Abstract
This paper describes a 1-out-of-N oblivious transfer (OT) extension protocol with active security, which achieves very low overhead on top of the passively secure protocol of Kolesnikov and Kumaresan (Crypto 2011). Our protocol obtains active security using a consistency check which requires only simple computation and has a communication overhead that is independent of the total number of OTs to be produced. We prove its security in both the random oracle model and the standard model, assuming a variant of correlation robustness. We describe an implementation, which demonstrates our protocol only costs around 5–30% more than the passively secure protocol.
Random 1-out-of-N OT is a key building block in recent, very efficient, passively secure private set intersection (PSI) protocols. Our random OT extension protocol has the interesting feature that it even works when N is exponentially large in the security parameter, provided that the sender only needs to obtain polynomially many outputs. We show that this can be directly applied to improve the performance of PSI, allowing the core private equality test and private set inclusion subprotocols to be carried out using just a single OT each. This leads to a reduction in communication of up to 3 times for the main component of PSI.
Full version available at http://eprint.iacr.org/2016/933.pdf
M. Orrù–Work done while visiting University of Bristol.
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Notes
- 1.
We observe an interesting connection between our protocol and additively homomorphic UC commitment schemes [FJNT16, CDD+16]: our protocol essentially runs a homomorphic commitment protocol and hashes the resulting commitments to obtain random OTs. However, this mechanism seems very specific to the workings of these commitment schemes and appears unlikely to lead to a generic transformation.
- 2.
Note that our security reduction requires fixing the adversary’s random coins, so is non-uniform. Obtaining a uniform reduction seems to need at least \(\kappa + s\) base OTs, for statistical security parameter s.
- 3.
- 4.
References
Asharov, G., Lindell, Y., Schneider, T., Zohner, M.: More efficient oblivious transfer and extensions for faster secure computation. In: ACM Conference on Computer and Communications Security, CCS 2013, pp. 535–548 (2013)
Asharov, G., Lindell, Y., Schneider, T., Zohner, M.: More efficient oblivious transfer extensions with security for malicious adversaries. In: Proceedings of Advances in Cryptology - EUROCRYPT 2015, Sofia, Bulgaria, Part I, pp. 673–701, 26–30 April 2015
Asharov, G., Lindell, Y., Schneider, T., Zohner, M.: More efficient oblivious transfer extensions. J. Cryptol. 1–54 (2016)
Aumasson, J.-P., Neves, S., Wilcox-O’Hearn, Z., Winnerlein, C.: BLAKE2: simpler, smaller, fast as MD5. In: Jacobson, M., Locasto, M., Mohassel, P., Safavi-Naini, R. (eds.) ACNS 2013. LNCS, vol. 7954, pp. 119–135. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38980-1_8
Beaver, D.: Correlated pseudorandomness and the complexity of private computations. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 479–488. ACM (1996)
Cascudo, I., Damgård, I., David, B., Döttling, N., Nielsen, J.B.: Rate-1, linear time and additively homomorphic UC commitments. In: Proceedings of Advances in Cryptology - CRYPTO 2016, Santa Barbara, CA, USA, Part III, pp. 179–207, 14–18 August 2016
Chou, T., Orlandi, C.: The simplest protocol for oblivious transfer. In: Progress in Cryptology - LATINCRYPT 2015, Guadalajara, Mexico, pp. 40–58, 23–26 August 2015
Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Commun. ACM 28(6), 637–647 (1985)
Frederiksen, T.K., Jakobsen, T.P., Nielsen, J.B., Trifiletti, R.: On the complexity of additively homomorphic UC commitments. In: Proceedings of Theory of Cryptography - TCC 2016-A, Tel Aviv, Israel, 10–13 January 2016, Part I, pp. 542–565 (2016)
Ishai, Y., Kilian, J., Nissim, K., Petrank, E.: Extending oblivious transfers efficiently. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 145–161. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45146-4_9
Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Proceedings of the Twenty-First Annual ACM Symposium on Theory of Computing, pp. 44–61. ACM (1989)
Kolesnikov, V., Kumaresan, R.: Improved OT extension for transferring short secrets. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 54–70. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40084-1_4
Kolesnikov, V., Kumaresan, R., Rosulek, M., Trieu, N.: Efficient batched oblivious PRF with applications to private set intersection. In: ACM Conference on Computer and Communications Security, CCS (2016)
Keller, M., Orsini, E., Scholl, P.: Actively secure OT extension with optimal overhead. In: Advances in Cryptology - CRYPTO Santa Barbara, CA, USA, pp. 724–741, 16–20 August 2015
Keller, M., Orsini, E., Scholl, P.: MASCOT: faster malicious arithmetic secure computation with oblivious transfer. In: ACM Conference on Computer and Communications Security, Vienna, Austria, pp. 830–842 (2016)
Lambæk, M.: Breaking and fixing private set intersection protocols. Cryptology ePrint Archive, Report 2016/665 (2016)
Larraia, E., Orsini, E., Smart, N.P.: Dishonest majority multi-party computation for binary circuits. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8617, pp. 495–512. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44381-1_28
Nielsen, J.B., Nordholt, P.S., Orlandi, C., Burra, S.S.: A new approach to practical active-secure two-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 681–700. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32009-5_40
Naor, M., Pinkas, B.: Oblivious transfer and polynomial evaluation. In: Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, Atlanta, GA, USA, pp. 245–254 (1999)
Pinkas, B., Schneider, T., Segev, G., Zohner, M.: Phasing: private set intersection using permutation-based hashing. In: 24th USENIX Security Symposium, Washington, D.C., USA, 12–14 August 2015, pp. 515–530 (2015)
Pinkas, B., Schneider, T., Zohner, M.: Faster private set intersection based on OT extension. In: 23rd USENIX Security Symposium, San Diego, CA, pp. 797–812, August 2014
Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85174-5_31
Rabin, M.O.: How to exchange secrets with oblivious transfer (1981)
Shankar, B., Srinathan, K., Rangan, C.P.: Alternative protocols for generalized oblivious transfer. In: 9th International Conference on Distributed Computing and Networking, ICDCN (2008)
Yao, A.C.-C.: Protocols for secure computations (extended abstract). In: 23rd Annual Symposium on Foundations of Computer Science, pp. 160–164 (1982)
Acknowledgements
We thank Ranjit Kumaresan for providing us with an extended version of [KK13].
The work in this paper has been partially supported by the ERC via Advanced Grant ERC-2010-AdG-267188-CRIPTO and the Defense Advanced Research Projects Agency (DARPA) and Space and Naval Warfare Systems Center, Pacific (SSC Pacific) under contract No. N66001-15-C-4070.
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Orrù, M., Orsini, E., Scholl, P. (2017). Actively Secure 1-out-of-N OT Extension with Application to Private Set Intersection. In: Handschuh, H. (eds) Topics in Cryptology – CT-RSA 2017. CT-RSA 2017. Lecture Notes in Computer Science(), vol 10159. Springer, Cham. https://doi.org/10.1007/978-3-319-52153-4_22
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