On the Efficiency of Privacy-Preserving Smart Contract Systems

  • Karim BagheryEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11627)


Along with blockchain technology, smart contracts have found intense interest in lots of practical applications. A smart contract is a mechanism involving digital assets and some parties, where the parties deposit assets into the contract and the contract redistributes the assets among the parties based on provisions of the smart contract and inputs of the parties. Recently, several smart contract systems are constructed that use zk-SNARKs to provide privacy-preserving payments and interconnections in the contracts (e.g. Hawk [KMS+16] and Gyges [JKS16]). Efficiency of such systems severely are dominated by efficiency of the underlying UC-secure zk-SNARK that is achieved using C\(\emptyset \)C\(\emptyset \) framework [KZM+15] applied on a non-UC-secure zk-SNARK. In this paper, we show that recent progresses on zk-SNARKs, allow one to simplify the structure and also improve the efficiency of both systems with a UC-secure zk-SNARK that has simpler construction and better efficiency in comparison with the currently used ones. More precisely, with minimal changes, we present a variation of Groth and Maller’s zk-SNARK from Crypto 2017, and show that it achieves UC-security and has better efficiency than the ones that currently are used in Hawk and Gyges. We believe, new variation can be of independent interest.


Privacy-preserving smart contracts zk-SNARKs UC-security CRS model 



The author were supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 780477 (project PRIViLEDGE), and by the Estonian Research Council grant (PRG49).


  1. ABLZ17.
    Abdolmaleki, B., Baghery, K., Lipmaa, H., Zając, M.: A subversion-resistant SNARK. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017, Part III. LNCS, vol. 10626, pp. 3–33. Springer, Cham (2017). Scholar
  2. BCG+14.
    Ben-Sasson, E., et al.: Zerocash: decentralized anonymous payments from bitcoin. In: 2014 IEEE Symposium on Security and Privacy, pp. 459–474. IEEE Computer Society Press, May 2014Google Scholar
  3. BCPR14.
    Bitansky, N., Canetti, R., Paneth, O., Rosen, A.: On the existence of extractable one-way functions. In: Shmoys, D.B. (ed.) 46th ACM STOC, pp. 505–514. ACM Press, May/June 2014Google Scholar
  4. BCTV13.
    Ben-Sasson, E., Chiesa, A., Tromer, E., Virza, M.: Succinct non-interactive arguments for a von neumann architecture. Cryptology ePrint Archive, Report 2013/879 (2013).
  5. Can01.
    Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: 42nd FOCS, pp. 136–145. IEEE Computer Society Press, October 2001Google Scholar
  6. CL06.
    Chase, M., Lysyanskaya, A.: On signatures of knowledge. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 78–96. Springer, Heidelberg (2006). Scholar
  7. CLOS02.
    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 2002Google Scholar
  8. Dam91.
    Damgård, I.: Towards practical public key systems secure against chosen ciphertext attacks. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 445–456. Springer, Heidelberg (1992). Scholar
  9. GM17.
    Groth, J., Maller, M.: Snarky signatures: minimal signatures of knowledge from simulation-extractable SNARKs. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part II. LNCS, vol. 10402, pp. 581–612. Springer, Cham (2017). Scholar
  10. GOS06.
    Groth, J., Ostrovsky, R., Sahai, A.: Perfect non-interactive zero knowledge for NP. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 339–358. Springer, Heidelberg (2006). Scholar
  11. Gro06.
    Groth, J.: Simulation-sound NIZK proofs for a practical language and constant size group signatures. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 444–459. Springer, Heidelberg (2006). Scholar
  12. Gro10.
    Groth, J.: Short pairing-based non-interactive zero-knowledge arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321–340. Springer, Heidelberg (2010). Scholar
  13. Gro16.
    Groth, J.: On the size of pairing-based non-interactive arguments. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016, Part II. LNCS, vol. 9666, pp. 305–326. Springer, Heidelberg (2016). Scholar
  14. GW11.
    Gentry, C., Wichs, D.: Separating succinct non-interactive arguments from all falsifiable assumptions. In: Fortnow, L., Vadhan, S.P. (eds.) 43rd ACM STOC, pp. 99–108. ACM Press, June 2011Google Scholar
  15. JKS16.
    Juels, A., Kosba, A.E., Shi, E.: The ring of gyges: investigating the future of criminal smart contracts. In: Weippl, E.R., Katzenbeisser, S., Kruegel, C., Myers, A.C., Halevi, S. (eds.), ACM CCS 16, pp. 283–295. ACM Press, October 2016Google Scholar
  16. KMS+16.
    Kosba, A.E., Miller, A., Shi, E., Wen, Z., Papamanthou, C.: Hawk: the blockchain model of cryptography and privacy-preserving smart contracts. In: 2016 IEEE Symposium on Security and Privacy, pp. 839–858. IEEE Computer Society Press, May 2016Google Scholar
  17. KZM+15.
    Kosba, A.E., et al.: C\(\emptyset \)C\(\emptyset \): A Framework for Building Composable Zero-Knowledge Proofs. Technical Report 2015/1093, IACR, 10 November 2015. Accessed 9 Apr 2017
  18. Lip12.
    Lipmaa, H.: Progression-free sets and sublinear pairing-based non-interactive zero-knowledge arguments. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 169–189. Springer, Heidelberg (2012). Scholar
  19. Noe15.
    Noether, Shen: Ring signature confidential transactions for monero. IACR Cryptology ePrint Archive 2015:1098 (2015)Google Scholar
  20. NVV18.
    Narula, N., Vasquez, W., Virza, M.: zkledger: privacy-preserving auditing for distributed ledgers. In: 15th \(\{\)USENIX\(\}\) Symposium on Networked Systems Design and Implementation (\(\{\)NSDI\(\}\) 18), pp. 65–80 (2018)Google Scholar
  21. PBF+18.
    Poelstra, A., Back, A., Friedenbach, M., Maxwell, G., Wuille, P.: Confidential assets. In: Zohar, A., et al. (eds.) FC 2018. LNCS, vol. 10958, pp. 43–63. Springer, Heidelberg (2019). Scholar
  22. PHGR13.
    Parno, B., Howell, J., Gentry, C., Raykova, M.: Pinocchio: nearly practical verifiable computation. In: 2013 IEEE Symposium on Security and Privacy, pp. 238–252. IEEE Computer Society Press, May 2013Google Scholar
  23. WLB14.
    Wilkinson, S., Lowry, J., Boshevski, T.: Metadisk a blockchain-based decentralized file storage application. Storj Labs Inc., Technical Report, hal, pp. 1–11 (2014)Google Scholar
  24. Woo14.
    Wood, G.: Ethereum: a secure decentralised generalised transaction ledger. Ethereum Project Yellow Paper 151, 1–32 (2014)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of TartuTartuEstonia

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