Abstract
We investigate the relationship between Functional Encryption (FE) and Fully Homomorphic Encryption (FHE), demonstrating that, under certain assumptions, a Functional Encryption scheme supporting evaluation on two ciphertexts implies Fully Homomorphic Encryption. We first introduce the notion of Randomized Functional Encryption (RFE), a generalization of Functional Encryption dealing with randomized functionalities of interest in its own right, and show how to construct an RFE from a (standard) semantically secure FE. For this we define the notion of entropically secure FE and use it as an intermediary step in the construction. Finally we show that RFEs constructed in this way can be used to construct FHE schemes thereby establishing a relation between the FHE and FE primitives. We conclude the paper by recasting the construction of RFE schemes in the context of obfuscation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adida, B., Wikström, D.: How to Shuffle in Public. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 555–574. Springer, Heidelberg (2007)
Agrawal, S., Gorbunov, S., Vaikuntanathan, V., Wee, H.: Functional encryption: new perspectives and lower bounds. Cryptology ePrint Archive, Report 2012/468 (2012)
Barbosa, M., Farshim, P.: On the semantic security of functional encryption schemes. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 143–161. Springer, Heidelberg (2013)
Bellare, M., Cash, D.: Pseudorandom functions and permutations provably secure against related-key attacks. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 666–684. Springer, Heidelberg (2010)
Bellare, M., Kohno, T.: A theoretical treatment of related-key attacks: RKA-PRPs, RKA-PRFs, and applications. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 491–506. Springer, Heidelberg (2003)
Bellare, M., O’Neill, A.: Semantically-secure functional encryption: possibility results, impossibility results and the quest for a general definition. Cryptology ePrint Archive, Report 2012/515 (2012)
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)
Canetti, R., Rothblum, G.N., Varia, M.: Obfuscation of Hyperplane Membership. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 72–89. Springer, Heidelberg (2010)
Chandran, N., Chase, M., Vaikuntanathan, V.: Functional re-encryption and collusion-resistant obfuscation. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 404–421. Springer, Heidelberg (2012)
Dodis, Y., Smith, A.: Correcting Errors Without Leaking Partial Information. In: Gabow, H.N., Fagin, R. (eds.) STOC 2005, pp. 654–663. ACM Press (May 2005)
Gentry, C.: A fully homomorphic encryption scheme. Ph.D. thesis, Stanford University (2009)
Goldwasser, S., Kalai, Y.T., Popa, R.A., Vaikuntanathan, V., Zeldovich, N.: Succinct functional encryption and applications: reusable garbled circuits and beyond. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) STOC 2013, pp. 555–564. ACM (2013)
Gorbunov, S., Vaikuntanathan, V., Wee, H.: Functional encryption with bounded collusions via multi-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 162–179. Springer, Heidelberg (2012)
Hohenberger, S., Rothblum, G.N., Shelat, A., Vaikuntanathan, V.: Securely Obfuscating Re-encryption. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 233–252. Springer, Heidelberg (2007)
Nielsen, J.B.: Separating random oracle proofs from complexity theoretic proofs: the non-committing encryption case. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 111–126. Springer, Heidelberg (2002)
O’Neill, A.: Definitional issues in functional encryption. Cryptology ePrint Archive, Report 2010/556 (2010)
Regev, O.: On Lattices, Learning with Errors, Random Linear Codes, and Cryptography. In: Gabow, H.N., Fagin, R. (eds.) STOC 2005, pp. 84–93. ACM Press (May 2005)
Russell, A.Y., Wang, H.: How to Fool an Unbounded Adversary with a Short Key. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 133–148. Springer, Heidelberg (2002)
Waters, B.: Functional encryption for regular languages. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 218–235. Springer, Heidelberg (2012)
Wee, H.: On Obfuscating Point Functions. In: Gabow, H.N., Fagin, R. (eds.) STOC 2005, pp. 523–532. ACM Press (May 2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alwen, J. et al. (2013). On the Relationship between Functional Encryption, Obfuscation, and Fully Homomorphic Encryption. In: Stam, M. (eds) Cryptography and Coding. IMACC 2013. Lecture Notes in Computer Science, vol 8308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45239-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-45239-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45238-3
Online ISBN: 978-3-642-45239-0
eBook Packages: Computer ScienceComputer Science (R0)