Skip to main content
Springer Nature Link
Log in

More Efficient Verifiable Functional Encryption

  • Conference paper
  • First Online:
Provable and Practical Security (ProvSec 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13600))

Included in the following conference series:

  • 644 Accesses

Abstract

Functional encryption (FE for short) can be used to calculate a function output of a message when given the corresponding function key, without revealing other information about the message. However, the original FE does not guarantee the unforgeability of either ciphertexts or function keys. In 2016, Badrinarayanan et al. provide a new primitive called verifiable functional encryption (VFE for short), and give a generic transformation from FE to VFE using non-interactive witness-indistinguishable proof (NIWI proof). In their construction, each VFE ciphertext (resp. function key) consists of 4 FE ciphertexts (resp. function keys) generated from independent FE public keys (resp. secret keys) and a NIWI proof on the correctness.

In this paper, we show that there is redundancy in their construction. Concretely, we give a new construction for VFE which uses only 3 FE ciphertexts and function keys, and prove the verifiability and security of the construction. Since the NIWI proof is also simpler in our scheme, our construction may lead to an about 25% decrease in both ciphertext/key size and encryption/decryption cost.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Abdalla, M., Bourse, F., De 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). https://doi.org/10.1007/978-3-662-46447-2_33

    Chapter  Google Scholar 

  2. Agrawal, S., Libert, B., Maitra, M., Titiu, R.: Adaptive simulation security for inner product functional encryption. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12110, pp. 34–64. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45374-9_2

    Chapter  Google Scholar 

  3. 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). https://doi.org/10.1007/978-3-662-53015-3_12

    Chapter  Google Scholar 

  4. Ananth, P., Jain, A.: Indistinguishability obfuscation from compact functional encryption. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 308–326. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47989-6_15

    Chapter  Google Scholar 

  5. Badrinarayanan, S., Goyal, V., Jain, A., Sahai, A.: Verifiable functional encryption. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 557–587. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_19

    Chapter  Google Scholar 

  6. Badrinarayanan, S., Goyal, V., Jain, A., Sahai, A.: A note on VRFs from verifiable functional encryption. IACR Cryptology ePrint Archive, p. 51 (2017)

    Google Scholar 

  7. Barak, B., Ong, S.J., Vadhan, S.: Derandomization in cryptography. SIAM J. Comput. 37(2), 380–400 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Barbosa, M., Farshim, P.: Delegatable homomorphic encryption with applications to secure outsourcing of computation. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 296–312. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-27954-6_19

    Chapter  Google Scholar 

  9. Bitansky, N., Paneth, O.: ZAPs and non-interactive witness indistinguishability from indistinguishability obfuscation. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 401–427. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_16

    Chapter  MATH  Google Scholar 

  10. 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 

  11. 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). https://doi.org/10.1007/978-3-642-19571-6_16

    Chapter  Google Scholar 

  12. 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. ACM (2012)

    Google Scholar 

  13. Cheon, J.H., Kim, A., Kim, M., Song, Y.: Homomorphic encryption for arithmetic of approximate numbers. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 409–437. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_15

    Chapter  Google Scholar 

  14. Dwork, C., Naor, M.: Zaps and their applications. SIAM J. Comput. 36(6), 1513–1543 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Fisch, B., Vinayagamurthy, D., Boneh, D., Gorbunov, S.: IRON: functional encryption using intel SGX. In: ACM-CCS 2017, pp. 765–782. ACM (2017)

    Google Scholar 

  16. Gorbunov, S., Vaikuntanathan, V., Wee, H.: Attribute-based encryption for circuits. In: STOC’13, pp. 545–554. ACM (2013)

    Google Scholar 

  17. Gorbunov, S., Vaikuntanathan, V., Wee, H.: Predicate encryption for circuits from LWE. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 503–523. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_25

    Chapter  Google Scholar 

  18. Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: ACM-CCS 2006, pp. 89–98. ACM (2006)

    Google Scholar 

  19. Groth, J., Ostrovsky, R., Sahai, A.: Non-interactive zaps and new techniques for NIZK. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 97–111. Springer, Heidelberg (2006). https://doi.org/10.1007/11818175_6

    Chapter  Google Scholar 

  20. 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). https://doi.org/10.1007/978-3-540-78967-3_9

    Chapter  Google Scholar 

  21. Kim, S., Lewi, K., Mandal, A., Montgomery, H., Roy, A., Wu, D.J.: Function-hiding inner product encryption is practical. In: Catalano, D., De Prisco, R. (eds.) SCN 2018. LNCS, vol. 11035, pp. 544–562. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98113-0_29

    Chapter  Google Scholar 

  22. Marc, T., Stopar, M., Hartman, J., Bizjak, M., Modic, J.: Privacy-enhanced machine learning with functional encryption. In: Sako, K., Schneider, S., Ryan, P.Y.A. (eds.) ESORICS 2019. LNCS, vol. 11735, pp. 3–21. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-29959-0_1

    Chapter  Google Scholar 

  23. Naor, M., Ostrovsky, R., Venkatesan, R., Yung, M.: Perfect zero-knowledge arguments for NP using any one-way permutation. J. Crypt. 11(2), 87–108 (1998). https://doi.org/10.1007/s001459900037

    Article  MathSciNet  MATH  Google Scholar 

  24. Ryffel, T., Dufour-Sans, E., Gay, R., Bach, F., Pointcheval, D.: Partially encrypted machine learning using functional encryption. CoRR, abs/1905.10214 (2019)

    Google Scholar 

  25. Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_27

    Chapter  Google Scholar 

  26. Soroush, N., Iovino, V., Rial, A., Roenne, P.B., Ryan, P.Y.A.: Verifiable inner product encryption scheme. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12110, pp. 65–94. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45374-9_3

    Chapter  Google Scholar 

  27. Suzuki, T., Emura, K., Ohigashi, T., Omote, K.: Verifiable functional encryption using intel SGX. In: Huang, Q., Yu, Yu. (eds.) ProvSec 2021. LNCS, vol. 13059, pp. 215–240. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-90402-9_12

    Chapter  Google Scholar 

  28. Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_7

    Chapter  Google Scholar 

Download references

Acknowledgement

This work is partially supported by the National Key R &D Program of China (No. 2020YFA0712300) and the National Natural Science Foundation of China (No. 62202294).

Author information

Authors and Affiliations

  1. School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Geng Wang, Ming Wan & Dawu Gu

Authors
  1. Geng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ming Wan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dawu Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Geng Wang .

Editor information

Editors and Affiliations

  1. Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Chunpeng Ge

  2. University of Wollongong, Wollongong, NSW, Australia

    Fuchun Guo

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Wang, G., Wan, M., Gu, D. (2022). More Efficient Verifiable Functional Encryption. In: Ge, C., Guo, F. (eds) Provable and Practical Security. ProvSec 2022. Lecture Notes in Computer Science, vol 13600. Springer, Cham. https://doi.org/10.1007/978-3-031-20917-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-20917-8_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-20916-1

  • Online ISBN: 978-3-031-20917-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics