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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 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.
All the functions inside the same set \(\mathcal {F}_\rho \) have the same domain and the same range.
- 3.
The integer L can depend on the public parameters \(\mathsf {pp}\).
- 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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
O’Neill, A.: Definitional issues in functional encryption. Cryptology ePrint Archive, Report 2010/556 (2010). http://eprint.iacr.org/2010/556
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
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
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
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 International Association for Cryptologic Research
About this paper
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)