Skip to main content

Decentralizing Inner-Product Functional Encryption

  • Conference paper
  • First Online:
Public-Key Cryptography – PKC 2019 (PKC 2019)

Abstract

Multi-client functional encryption (MCFE) is a more flexible variant of functional encryption whose functional decryption involves multiple ciphertexts from different parties. Each party holds a different secret key and can independently and adaptively be corrupted by the adversary. We present two compilers for MCFE schemes for the inner-product functionality, both of which support encryption labels. Our first compiler transforms any scheme with a special key-derivation property into a decentralized scheme, as defined by Chotard et al. (ASIACRYPT 2018), thus allowing for a simple distributed way of generating functional decryption keys without a trusted party. Our second compiler allows to lift an unnatural restriction present in existing (decentralized) MCFE schemes, which requires the adversary to ask for a ciphertext from each party. We apply our compilers to the works of Abdalla et al. (CRYPTO 2018) and Chotard et al. (ASIACRYPT 2018) to obtain schemes with hitherto unachieved properties. From Abdalla et al., we obtain instantiations of DMCFE schemes in the standard model (from DDH, Paillier, or LWE) but without labels. From Chotard et al., we obtain a DMCFE scheme with labels still in the random oracle model, but without pairings.

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

Access this chapter

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
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
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

Similar content being viewed by others

Notes

  1. 1.

    We note that our compiler actually is not restricted to the inner-product functionality. The only requirement is the special key derivation property.

  2. 2.

    All the functions inside the same set \(\mathcal {F}_\rho \) have the same domain and the same range.

  3. 3.

    The integer L can depend on the public parameters \(\mathsf {pp}\).

  4. 4.

    Note that the schemes in [3] were presented as a MIFE scheme with a unique encryption and secret key. It is however straightforward to split the encryption key and secret key into a key \(\mathsf {sk}_i\) for each party.

  5. 5.

    As in [3], note that these vectors have norm less than 3X, and as such, are a valid input to the encryption oracle. Furthermore, these queries are allowed, since as explained at the beginning of the proof: it holds that \(\langle \varvec{x}_i^{0,j}-\varvec{x}_i^{0,1},\varvec{y}_i\rangle =\langle \varvec{x}_i^{1,j}-\varvec{x}_i^{1,1},\varvec{y}_i\rangle \).

References

  1. Abdalla, M., Benhamouda, F., Kolhweiss, M., Waldner, H.: Decentralizing inner-product functional encryption. Cryptology ePrint Archive, Report 2019/020 (2019). http://eprint.iacr.org/2019/020

  2. 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 

  3. Abdalla, M., Catalano, D., Fiore, D., Gay, R., Ursu, B.: Multi-input functional encryption for inner products: function-hiding realizations and constructions without pairings. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part I. LNCS, vol. 10991, pp. 597–627. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96884-1_20

    Chapter  Google Scholar 

  4. Abdalla, M., Gay, R., Raykova, M., Wee, H.: Multi-input inner-product functional encryption from pairings. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017, Part I. LNCS, vol. 10210, pp. 601–626. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56620-7_21

    Chapter  Google Scholar 

  5. Agrawal, S., Libert, B., Stehlé, D.: Fully secure functional encryption for inner products, from standard assumptions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016, Part III. LNCS, vol. 9816, pp. 333–362. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53015-3_12

    Chapter  Google Scholar 

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

    Chapter  Google Scholar 

  7. Badrinarayanan, S., Gupta, D., Jain, A., Sahai, A.: Multi-input functional encryption for unbounded arity functions. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015, Part I. LNCS, vol. 9452, pp. 27–51. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48797-6_2

    Chapter  Google Scholar 

  8. Baltico, C.E.Z., Catalano, D., Fiore, D., Gay, R.: Practical functional encryption for quadratic functions with applications to predicate encryption. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part I. LNCS, vol. 10401, pp. 67–98. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_3

    Chapter  Google Scholar 

  9. Bellare, M., Desai, A., Jokipii, E., Rogaway, P.: A concrete security treatment of symmetric encryption. In: 38th FOCS, pp. 394–403. IEEE Computer Society Press, October 1997. https://doi.org/10.1109/SFCS.1997.646128

  10. Benhamouda, F., Joye, M., Libert, B.: A new framework for privacy-preserving aggregation of time-series data. ACM Trans. Inf. Syst. Secur. 18(3), 101–1021 (2016). https://doi.org/10.1145/2873069

    Article  Google Scholar 

  11. Bishop, A., Jain, A., Kowalczyk, L.: Function-hiding inner product encryption. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015, Part I. LNCS, vol. 9452, pp. 470–491. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48797-6_20

    Chapter  Google Scholar 

  12. 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 

  13. Brakerski, Z., Komargodski, I., Segev, G.: Multi-input functional encryption in the private-key setting: stronger security from weaker assumptions. J. Cryptol. 31(2), 434–520 (2018). https://doi.org/10.1007/s00145-017-9261-0

    Article  MathSciNet  MATH  Google Scholar 

  14. Chan, T.-H.H., Shi, E., Song, D.: Privacy-preserving stream aggregation with fault tolerance. In: Keromytis, A.D. (ed.) FC 2012. LNCS, vol. 7397, pp. 200–214. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32946-3_15

    Chapter  Google Scholar 

  15. Chotard, J., Dufour Sans, E., Gay, R., Phan, D.H., Pointcheval, D.: Decentralized multi-client functional encryption for inner product. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018, Part II. LNCS, vol. 11273, pp. 703–732. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03329-3_24

    Chapter  Google Scholar 

  16. Chotard, J., Dufour Sans, E., Gay, R., Phan, D.H., Pointcheval, D.: Multi-client functional encryption with repetition for inner product. Cryptology ePrint Archive, Report 2018/1021 (2018). http://eprint.iacr.org/2018/1021

  17. Datta, P., Dutta, R., Mukhopadhyay, S.: Functional encryption for inner product with full function privacy. In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016, Part I. LNCS, vol. 9614, pp. 164–195. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49384-7_7

    Chapter  Google Scholar 

  18. Emura, K.: Privacy-preserving aggregation of time-series data with public verifiability from simple assumptions. In: Pieprzyk, J., Suriadi, S. (eds.) ACISP 2017. LNCS, vol. 10343, pp. 193–213. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59870-3_11

    Chapter  MATH  Google Scholar 

  19. Fan, X., Tang, Q.: Making public key functional encryption function private, distributively. In: Abdalla, M., Dahab, R. (eds.) PKC 2018, Part II. LNCS, vol. 10770, pp. 218–244. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76581-5_8

    Chapter  Google Scholar 

  20. Goldwasser, S., et al.: Multi-input functional encryption. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 578–602. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_32

    Chapter  Google Scholar 

  21. Joye, M., Libert, B.: A scalable scheme for privacy-preserving aggregation of time-series data. In: Sadeghi, A.-R. (ed.) FC 2013. LNCS, vol. 7859, pp. 111–125. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39884-1_10

    Chapter  MATH  Google Scholar 

  22. Li, Q., Cao, G.: Efficient and privacy-preserving data aggregation in mobile sensing. In: 20th IEEE International Conference on Network Protocols, ICNP, pp. 1–10. IEEE Computer Society, Austin (2012). https://doi.org/10.1109/ICNP.2012.6459985

  23. O’Neill, A.: Definitional issues in functional encryption. Cryptology ePrint Archive, Report 2010/556 (2010). http://eprint.iacr.org/2010/556

  24. Sahai, A., Waters, B.R.: 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 

  25. Shi, E., Chan, T.H.H., Rieffel, E.G., Chow, R., Song, D.: Privacy-preserving aggregation of time-series data. In: NDSS 2011. The Internet Society, February 2011

    Google Scholar 

Download references

Acknowledgments

This work was supported in part by the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement 780108 (FENTEC), by the ERC Project aSCEND (H2020 639554), by the French Programme d’Investissement d’Avenir under national project RISQ P141580, and by the French FUI project ANBLIC.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michel Abdalla .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 International Association for Cryptologic Research

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Abdalla, M., Benhamouda, F., Kohlweiss, M., Waldner, H. (2019). Decentralizing Inner-Product Functional Encryption. In: Lin, D., Sako, K. (eds) Public-Key Cryptography – PKC 2019. PKC 2019. Lecture Notes in Computer Science(), vol 11443. Springer, Cham. https://doi.org/10.1007/978-3-030-17259-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-17259-6_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-17258-9

  • Online ISBN: 978-3-030-17259-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics