springer, Heidelberg (2012). Scholar
  4. 4.
    Bogdanov, A., Guo, S., Masny, D., Richelson, S., Rosen, A.: On the hardness of learning with rounding over small modulus. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9562, pp. 209–224. Springer, Heidelberg (2016). Scholar
  5. 5.
    Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523–552. Springer, Heidelberg (2010). Scholar
  6. 6.
    Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC 2008, pp. 197–206 (2008)Google Scholar
  7. 7.
    Gentry, C., Silverberg, A.: Hierarchical ID-based cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002). Scholar
  8. 8.
    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). Scholar
  9. 9.
    Katsumata, S., Yamada, S.: Partitioning via non-linear polynomial functions: more compact IBEs from ideal lattices and bilinear maps. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 682–712. Springer, Heidelberg (2016). Scholar
  10. 10.
    Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012). Scholar
  11. 11.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC 2005, pp. 84–93 (2005)Google Scholar
  12. 12.
    Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985). Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Daode Zhang
    • 1
    • 2
    • 3
  • Fuyang Fang
    • 4
  • Bao Li
    • 1
    • 2
    • 3
  • Haiyang Xue
    • 1
  • Bei Liang
    • 5
  1. 1.School of Cyber SecurityUniversity of Chinese Academy of SciencesBeijingChina
  2. 2.State Key Laboratory of Information SecurityInstitute of Information EngineeringBeijingChina
  3. 3.Science and Technology on Communication Security LaboratoryChengduChina
  4. 4.Information Science AcademyChina Electronics Technology Group CorporationBeijingChina
  5. 5.Chalmers University of TechnologyGothenburgSweden

Personalised recommendations