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Hierarchical Functional Encryption for Linear Transformations

  • Shiwei ZhangEmail author
  • Yi Mu
  • Guomin Yang
  • Xiaofen Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10342)

Abstract

In contrast to the conventional all-or-nothing encryption, functional encryption (FE) allows partial revelation of encrypted information based on the keys associated with different functionalities. Extending FE with key delegation ability, hierarchical functional encryption (HFE) enables a secret key holder to delegate a portion of its decryption ability to others and the delegation can be done hierarchically. All HFE schemes in the literature are for general functionalities and not very practical. In this paper, we focus on the functionality of linear transformations (i.e. matrix product evaluation). We refine the definition of HFE and further extend the delegation to accept multiple keys. We also propose a generic HFE construction for linear transformations with IND-CPA security in the standard model from hash proof systems. In addition, we give two instantiations from the DDH and DCR assumptions which to the best of our knowledge are the first practical concrete HFE constructions.

Keywords

Hierarchical Functional encryption Matrix product Hash proof system 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants 61502086 and 61572115, the foundation from Guangxi Colleges and Universities Key Laboratory of Cloud Computing and Complex Systems (No. YF16202) and the foundation from Guangxi Key Laboratory of Trusted Software (No. PF16116X).

References

  1. 1.
    Abdalla, M., Bourse, F., Caro, A.D., Pointcheval, D.: Better security for functional encryption for inner product evaluations. Cryptology ePrint Archive, Report 2016/011 (2016)Google Scholar
  2. 2.
    Abdalla, M., Bourse, F., Caro, A., Pointcheval, D.: Simple functional encryption schemes for inner products. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 733–751. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-46447-2_33 Google Scholar
  3. 3.
    Abdalla, M., Raykova, M., Wee, H.: Multi-input inner-product functional encryption from pairings. Cryptology ePrint Archive, Report 2016/425 (2016)Google Scholar
  4. 4.
    Agrawal, S., Libert, B., Stehlé, D.: Fully secure functional encryption for inner products, from standard assumptions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 333–362. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-53015-3_12 CrossRefGoogle Scholar
  5. 5.
    Ananth, P., Boneh, D., Garg, S., Sahai, A., Zhandry, M.: Differing-inputs obfuscation and applications. Cryptology ePrint Archive, Report 2013/689 (2013)Google Scholar
  6. 6.
    Bishop, A., Jain, A., Kowalczyk, L.: Function-hiding inner product encryption. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 470–491. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-48797-6_20 CrossRefGoogle Scholar
  7. 7.
    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). doi: 10.1007/11426639_26 CrossRefGoogle Scholar
  8. 8.
    Boneh, D., Sahai, A., Waters, B.: Functional encryption: definitions and challenges. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 253–273. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-19571-6_16 CrossRefGoogle Scholar
  9. 9.
    Brakerski, Z., Segev, G.: Hierarchical functional encryption. Cryptology ePrint Archive, Report 2015/1011 (2015)Google Scholar
  10. 10.
    Bresson, E., Catalano, D., Pointcheval, D.: A simple public-key cryptosystem with a double trapdoor decryption mechanism and its applications. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 37–54. Springer, Heidelberg (2003). doi: 10.1007/978-3-540-40061-5_3 CrossRefGoogle Scholar
  11. 11.
    Chandran, N., Goyal, V., Jain, A., Sahai, A.: Functional encryption: Decentralised and delegatable. Cryptology ePrint Archive, Report 2015/1017 (2015)Google Scholar
  12. 12.
    Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002). doi: 10.1007/3-540-46035-7_4 CrossRefGoogle Scholar
  13. 13.
    Diffie, W., Hellman, M.: New directions in cryptography. IEEE Trans. Inf. Theor. 22(6), 644–654 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. Cryptology ePrint Archive, Report 2013/451 (2013)Google Scholar
  15. 15.
    Katz, J., Sahai, A., Waters, B.: Predicate encryption supporting disjunctions, polynomial equations, and inner products. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 146–162. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-78967-3_9 CrossRefGoogle Scholar
  16. 16.
    Lewko, A., Okamoto, T., Sahai, A., Takashima, K., Waters, B.: Fully secure functional encryption: attribute-based encryption and (hierarchical) inner product encryption. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 62–91. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-13190-5_4 CrossRefGoogle Scholar
  17. 17.
    Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999). doi: 10.1007/3-540-48910-X_16 CrossRefGoogle Scholar
  18. 18.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: ACM Symposium on Theory of Computing - STOC 2005, pp. 84–93 (2005)Google Scholar
  19. 19.
    Zhang, S., Mu, Y., Yang, G.: Achieving IND-CCA security for functional encryption for inner products. In: Chen, K., Lin, D., Yung, M. (eds.) Inscrypt 2016. LNCS, vol. 10143, pp. 119–139. Springer, Cham (2017). doi: 10.1007/978-3-319-54705-3_8 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Shiwei Zhang
    • 1
    Email author
  • Yi Mu
    • 1
  • Guomin Yang
    • 1
  • Xiaofen Wang
    • 2
    • 3
  1. 1.Institute of Cybersecurity and Cryptology, School of Computing and Information TechnologyUniversity of WollongongWollongongAustralia
  2. 2.The Center for Cyber SecurityUniversity of Electronic Science and Technology of ChinaChengduChina
  3. 3.Guangxi Key Laboratory of Trusted SoftwareGuilin University of Electronic TechnologyGuilinChina

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