Abstract
Actively secure two-party computation (2PC) is one of the canonical building blocks in modern cryptography. One main goal for designing actively secure 2PC protocols is to reduce the communication overhead, compared to semi-honest 2PC protocols. In this paper, we propose a new actively secure constant-round 2PC protocol with one-way communication of \(2\kappa +5\) bits per AND gate (for \(\kappa \)-bit computational security and any statistical security), essentially matching the one-way communication of semi-honest half-gates protocol. This is achieved by two new techniques:
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1.
The recent compression technique by Dittmer et al. (Crypto 2022) shows that a relaxed preprocessing is sufficient for authenticated garbling that does not reveal masked wire values to the garbler. We introduce a new form of authenticated bits and propose a new technique of generating authenticated AND triples to reduce the one-way communication of preprocessing from \(5\rho +1\) bits to 2 bits per AND gate for \(\rho \)-bit statistical security.
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2.
Unfortunately, the above compressing technique is only compatible with a less compact authenticated garbled circuit of size \(2\kappa +3\rho \) bits per AND gate. We designed a new authenticated garbling that does not use information theoretic MACs but rather dual execution without leakage to authenticate wire values in the circuit. This allows us to use a more compact half-gates based authenticated garbled circuit of size \(2\kappa +1\) bits per AND gate, and meanwhile keep compatible with the compression technique. Our new technique can achieve one-way communication of \(2\kappa +5\) bits per AND gate.
Our technique of yielding authenticated AND triples can also be used to optimize the two-way communication (i.e., the total communication) by combining it with the authenticated garbled circuits by Dittmer et al., which results in an actively secure 2PC protocol with two-way communication of \(2\kappa +3\rho +4\) bits per AND gate.
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Notes
- 1.
VOLE is an arithmetic generalization of COT, and enables \(\mathsf P_{A}\) to obtain \((\varDelta , \textsf{K}[{\boldsymbol{u}}]) \in \mathbb F \times \mathbb F ^\ell \) and \(\mathsf P_{B}\) to get \(({\boldsymbol{u}}, \textsf{M}[{\boldsymbol{u}}]) \in \mathbb F ^\ell \times \mathbb F ^\ell \) such that \(\textsf{M}[{\boldsymbol{u}}]=\textsf{K}[{\boldsymbol{u}}]+{\boldsymbol{u}}\cdot \varDelta \), where \(\mathbb F \) is a large field such as \(\mathbb F =\mathbb F _{2^\rho }\).
- 2.
An independent global key is necessary to perform the consistency check, and otherwise a malicious \(\mathsf P_{B}\) will always pass the check if is reused.
- 3.
We define \(a_w, a_w', b_w, b_w'\) by the MAC tag and keys to implicitly authenticate them.
References
Abascal, J., Sereshgi, M.H.F., Hazay, C., Ishai, Y., Venkitasubramaniam, M.: Is the classical GMW paradigm practical? the case of non-interactive actively secure 2PC. In: ACM Conference on Computer and Communications Security (CCS) 2020, pp. 1591–1605. ACM Press (2020). https://doi.org/10.1145/3372297.3423366
Baum, C., Braun, L., Munch-Hansen, A., Razet, B., Scholl, P.: Appenzeller to brie: efficient zero-knowledge proofs for mixed-mode arithmetic and Z2k. In: ACM Conference on Computer and Communications Security (CCS) 2021, pp. 192–211. ACM Press (2021). https://doi.org/10.1145/3460120.3484812
Baum, C., Braun, L., Munch-Hansen, A., Scholl, P.: Moz\(\mathbb{Z} _{2^k}\)arella: efficient vector-OLE and zero-knowledge proofs over \(\mathbb{Z} _{2^k}\). In: Dodis, Y., Shrimpton, T. (eds.) CRYPTO 2022, Part IV. LNCS, vol. 13510, pp. 329–358. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-15985-5_12
Baum, C., Malozemoff, A.J., Rosen, M.B., Scholl, P.: Mac’n’Cheese: zero-knowledge proofs for Boolean and arithmetic circuits with nested disjunctions. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021, Part IV. LNCS, vol. 12828, pp. 92–122. Springer, Cham (2021)
Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: 22nd Annual ACM Symposium on Theory of Computing (STOC), pp. 503–513. ACM Press (1990). https://doi.org/10.1145/100216.100287
Bellare, M., Hoang, V.T., Keelveedhi, S., Rogaway, P.: Efficient garbling from a fixed-key blockcipher. In: IEEE Symposium on Security and Privacy (S &P) 2013, pp. 478–492 (2013). https://doi.org/10.1109/SP.2013.39
Bendlin, R., Damgård, I., Orlandi, C., Zakarias, S.: Semi-homomorphic encryption and multiparty computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169–188. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_11
Blum, A., Furst, M., Kearns, M., Lipton, R.J.: Cryptographic primitives based on hard learning problems. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 278–291. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48329-2_24
Boyle, E., et al.: Correlated pseudorandomness from expand-accumulate codes. In: Dodis, Y., Shrimpton, T. (eds.) CRYPTO 2022, Part II. LNCS, vol. 13508, pp. 603–633. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-15979-4_21
Boyle, E., et al.: Efficient two-round OT extension and silent non-interactive secure computation. In: ACM Conference on Computer and Communications Security (CCS) 2019, pp. 291–308. ACM Press (2019). https://doi.org/10.1145/3319535.3354255
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
Canetti, R.: Security and composition of multiparty cryptographic protocols. J. Cryptology 13(1), 143–202 (2000). https://doi.org/10.1007/s001459910006
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
Cui, H., Wang, X., Yang, K., Yu, Y.: Actively Secure Half-Gates with Minimum Overhead under Duplex Networks. Cryptology ePrint Archive, Paper 2023/278 (2023). https://eprint.iacr.org/2023/278
Damgård, I., Nielsen, J.B., Nielsen, M., Ranellucci, S.: The TinyTable protocol for 2-party secure computation, or: gate-scrambling revisited. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part I. LNCS, vol. 10401, pp. 167–187. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_6
Dittmer, S., Ishai, Y., Lu, S., Ostrovsky, R.: Authenticated garbling from simple correlations. In: Dodis, Y., Shrimpton, T. (eds.) CRYPTO 2022, Part IV. LNCS, vol. 13510, pp. 57–87. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-15985-5_3
Dittmer, S., Ishai, Y., Lu, S., Ostrovsky, R.: Improving line-point zero knowledge: two multiplications for the price of one. In: ACM Conference on Computer and Communications Security (CCS) 2022, pp. 829–841. ACM Press (2022). https://doi.org/10.1145/3548606.3559385
Dittmer, S., Ishai, Y., Ostrovsky, R.: Line-point zero knowledge and its applications. In: 2nd Conference on Information-Theoretic Cryptography (2021)
Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_12
Goldreich, O.: Foundations of Cryptography: Basic Applications, vol. 2. Cambridge University Press, Cambridge, UK (2004)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: 19th Annual ACM Symposium on Theory of Computing (STOC), pp. 218–229. ACM Press (1987). https://doi.org/10.1145/28395.28420
Guo, C., Katz, J., Wang, X., Weng, C., Yu, Yu.: Better Concrete security for half-gates garbling (in the multi-instance setting). In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020, Part II. LNCS, vol. 12171, pp. 793–822. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56880-1_28
Guo, C., Katz, J., Wang, X., Yu, Y.: Efficient and secure multiparty computation from fixed-key block ciphers. In: IEEE Symposium on Security and Privacy (S &P) 2020, pp. 825–841 (2020). https://doi.org/10.1109/SP40000.2020.00016
Hazay, C., Ishai, Y., Venkitasubramaniam, M.: Actively secure garbled circuits with constant communication overhead in the plain model. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 3–39. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70503-3_1
Hazay, C., Scholl, P., Soria-Vazquez, E.: Low cost constant round MPC combining BMR and oblivious transfer. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017, Part I. LNCS, vol. 10624, pp. 598–628. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_21
Hazay, C., Scholl, P., Soria-Vazquez, E.: Low cost constant round MPC combining BMR and oblivious transfer. J. Cryptology 33(4), 1732–1786 (2020). https://doi.org/10.1007/s00145-020-09355-y
Hazay, C., Shelat, A., Venkitasubramaniam, M.: Going beyond dual execution: MPC for functions with efficient verification. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020, Part II. LNCS, vol. 12111, pp. 328–356. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45388-6_12
Huang, Y., Katz, J., Evans, D.: Quid-Pro-Quo-tocols: strengthening semi-honest protocols with dual execution. In: IEEE Symposium on Security and Privacy (S &P) 2012, pp. 272–284 (2012). https://doi.org/10.1109/SP.2012.43
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
Kolesnikov, V., Schneider, T.: Improved garbled circuit: free XOR gates and applications. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5126, pp. 486–498. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70583-3_40
Lindell, Y., Pinkas, B., Smart, N.P., Yanai, A.: Efficient constant round multi-party computation combining BMR and SPDZ. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015, Part II. LNCS, vol. 9216, pp. 319–338. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_16
Lindell, Y., Smart, N.P., Soria-Vazquez, E.: More efficient constant-round multi-party computation from BMR and SHE. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9985, pp. 554–581. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53641-4_21
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
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). https://doi.org/10.1007/978-3-642-32009-5_40
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
Wang, X., Ranellucci, S., Katz, J.: Authenticated garbling and efficient maliciously secure two-party computation. In: ACM Conference on Computer and Communications Security (CCS) 2017, pp. 21–37. ACM Press (2017). https://doi.org/10.1145/3133956.3134053
Wang, X., Ranellucci, S., Katz, J.: Global-scale secure multiparty computation. In: ACM Conference on Computer and Communications Security (CCS) 2017, pp. 39–56. ACM Press (2017). https://doi.org/10.1145/3133956.3133979
Weng, C., Yang, K., Katz, J., Wang, X.: Wolverine: fast, scalable, and communication-efficient zero-knowledge proofs for Boolean and arithmetic circuits. In: IEEE Symposium on Security and Privacy (S &P) 2021, pp. 1074–1091 (2021). https://doi.org/10.1109/SP40001.2021.00056
Weng, C., Yang, K., Xie, X., Katz, J., Wang, X.: Mystique: efficient conversions for zero-knowledge proofs with applications to machine learning. In: USENIX Security Symposium 2021, pp. 501–518. USENIX Association (2021)
Weng, C., Yang, K., Yang, Z., Xie, X., Wang, X.: AntMan: interactive zero-knowledge proofs with sublinear communication. In: ACM Conference on Computer and Communications Security (CCS) 2022, pp. 2901–2914. ACM Press (2022). https://doi.org/10.1145/3548606.3560667
Yang, K., Sarkar, P., Weng, C., Wang, X.: QuickSilver: efficient and affordable zero-knowledge proofs for circuits and polynomials over any field. In: ACM Conference on Computer and Communications Security (CCS) 2021, pp. 2986–3001. ACM Press (2021). https://doi.org/10.1145/3460120.3484556
Yang, K., Wang, X., Zhang, J.: More efficient MPC from improved triple generation and authenticated garbling. In: ACM Conference on Computer and Communications Security (CCS) 2020, pp. 1627–1646. ACM Press (2020). https://doi.org/10.1145/3372297.3417285
Yang, K., Weng, C., Lan, X., Zhang, J., Wang, X.: Ferret: fast extension for correlated OT with small communication. In: ACM Conference on Computer and Communications Security (CCS) 2020, pp. 1607–1626. ACM Press (2020). https://doi.org/10.1145/3372297.3417276
Yao, A.C.C.: How to generate and exchange secrets (extended abstract). In: 27th Annual Symposium on Foundations of Computer Science (FOCS), pp. 162–167. IEEE (1986). https://doi.org/10.1109/SFCS.1986.25
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
Kang Yang is supported by the National Key Research and Development Program of China (Grant No. 2022YFB2702000), and by the National Natural Science Foundation of China (Grant Nos. 62102037, 61932019, 62022018). Yu Yu is supported by the National Natural Science Foundation of China (Grant Nos. 62125204 and 92270201), the National Key Research and Development Program of China (Grant No. 2018YFA0704701), and the Major Program of Guangdong Basic and Applied Research (Grant No. 2019B030302008). Yu Yu also acknowledges the support from the XPLORER PRIZE. Xiao Wang is supported by DARPA under Contract No. HR001120C0087, NSF award #2016240, #2236819, and research awards from Meta and Google. The views, opinions, and/or findings expressed are those of the author(s) and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government. We thanks anonymous reviewers for their helpful comments.
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Cui, H., Wang, X., Yang, K., Yu, Y. (2023). Actively Secure Half-Gates with Minimum Overhead Under Duplex Networks. In: Hazay, C., Stam, M. (eds) Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023. Lecture Notes in Computer Science, vol 14005. Springer, Cham. https://doi.org/10.1007/978-3-031-30617-4_2
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