Abstract
We present a framework for transforming FHE (fully homomorphic encryption) schemes with no circuit privacy requirements into maliciously circuit-private FHE. That is, even if both maliciously formed public key and ciphertext are used, encrypted outputs only reveal the evaluation of the circuit on some well-formed input x*. Previous literature on FHE only considered semi-honest circuit privacy. Circuit-private FHE schemes have direct applications to computing on encrypted data. In that setting, one party (a receiver) holding an input x wishes to learn the evaluation of a circuit C held by another party (a sender). The goal is to make receiver’s work sublinear (and ideally independent) of \(\left\lvert C \right\rvert \), using a 2-message protocol. The transformation technique may be of independent interest, and have various additional applications. The framework uses techniques akin to Gentry’s bootstrapping and conditional disclosure of secrets (CDS [AIR01]) combining a non circuit private FHE scheme, with a homomorphic encryption (HE) scheme for a smaller class of circuits which is maliciously circuit-private. We devise the first known circuit private FHE, by instantiating our framework by various (standard) FHE schemes from the literature.
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Boneh, D., Kushilevitz, E., Ostrovsky, R., Skeith III, W.E.: Public key encryption that allows PIR queries. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 50–67. Springer, Heidelberg (2007)
Boneh, D., Kushilevitz, E., Ostrovsky, R., Skeith III, W.E.: Public Key Encryption That Allows PIR Queries. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 50–67. Springer, Heidelberg (2007)
Barak, B., Lindell, Y., Vadhan, S.P.: Lower bounds for non-black-box zero knowledge. In: Electronic Colloquium on Computational Complexity (ECCC), vol. (83) (2004)
Brakerski, Z.: Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868–886. Springer, Heidelberg (2012)
Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) lwe. Cryptology ePrint Archive, Report 2011/344 (2011), http://eprint.iacr.org/2011/344
Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: FOCS, pp. 136–145. IEEE Computer Society (2001)
Damgård, I., Faust, S., Hazay, C.: Secure Two-Party Computation with Low Communication. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 54–74. Springer, Heidelberg (2012)
Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of paillier’s probabilistic public-key system. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001)
Gentry, C.: A fully homomorphic encryption scheme. PhD thesis, Stanford University (2009), http://crypto.stanford.edu/craig
Gentry, C., Halevi, S., Vaikuntanathan, V.: i-Hop Homomorphic Encryption and Rerandomizable Yao Circuits. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 155–172. Springer, Heidelberg (2010)
Gertner, Y., Ishai, Y., Kushilevitz, E., Malkin, T.: Protecting data privacy in private information retrieval schemes. In: Vitter, J.S. (ed.) STOC, pp. 151–160. ACM (1998)
Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)
Gentry, C., Sahai, A., Waters, B.: Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013)
Halevi, S., Kalai, Y.T.: Smooth projective hashing and two-message oblivious transfer. J. Cryptology 25(1), 158–193 (2012)
Ishai, Y., Kushilevitz, E.: Perfect constant-round secure computation via perfect randomizing polynomials (2002)
Ishai, Y., Paskin, A.: Evaluating Branching Programs on Encrypted Data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 575–594. Springer, Heidelberg (2007), Full version in, http://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-info.cgi/2012/PHD/PHD-2012-16
Lipmaa, H.: An Oblivious Transfer Protocol with Log-Squared Communication. In: Zhou, J., López, J., Deng, R.H., Bao, F. (eds.) ISC 2005. LNCS, vol. 3650, pp. 314–328. Springer, Heidelberg (2005)
Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: Rao Kosaraju, S. (ed.) SODA, pp. 448–457. ACM/SIAM (2001)
van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. Cryptology ePrint Archive, Report 2009/616 (2009), http://eprint.iacr.org/2009/616
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Ostrovsky, R., Paskin-Cherniavsky, A., Paskin-Cherniavsky, B. (2014). Maliciously Circuit-Private FHE. In: Garay, J.A., Gennaro, R. (eds) Advances in Cryptology – CRYPTO 2014. CRYPTO 2014. Lecture Notes in Computer Science, vol 8616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44371-2_30
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