Abstract
We revisit the problem of constant-round malicious secure two-party computation by considering the use of simple correlations, namely sources of correlated randomness that can be securely generated with sublinear communication complexity and good concrete efficiency. The current state-of-the-art protocol of Katz et al. (Crypto 2018) achieves malicious security by realizing a variant of the authenticated garbling functionality of Wang et al. (CCS 2017). Given oblivious transfer correlations, the communication cost of this protocol (with 40 bits of statistical security) is comparable to roughly 10 garbled circuits (GCs). This protocol inherently requires more than 2 rounds of interaction.
In this work, we use other kinds of simple correlations to realize the authenticated garbling functionality with better efficiency. Concretely, we get the following reduced costs in the random oracle model:
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Using variants of both vector oblivious linear evaluation (VOLE) and multiplication triples (MT), we reduce the cost to 1.31 GCs.
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Using only variants of VOLE, we reduce the cost to 2.25 GCs.
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Using only variants of MT, we obtain a non-interactive (i.e., 2-message) protocol with cost comparable to 8 GCs.
Finally, we show that by using recent constructions of pseudorandom correlation generators (Boyle et al., CCS 2018, Crypto 2019, 2020), the simple correlations consumed by our protocols can be securely realized without forming an efficiency bottleneck.
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References
Afshar, A., Mohassel, P., Pinkas, B., Riva, B.: Non-interactive secure computation based on cut-and-choose. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 387–404. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_22
Beaver, D.: Efficient multiparty protocols using circuit randomization. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 420–432. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1_34
Boyle, E., Couteau, G., Gilboa, N., Ishai, Y.: Compressing vector OLE. In: CCS 2018, pp. 896–912 (2018)
Boyle, E., et al.: Efficient two-round OT extension and silent non-interactive secure computation. In: CCS 2019, pp. 291–308 (2019)
Boyle, E., Couteau, G., Gilboa, N., Ishai, Y., Kohl, L., Scholl, P.: Efficient pseudorandom correlation generators: silent OT extension and more. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part III. LNCS, vol. 11694, pp. 489–518. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_16
Boyle, E., Couteau, G., Gilboa, N., Ishai, Y., Kohl, L., Scholl, P.: Efficient pseudorandom correlation generators from ring-LPN. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020, Part II. LNCS, vol. 12171, pp. 387–416. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56880-1_14
Couteau, G., Rindal, P., Raghuraman, S.: Silver: silent VOLE and oblivious transfer from hardness of decoding structured LDPC codes. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021, Part III. LNCS, vol. 12827, pp. 502–534. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84252-9_17
Damelin, S.B., Michalski, G., Mullen, G.L.: The cardinality of sets of k-independent vectors over finite fields. Monatshefte für Mathematik 150(4), 289–295 (2007)
Damelin, S.B., Michalski, G., Mullen, G.L., Stone, D.: The number of linearly independent binary vectors with applications to the construction of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes. Monatshefte für Mathematik 141(4), 277–288 (2004)
Damgård, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_38
Dittmer, S., Ishai, Y., Ostrovsky, R.: Line-point zero knowledge and its applications. In: ITC 2021 (2021). Full version: https://eprint.iacr.org/2020/1446
Dittmer, S., Ishai, Y., Lu, S., Ostrovsky, R.: Authenticated garbling from simple correlations. Cryptology ePrint Archive (2022)
Dodis, Y., Khanna, S.: Space-time tradeoffs for graph properties. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 291–300. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48523-6_26
Ishai, Y., Kushilevitz, E., Ostrovsky, R., Prabhakaran, M., Sahai, A.: Efficient non-interactive secure computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 406–425. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_23
Katz, J., Ranellucci, S., Rosulek, M., Wang, X.: Optimizing authenticated garbling for faster secure two-party computation. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part III. LNCS, vol. 10993, pp. 365–391. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96878-0_13
Lindell, Y., Pinkas, B.: An efficient protocol for secure two-party computation in the presence of malicious adversaries. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 52–78. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72540-4_4
Mohassel, P., Franklin, M.: Efficiency tradeoffs for malicious two-party computation. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 458–473. Springer, Heidelberg (2006). https://doi.org/10.1007/11745853_30
Rosulek, M., Roy, L.: Three halves make a whole? Beating the half-gates lower bound for garbled circuits. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021, Part I. LNCS, vol. 12825, pp. 94–124. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84242-0_5
Schoppmann, P., Gascón, A., Reichert, L., Raykova, M.: Distributed vector-OLE: improved constructions and implementation. In: CCS 2019, pp. 1055–1072 (2019)
Tassa, T., Villar, J.L.: On proper secrets, \((t, k)\)-bases and linear codes. Designs Codes Cryptogr. 52(2), 129–154 (2009)
Wang, X., Ranellucci, S., Katz, J.: Authenticated garbling and efficient maliciously secure two-party computation. In: CCS 2017, pp. 21–37 (2017)
Yang, K., Sarkar, P., Weng, C., Wang, X.: Quicksilver: efficient and affordable zero-knowledge proofs for circuits and polynomials over any field. In: CCS (2021). Full version: https://eprint.iacr.org/2021/076
Yang, K., Weng, C., Lan, X., Zhang, J., Wang, X.: Ferret: fast extension for correlated OT with small communication. In: CCS 2020, pp. 1607–1626 (2020)
Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: FOCS, pp. 162–167 (1986)
Zahur, S., Rosulek, M., Evans, D.: Two halves make a whole. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 220–250. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_8
Acknowledgements
Supported in part by DARPA Contract No. HR001120C0087. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of DARPA. Y. Ishai supported in part by ERC Project NTSC (742754), BSF grant 2018393, and ISF grant 2774/20.
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Dittmer, S., Ishai, Y., Lu, S., Ostrovsky, R. (2022). Authenticated Garbling from Simple Correlations. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13510. Springer, Cham. https://doi.org/10.1007/978-3-031-15985-5_3
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