Skip to main content
SpringerLink
Log in

Leveled Hierarchical Identity-Based Fully Homomorphic Encryption from Learning with Rounding

  • Conference paper
  • First Online:
Information Security Practice and Experience (ISPEC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11125))

Abstract

Hierarchical identity-based fully homomorphic encryption (HIBFHE) aggregates the advantages of both fully homomorphic encryption (FHE) and hierarchical identity-based encryption (HIBE) that permits data encrypted by HIBE to be processed homomorphically. This paper mainly constructs a new leveled HIBFHE scheme based on Learning with Rounding (\(\textsf {LWR}\)) problem, which removes Gaussian noise sampling in encryption process. In more detail, we use the lattice basis delegation method proposed by Agrawal, Boneh and Boyen at CRYPTO 2010 to generate delegated basis, while cleverly exploit a scaled rounding function of LWR problem to hide plaintext rather than adding an auxiliary Gaussian noise matrix. Besides, Gentry, Sahai and Waters constructed the first leveled LWE-based HIBFHE schemes from identity-based encryption scheme at CRYPTO 2013, in this work, however, we also focus on improving their leveled HIBFHE scheme, using Alperin-Sheriff and Peikert’s technically simpler method. We prove that our schemes are adaptively secure under classic lattice hardness assumptions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Leveled FHE is capable of evaluating arbitrary polynomial-depth circuits, without Gentry’s bootstrapping procedure.

References

  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). https://doi.org/10.1007/978-3-642-13190-5_28

    Chapter  MATH  Google Scholar 

  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). https://doi.org/10.1007/978-3-642-14623-7_6

    Chapter  MATH  Google Scholar 

  3. Alperin-Sheriff, J., Peikert, C.: Faster bootstrapping with polynomial error. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 297–314. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_17

    Chapter  Google Scholar 

  4. Alwen, J., Krenn, S., Pietrzak, K., Wichs, D.: Learning with rounding, revisited. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 57–74. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_4

    Chapter  Google Scholar 

  5. 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). https://doi.org/10.1007/978-3-642-29011-4_42

    Chapter  Google Scholar 

  6. 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). https://doi.org/10.1007/978-3-662-49096-9_9

    Chapter  MATH  Google Scholar 

  7. 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). https://doi.org/10.1007/3-540-44647-8_13

    Chapter  Google Scholar 

  8. Boneh, D., Gentry, C., Hamburg, M.: Space-efficient identity based encryption without pairings. In: 48th Annual IEEE Symposium on Foundations of Computer Science 2007. FOCS 2007, pp. 647–657. IEEE (2007)

    Google Scholar 

  9. Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868–886. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_50

    Chapter  Google Scholar 

  10. Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: Innovations in Theoretical Computer Science 2012, Cambridge, MA, USA, 8–10 January 2012, pp. 309–325 (2012)

    Google Scholar 

  11. Brakerski, Z., Langlois, A., Peikert, C., Regev, O., Stehlé, D.: Classical hardness of learning with errors. In: Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, pp. 575–584. ACM (2013)

    Google Scholar 

  12. Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: IEEE 52nd Annual Symposium on Foundations of Computer Science. FOCS 2011, Palm Springs, CA, USA, 22–25 October 2011, pp. 97–106 (2011)

    Google Scholar 

  13. Groot Bruinderink, L., Hülsing, A., Lange, T., Yarom, Y.: Flush, gauss, and reload – a cache attack on the BLISS lattice-based signature scheme. In: Gierlichs, B., Poschmann, A.Y. (eds.) CHES 2016. LNCS, vol. 9813, pp. 323–345. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53140-2_16

    Chapter  Google Scholar 

  14. 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). https://doi.org/10.1007/978-3-642-13190-5_27

    Chapter  Google Scholar 

  15. Clear, M., Hughes, A., Tewari, H.: Homomorphic encryption with access policies: characterization and new constructions. In: Youssef, A., Nitaj, A., Hassanien, A.E. (eds.) AFRICACRYPT 2013. LNCS, vol. 7918, pp. 61–87. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38553-7_4

    Chapter  Google Scholar 

  16. Clear, M., McGoldrick, C.: Bootstrappable identity-based fully homomorphic encryption. In: Gritzalis, D., Kiayias, A., Askoxylakis, I. (eds.) CANS 2014. LNCS, vol. 8813, pp. 1–19. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12280-9_1

    Chapter  Google Scholar 

  17. 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). https://doi.org/10.1007/3-540-45325-3_32

    Chapter  Google Scholar 

  18. Fang, F., Li, B., Lu, X., Liu, Y., Jia, D., Xue, H.: (Deterministic) hierarchical identity-based encryption from learning with rounding over small modulus. In: Proceedings of the 11th ACM on Asia Conference on Computer and Communications Security, pp. 907–912. ACM (2016)

    Google Scholar 

  19. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing. STOC 2009, Bethesda, MD, USA, 31 May–2 June 2009, pp. 169–178 (2009)

    Google Scholar 

  20. Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, pp. 197–206. ACM (2008)

    Google Scholar 

  21. Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_5

    Chapter  Google Scholar 

  22. Gentry, C., Silverberg, A.: Hierarchical ID-based cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36178-2_34

    Chapter  Google Scholar 

  23. Halevi, S., Shoup, V.: Bootstrapping for HElib. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 641–670. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_25

    Chapter  Google Scholar 

  24. 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). https://doi.org/10.1007/978-3-642-29011-4_41

    Chapter  Google Scholar 

  25. Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem. In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing, pp. 333–342. ACM (2009)

    Google Scholar 

  26. Pessl, P.: Analyzing the shuffling side-channel countermeasure for lattice-based signatures. In: Dunkelman, O., Sanadhya, S.K. (eds.) INDOCRYPT 2016. LNCS, vol. 10095, pp. 153–170. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49890-4_9

    Chapter  Google Scholar 

  27. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM (JACM) 56(6), 34 (2009)

    Article  MathSciNet  Google Scholar 

  28. 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). https://doi.org/10.1007/3-540-39568-7_5

    Chapter  Google Scholar 

  29. Sun, X., Yu, J., Wang, T., Sun, Z., Zhang, P.: Efficient identity-based leveled fully homomorphic encryption from RLWE. Secur. Commun. Netw. 9(18), 5155–5165 (2016)

    Article  Google Scholar 

  30. Wang, F., Wang, K., Li, B.: An efficient leveled identity-based FHE. Network and System Security. LNCS, vol. 9408, pp. 303–315. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25645-0_20

    Chapter  Google Scholar 

  31. 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). https://doi.org/10.1007/978-3-642-03356-8_36

    Chapter  Google Scholar 

  32. Xie, X., Xue, R., Zhang, R.: Deterministic public key encryption and identity-based encryption from lattices in the auxiliary-input setting. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 1–18. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32928-9_1

    Chapter  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers for their detailed reviews and helpful comments. This research is supported in part by the National Nature Science Foundation of China (Nos. 61672030, 61272040 and U1705264; Nos. 61572132 and U1705264).

Author information

Authors and Affiliations

  1. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

    Fucai Luo & Kunpeng Wang

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Fucai Luo & Kunpeng Wang

  3. College of Mathematic and Informatics, Fujian Normal University, Fuzhou, China

    Changlu Lin

Authors
  1. Fucai Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kunpeng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Changlu Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fucai Luo .

Editor information

Editors and Affiliations

  1. University of Aizu, Aizuwakamatsu, Japan

    Chunhua Su

  2. Meiji University, Tokyo, Japan

    Hiroaki Kikuchi

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Luo, F., Wang, K., Lin, C. (2018). Leveled Hierarchical Identity-Based Fully Homomorphic Encryption from Learning with Rounding. In: Su, C., Kikuchi, H. (eds) Information Security Practice and Experience. ISPEC 2018. Lecture Notes in Computer Science(), vol 11125. Springer, Cham. https://doi.org/10.1007/978-3-319-99807-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-99807-7_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99806-0

  • Online ISBN: 978-3-319-99807-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation