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2018 | OriginalPaper | Buchkapitel

Two-Round Adaptively Secure Multiparty Computation from Standard Assumptions

verfasst von : Fabrice Benhamouda, Huijia Lin, Antigoni Polychroniadou, Muthuramakrishnan Venkitasubramaniam

Erschienen in: Theory of Cryptography

Verlag: Springer International Publishing

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Abstract

We present the first two-round multiparty computation (MPC) protocols secure against malicious adaptive corruption in the common reference string (CRS) model, based on DDH, LWE, or QR. Prior two-round adaptively secure protocols were known only in the two-party setting against semi-honest adversaries, or in the general multiparty setting assuming the existence of indistinguishability obfuscation (iO).

Our protocols are constructed in two steps. First, we construct two-round oblivious transfer (OT) protocols secure against malicious adaptive corruption in the CRS model based on DDH, LWE, or QR. We achieve this by generically transforming any two-round OT that is only secure against static corruption but has certain oblivious sampleability properties, into a two-round adaptively secure OT. Prior constructions were only secure against semi-honest adversaries or based on iO.

Second, building upon recent constructions of two-round MPC from two-round OT in the weaker static corruption setting [Garg and Srinivasan, Benhamouda and Lin, Eurocrypt’18] and using equivocal garbled circuits from [Canetti, Poburinnaya and Venkitasubramaniam, STOC’17], we show how to construct two-round adaptively secure MPC from two-round adaptively secure OT and constant-round adaptively secure MPC, with respect to both malicious and semi-honest adversaries. As a corollary, we also obtain the first 2-round MPC secure against semi-honest adaptive corruption in the plain model based on augmented non-committing encryption (NCE), which can be based on a variety of assumptions, CDH, RSA, DDH, LWE, or factoring Blum integers. Finally, we mention that our OT and MPC protocols in the CRS model are, in fact, adaptively secure in the Universal Composability framework.

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Vorheriges Kapitel Perfect Secure Computation in Two Rounds

Nächstes Kapitel One-Message Zero Knowledge and Non-malleable Commitments

Actually, the protocol of [5] additionally relies on Non-Interactive Zero-Knowledge (NIZK) proofs in the CRS model. But as observed in [28] and this work, the use of NIZK can be removed.

Abdalla et al. [1] constructed a two-round OT protocol secure against the weaker semi-adaptive corruption model where the adversary corrupts one of the two parties at the beginning of the execution and the other party adaptively during or after the execution. It is known that such a protocol can be generically converted to become secure against adaptive corruption using NCE. However, the resulting protocol would be 3-round.

In fact, it suffices if the OT protocol \(\varPi \) is secure against semi-honest senders, and malicious receivers.

For example, the complexity of all equivocal garbled circuits can simply be proportional to the entropy of the secrets that need to be equivocated, which in the case of MPC are the inputs and randomness of the uncorrupted parties.

We emphasize that the CLOS model of single CRS should be differentiated from the global CRS model formalized in [11]. The key difference lies in that the latter allows the environment to access the global CRS (and hence the CRS cannot be programmed), whereas in the former all protocol execution can access the same CRS but not the environment.

Formally, we need a CRS \(\mathrm {crs}_{\mathsf {OT}}\) for each instantiation of the OT protocol. For the sake of simplicity, we assume that there is a single CRS.

Abdalla, M., Benhamouda, F., Pointcheval, D.: Removing erasures with explainable hash proof systems. In: Fehr, S. (ed.) PKC 2017, Part I. LNCS, vol. 10174, pp. 151–174. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54365-8_7 CrossRef

Asharov, G., Jain, A., López-Alt, A., Tromer, E., Vaikuntanathan, V., Wichs, D.: Multiparty computation with low communication, computation and interaction via threshold FHE. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 483–501. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_29 CrossRef

Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: 20th ACM STOC, pp. 1–10. ACM Press, May 1988

Benhamouda, F., Blazy, O., Ducas, L., Quach, W.: Hash proof systems over lattices revisited. In: Abdalla, M., Dahab, R. (eds.) PKC 2018. LNCS, vol. 10770, pp. 644–674. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76581-5_22 CrossRef

Benhamouda, F., Lin, H.: k-round multiparty computation from k-round oblivious transfer via garbled interactive circuits. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018, Part II. LNCS, vol. 10821, pp. 500–532. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78375-8_17 CrossRef

Boyle, E., Gilboa, N., Ishai, Y.: Function secret sharing: improvements and extensions. In: Weippl, E.R., Katzenbeisser, S., Kruegel, C., Myers, A.C., Halevi, S. (eds.) ACM CCS 16, pp. 1292–1303. ACM Press, October 2016

Boyle, E., Gilboa, N., Ishai, Y.: Group-based secure computation: optimizing rounds, communication, and computation. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017, Part II. LNCS, vol. 10211, pp. 163–193. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56614-6_6 CrossRef

Boyle, E., Gilboa, N., Ishai, Y., Lin, H., Tessaro, S.: Foundations of homomorphic secret sharing. In: ITCS (2018, to appear)

Brakerski, Z., Perlman, R.: Lattice-based fully dynamic multi-key FHE with short ciphertexts. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016, Part I. LNCS, vol. 9814, pp. 190–213. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_8 CrossRef

10.

Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: 42nd FOCS, pp. 136–145. IEEE Computer Society Press, October 2001

11.

Canetti, R., Dodis, Y., Pass, R., Walfish, S.: Universally composable security with global setup. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 61–85. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-70936-7_4 CrossRef

12.

Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively secure multi-party computation. In: 28th ACM STOC, pp. 639–648. ACM Press, May 1996

13.

Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_2 CrossRef

14.

Canetti, R., Goldwasser, S., Poburinnaya, O.: Adaptively secure two-party computation from indistinguishability obfuscation. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 557–585. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_22 CrossRef

15.

Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: 34th ACM STOC, pp. 494–503. ACM Press, May 2002

16.

Canetti, R., Poburinnaya, O., Venkitasubramaniam, M.: Better two-round adaptive multi-party computation. In: Fehr, S. (ed.) PKC 2017, Part II. LNCS, vol. 10175, pp. 396–427. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54388-7_14 CrossRef

17.

Canetti, R., Poburinnaya, O., Venkitasubramaniam, M.: Equivocating yao: constant-round adaptively secure multiparty computation in the plain model. In: Hatami, H., McKenzie, P., King, V. (eds.) 49th ACM STOC, pp. 497–509. ACM Press, June 2017

18.

Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H.: Improved non-committing encryption with applications to adaptively secure protocols. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 287–302. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_17 CrossRef

19.

Choi, S.G., Katz, J., Wee, H., Zhou, H.-S.: Efficient, adaptively secure, and composable oblivious transfer with a single, global CRS. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 73–88. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_6 CrossRef

20.

Clear, M., McGoldrick, C.: Multi-identity and multi-key leveled FHE from learning with errors. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015, Part II. LNCS, vol. 9216, pp. 630–656. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_31 CrossRef

21.

Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_4 CrossRef

22.

Dachman-Soled, D., Katz, J., Rao, V.: Adaptively secure, universally composable, multiparty computation in constant rounds. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 586–613. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_23 CrossRef

23.

Damgård, I., Polychroniadou, A., Rao, V.: Adaptively secure multi-party computation from LWE (via equivocal FHE). In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016, Part II. LNCS, vol. 9615, pp. 208–233. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49387-8_9 CrossRef

24.

Garay, J.A., Wichs, D., Zhou, H.-S.: Somewhat non-committing encryption and efficient adaptively secure oblivious transfer. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 505–523. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_30 CrossRef

25.

Garg, S., Gentry, C., Halevi, S., Raykova, M.: Two-round secure MPC from indistinguishability obfuscation. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 74–94. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54242-8_4 CrossRef

26.

Garg, S., Polychroniadou, A.: Two-round adaptively secure MPC from indistinguishability obfuscation. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 614–637. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_24 CrossRef

27.

Garg, S., Srinivasan, A.: Garbled protocols and two-round MPC from bilinear maps. In: 58th FOCS, pp. 588–599. IEEE Computer Society Press (2017)

28.

Garg, S., Srinivasan, A.: Two-round multiparty secure computation from minimal assumptions. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018, Part II. LNCS, vol. 10821, pp. 468–499. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78375-8_16 CrossRef

29.

Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: Aho, A. (ed.) 19th ACM STOC, pp. 218–229. ACM Press, May 1987

30.

Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)MathSciNetCrossRef

31.

Dov Gordon, S., Liu, F.-H., Shi, E.: Constant-round MPC with fairness and guarantee of output delivery. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015, Part II. LNCS, vol. 9216, pp. 63–82. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_4 CrossRef

32.

Halevi, S., Kalai, Y.T.: Smooth projective hashing and two-message oblivious transfer. J. Cryptol. 25(1), 158–193 (2012)MathSciNetCrossRef

33.

Hofheinz, D., Kiltz, E.: The group of signed quadratic residues and applications. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 637–653. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_37 CrossRef

34.

Mukherjee, P., Wichs, D.: Two round multiparty computation via multi-key FHE. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016, Part II. LNCS, vol. 9666, pp. 735–763. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_26 CrossRef

35.

Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: Kosaraju, S.R. (ed.) 12th SODA, pp. 448–457. ACM-SIAM, January 2001

36.

Peikert, C., Shiehian, S.: Multi-key FHE from LWE, revisited. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 217–238. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53644-5_9 CrossRef

37.

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). https://doi.org/10.1007/978-3-540-85174-5_31 CrossRef

38.

Yao, A.C.C.: Theory and applications of trapdoor functions (extended abstract). In: 23rd FOCS, pp. 80–91. IEEE Computer Society Press, November 1982

Titel: Two-Round Adaptively Secure Multiparty Computation from Standard Assumptions
verfasst von: Fabrice Benhamouda
Huijia Lin
Antigoni Polychroniadou
Muthuramakrishnan Venkitasubramaniam
Verlag: Springer International Publishing
Buch: Theory of Cryptography
Print ISBN: 978-3-030-03806-9

Electronic ISBN: 978-3-030-03807-6

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-030-03807-6_7

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