Abstract
In the public-key setting, known constructions of function-private functional encryption (FPFE) were limited to very restricted classes of functionalities like inner-product [Agrawal et al. - PKC 2015]. Moreover, its power has not been well investigated. In this paper, we construct FPFE for general functions and explore its powerful applications, both for general and specific functionalities.
As warmup, we construct from FPFE a natural generalization of a signature scheme endowed with functional properties, that we call functional anonymous signature (FAS) scheme. In a FAS, Alice can sign a circuit C chosen from some distribution D to get a signature \(\sigma \) and can publish a verification key that allows anybody holding a message m to verify that (1) \(\sigma \) is a valid signature of Alice for some (possibly unknown to him) circuit C and (2) \(C(m)=1\). Beyond unforgeability the security of FAS guarantees that the signature \(\sigma \) hide as much information as possible about C except what can be inferred from knowledge of D.
Then, we show that FPFE can be used to construct in a black-box way functional encryption schemes for randomized functionalities (RFE).
As further application, we show that specific instantiations of FPFE can be used to achieve adaptively-secure CNF/DNF encryption for bounded degree formulae (BoolEnc). Though it was known how to implement BoolEnc from inner-product encryption (IPE) [Katz et al. - EUROCRYPT 2008], as already observed by Katz et al. this reduction only works for selective security and completely breaks down for adaptive security; however, we show that the reduction works if the IPE scheme is function-private.
Finally, we present a general picture of the relations among all these related primitives. One key observation is that Attribute-based Encryption with function privacy implies FE, a notable fact that sheds light on the importance of the function privacy property for FE.
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.
The name quasi-siO is ours. The authors define a weakening of the their notion of siO (see the following) without explicitly naming it.
- 2.
Actually, for this implication to hold we only need “data privacy”, i.e., security of the encryptions. In fact, we could assume that the messages be encrypted in clear. Precisely, according to the definitions (given in the full version), we only need INDFP-Security and not also IND-Security.
- 3.
Such transformation was first reported in Boneh and Franklin [16].
- 4.
That is, it is not considered as a valid forgery if an adversary given a signature of circuit C can sign another circuit \(C'\) that computes the same function as C or is more restricted than C.
References
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)
Boneh, D., Di Crescenzo, G., Ostrovsky, R., Persiano, G.: Public key encryption with keyword search. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 506–522. Springer, Heidelberg (2004)
Boneh, D., Waters, B.: Conjunctive, subset, and range queries on encrypted data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 535–554. Springer, Heidelberg (2007). doi:10.1007/978-3-540-70936-7_29
Katz, J., Sahai, A., Waters, B.: Predicate encryption supporting disjunctions, polynomial equations, and inner products. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 146–162. Springer, Heidelberg (2008)
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)
Okamoto, T., Takashima, K.: Adaptively attribute-hiding (hierarchical) inner product encryption. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 591–608. Springer, Heidelberg (2012)
Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 54th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2013, Berkeley, CA, USA, pp. 40–49. IEEE Computer Society, 26–29 October 2013
Shen, E., Shi, E., Waters, B.: Predicate privacy in encryption systems. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 457–473. Springer, Heidelberg (2009). doi:10.1007/978-3-642-00457-5_27
Brakerski, Z., Segev, G.: Function-private functional encryption in the private-key setting. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 306–324. Springer, Heidelberg (2015)
Boneh, D., Raghunathan, A., Segev, G.: Function-private identity-based encryption: hiding the function in functional encryption. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 461–478. Springer, Heidelberg (2013)
Boneh, D., Raghunathan, A., Segev, G.: Function-private subspace-membership encryption and its applications. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 255–275. Springer, Heidelberg (2013)
Agrawal, S., Agrawal, S., Badrinarayanan, S., Kumarasubramanian, A., Prabhakaran, M., Amit S.: Function private functional encryption and property preserving encryption: New definitions and positive results. Cryptology ePrint Archive, (2013). http://eprint.iacr.org/2013/744
Agrawal, S., Agrawal, S., Badrinarayanan, S., Kumarasubramanian, A., Prabhakaran, M., Sahai, A.: On the practical security of inner product functional encryption. In: Katz, J. (ed.) Public-Key Cryptography - PKC 2015. LNCS, vol. 9020, pp. 777–798. Springer, Heidelberg (2015)
Bitansky, N., Canetti, R., Kalai, Y.T., Paneth, O.: On virtual grey box obfuscation for general circuits. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 108–125. Springer, Heidelberg (2014)
Goldwasser, S., Gordon, S.D., Goyal, V., Jain, A., Katz, J., Liu, F.-H., Sahai, A., Shi, E., Zhou, H.-S.: Multi-input functional encryption. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 578–602. Springer, Heidelberg (2014)
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)
Canetti, R.: Towards realizing random oracles: hash functions that hide all partial information. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 455–469. Springer, Heidelberg (1997)
Dent, A.W., Fischlin, M., Manulis, M., Stam, M., Schröder, D.: Confidential signatures and deterministic signcryption. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 462–479. Springer, Heidelberg (2010)
Goyal, V., Jain, A., Koppula, V., Sahai, A.: Functional encryption for randomized functionalities. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 325–351. Springer, Heidelberg (2015)
Iovino, V., Tang, Q., Żebrowski, K.: On the power of public-key functional encryption with function privacy. Cryptology ePrint Archive, Report 2015/470 (2015). http://eprint.iacr.org/2015/470
Agrawal, S., Freeman, D.M., Vaikuntanathan, V.: Functional encryption for inner product predicates from learning with errors. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 21–40. Springer, Heidelberg (2011)
Waters, B.: A punctured programming approach to adaptively secure functional encryption. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 678–697. Springer, Heidelberg (2015)
Acknowledgements
Vincenzo Iovino is supported by the Luxembourg National Research Fund (FNR grant no. 7884937) and Qiang Tang is supported by a CORE (junior track) grant from the Luxembourg National Research Fund.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Iovino, V., Tang, Q., Żebrowski, K. (2016). On the Power of Public-key Function-Private Functional Encryption. In: Foresti, S., Persiano, G. (eds) Cryptology and Network Security. CANS 2016. Lecture Notes in Computer Science(), vol 10052. Springer, Cham. https://doi.org/10.1007/978-3-319-48965-0_37
Download citation
DOI: https://doi.org/10.1007/978-3-319-48965-0_37
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48964-3
Online ISBN: 978-3-319-48965-0
eBook Packages: Computer ScienceComputer Science (R0)