Skip to main content
SpringerLink
Log in

On the Efficiency of Privacy-Preserving Smart Contract Systems

  • Conference paper
  • First Online:
Progress in Cryptology – AFRICACRYPT 2019 (AFRICACRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11627))

Included in the following conference series:

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    A tutorial about the system can be found in http://cryptowiki.net/index.php?title=Privacy_preserving_smart_contracts:_Hawk_project.

  2. 2.

    We use original construction of GM zk-SNARK that is published in Crypto 2017 [GM17] and implemented in \(\mathtt {Libsnark}\) library https://github.com/scipr-lab/libsnark. But one also can use the variation of GM zk-SNARK that recently is provided in full version of paper.

  3. 3.

    Based on reported implementation on https://github.com/scipr-lab/libsnark.

References

  1. 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). https://doi.org/10.1007/978-3-319-70700-6_1

    Chapter  Google Scholar 

  2. 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 2014

    Google Scholar 

  3. 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 2014

    Google Scholar 

  4. 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). http://eprint.iacr.org/2013/879

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

    Google Scholar 

  6. Chase, M., Lysyanskaya, A.: On signatures of knowledge. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 78–96. Springer, Heidelberg (2006). https://doi.org/10.1007/11818175_5

    Chapter  Google Scholar 

  7. 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

    Google Scholar 

  8. 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). https://doi.org/10.1007/3-540-46766-1_36

    Chapter  Google Scholar 

  9. 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). https://doi.org/10.1007/978-3-319-63715-0_20

    Chapter  Google Scholar 

  10. 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). https://doi.org/10.1007/11761679_21

    Chapter  Google Scholar 

  11. 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). https://doi.org/10.1007/11935230_29

    Chapter  Google Scholar 

  12. 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). https://doi.org/10.1007/978-3-642-17373-8_19

    Chapter  Google Scholar 

  13. 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). https://doi.org/10.1007/978-3-662-49896-5_11

    Chapter  Google Scholar 

  14. 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 2011

    Google Scholar 

  15. 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 2016

    Google Scholar 

  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 2016

    Google Scholar 

  17. 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. http://eprint.iacr.org/2015/1093. Accessed 9 Apr 2017

  18. 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). https://doi.org/10.1007/978-3-642-28914-9_10

    Chapter  Google Scholar 

  19. Noether, Shen: Ring signature confidential transactions for monero. IACR Cryptology ePrint Archive 2015:1098 (2015)

    Google Scholar 

  20. 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. 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). https://doi.org/10.1007/978-3-662-58820-8_4

    Chapter  Google Scholar 

  22. 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 2013

    Google Scholar 

  23. 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. Wood, G.: Ethereum: a secure decentralised generalised transaction ledger. Ethereum Project Yellow Paper 151, 1–32 (2014)

    Google Scholar 

Download references

Acknowledgement

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).

Author information

Authors and Affiliations

  1. University of Tartu, Tartu, Estonia

    Karim Baghery

Authors
  1. Karim Baghery
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karim Baghery .

Editor information

Editors and Affiliations

  1. Technical University of Darmstadt, Darmstadt, Germany

    Johannes Buchmann

  2. Université de Caen, Caen, France

    Abderrahmane Nitaj

  3. Al Akhawayn University, Ifrane, Morocco

    Tajjeeddine Rachidi

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Baghery, K. (2019). On the Efficiency of Privacy-Preserving Smart Contract Systems. In: Buchmann, J., Nitaj, A., Rachidi, T. (eds) Progress in Cryptology – AFRICACRYPT 2019. AFRICACRYPT 2019. Lecture Notes in Computer Science(), vol 11627. Springer, Cham. https://doi.org/10.1007/978-3-030-23696-0_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-23696-0_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-23695-3

  • Online ISBN: 978-3-030-23696-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation