Abstract
In Eurocrypt 2016, Kiayias, Zhou and Zikas (KZZ) have designed a multiparty protocol for computing an arbitrary function, which they prove to be secure in the malicious model with identifiable abort supporting robustness property. In their algorithm, the total transaction verification time has turned out to be \(O(n^6)\), where n is the number of parties participating in the protocol. The main contribution of this paper is the improvement of their verification time to \(O(n^3\log {n})\). We achieve this by observing that a deposit transaction created by a party in KZZ can be generated simply from the information contained in a different deposit transaction. This observation coupled with a host of novel techniques for addition and elimination of elements on a set relevant for our protocol is primarily the reason we were able to improve the verification time complexity of the KZZ protocol. Our trick can potentially be applied to speed up many other similar protocols (as much as it is prohibitive in some other specific scenarios). We compare our protocol with the others, based on various performance and security parameters, and, finally discuss the feasibility of implementing this in the Ethereum platform.
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Notes
- 1.
It ensures that the honest parties do not lose money during execution of the protocol.
References
Litecoin. https://litecoin.org/. Accessed 15 Apr 2018
Andrychowicz, M., Dziembowski, S., Malinowski, D., Mazurek, Ł.: Fair two-party computations via bitcoin deposits. In: Böhme, R., Brenner, M., Moore, T., Smith, M. (eds.) FC 2014. LNCS, vol. 8438, pp. 105–121. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44774-1_8
Andrychowicz, M., Dziembowski, S., Malinowski, D., Mazurek, Ł.: Secure multiparty computations on bitcoin. In: 2014 IEEE Symposium on Security and Privacy (SP), pp. 443–458. IEEE (2014)
Asharov, G., Lindell, Y., Zarosim, H.: Fair and efficient secure multiparty computation with reputation systems. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8270, pp. 201–220. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-42045-0_11
Asokan, N., Schunter, M., Waidner, M.: Optimistic protocols for fair exchange. In: Proceedings of the 4th ACM Conference on Computer and Communications Security, pp. 7–17. ACM (1997)
Bartoletti, M., Zunino, R.: Constant-deposit multiparty lotteries on bitcoin. In: Brenner, M., Rohloff, K., Bonneau, J., Miller, A., Ryan, P.Y.A., Teague, V., Bracciali, A., Sala, M., Pintore, F., Jakobsson, M. (eds.) FC 2017. LNCS, vol. 10323, pp. 231–247. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70278-0_15
Bentov, I., Kumaresan, R.: How to use bitcoin to design fair protocols. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8617, pp. 421–439. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44381-1_24
Boneh, D., Naor, M.: Timed commitments. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 236–254. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44598-6_15
Cachin, C., Camenisch, J.: Optimistic fair secure computation. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 93–111. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44598-6_6
Cleve, R.: Limits on the security of coin flips when half the processors are faulty. In: Proceedings of the Eighteenth Annual ACM Symposium on Theory of Computing, pp. 364–369. ACM (1986)
Dwork, C., Naor, M.: Pricing via processing or combatting junk mail. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 139–147. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-48071-4_10
Garay, J., Katz, J., Maurer, U., Tackmann, B., Zikas, V.: Rational protocol design: cryptography against incentive-driven adversaries. In: 2013 IEEE 54th Annual Symposium on Foundations of Computer Science (FOCS), pp. 648–657. IEEE (2013)
Garay, J., MacKenzie, P., Prabhakaran, M., Yang, K.: Resource fairness and composability of cryptographic protocols. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 404–428. Springer, Heidelberg (2006). https://doi.org/10.1007/11681878_21
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In: Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing, pp. 218–229. ACM (1987)
Ishai, Y., Ostrovsky, R., Zikas, V.: Secure multi-party computation with identifiable abort. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8617, pp. 369–386. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44381-1_21
Kiayias, A., Zhou, H.-S., Zikas, V.: Fair and Robust multi-party computation using a global transaction ledger. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 705–734. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_25
Kumaresan, R., Bentov, I.: How to use bitcoin to incentivize correct computations. In: Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security, pp. 30–41. ACM (2014)
Kumaresan, R., Moran, T., Bentov, I.: How to use bitcoin to play decentralized poker. In: Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, pp. 195–206. ACM (2015)
Kumaresan, R., Vaikuntanathan, V., Vasudevan, P.N.: Improvements to secure computation with penalties. In: Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, pp. 406–417. ACM (2016)
Miller, A., Bentov, I.: Zero-collateral lotteries in bitcoin and ethereum. In: 2017 IEEE European Symposium on Security and Privacy Workshops (EuroS&PW), pp. 4–13. IEEE (2017)
Nakamoto, S.: Bitcoin: a peer-to-peer electronic cash system. Consulted 1(2012), 28 (2008)
Pass, R., Shelat, A.: Micropayments for decentralized currencies. In: Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, pp. 207–218. ACM (2015)
Pass, R., Seeman, L., Shelat, A.: Analysis of the Blockchain protocol in asynchronous networks. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10211, pp. 643–673. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56614-6_22
Peyrott, S.: An introduction to ethereum and smart contracts: a programmable blockchain. https://auth0.com/blog/an-introduction-to-ethereum-and-smart-contracts-part-2/. Accessed 30 Jan 2018
Poon, J., Dryja, T.: The bitcoin lightning network: Scalable off-chain instant payments. Draft version 0.5, 14 January 2016
Ruffing, T., Kate, A., Schröder, D.: Liar, liar, coins on fire!: penalizing equivocation by loss of bitcoins. In: Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, pp. 219–230. ACM (2015)
Seito, T., Aikawa, T., Shikata, J., Matsumoto, T.: Information-theoretically secure key-insulated multireceiver authentication codes. In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol. 6055, pp. 148–165. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12678-9_10
Swanson, C.M., Stinson, D.R.: Unconditionally secure signature schemes revisited. In: Fehr, S. (ed.) ICITS 2011. LNCS, vol. 6673, pp. 100–116. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20728-0_10
Wood, G.: Ethereum: a secure decentralised generalised transaction ledger. Ethereum Proj. Yellow Pap. 151, 1–32 (2014)
Yao, A.C.: Protocols for secure computations. In: FOCS, pp. 160–164. IEEE (1982)
Acknowledgement
The second author is supported by Tata Consultancy Services (TCS) research fellowship. We thank anonymous reviewers for their constructive comments.
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Paul, S., Shrivastava, A. (2018). Robust Multiparty Computation with Faster Verification Time. In: Susilo, W., Yang, G. (eds) Information Security and Privacy. ACISP 2018. Lecture Notes in Computer Science(), vol 10946. Springer, Cham. https://doi.org/10.1007/978-3-319-93638-3_8
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