Abstract
Among various NIZK arguments, zk-SNARKs are the most efficient constructions in terms of proof size and verification which are two critical criteria for large scale applications. Currently, Groth’s construction, \(\textsf {Groth16}\), from Eurocrypt’16 is the most efficient and widely deployed one. However, it is proven to achieve only knowledge soundness, which does not prevent attacks from the adversaries who have seen simulated proofs. There has been considerable progress in modifying \(\textsf {Groth16}\) to achieve simulation extractability to guarantee the non-malleability of proofs. We revise the Simulation Extractable (SE) version of \(\textsf {Groth16}\) proposed by Bowe and Gabizon that has the most efficient prover and \(\mathsf {crs}\) size among the candidates, although it adds Random Oracle (RO) to the original construction. We present a new version which requires 4 parings in the verification, instead of 5. We also get rid of the RO at the cost of a collision resistant hash function and a single new element in the \(\mathsf {crs}\). Our construction is proven in the generic group model and seems to result in the most efficient SE variant of \(\textsf {Groth16}\) in most dimensions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
In the full version, we show that using a RO we can set \(\gamma =0\) and do not need to add any new element.
- 2.
References
Atapoor, S., Baghery, K.: Simulation extractability in Groth’s zk-SNARK. In: Pérez-Solà, C., Navarro-Arribas, G., Biryukov, A., Garcia-Alfaro, J. (eds.) DPM/CBT -2019. LNCS, vol. 11737, pp. 336–354. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-31500-9_22
Baghery, K.: Subversion-resistant simulation (knowledge) sound NIZKs. In: Albrecht, M. (ed.) IMACC 2019. LNCS, vol. 11929, pp. 42–63. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-35199-1_3
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
Bowe, S., Gabizon, A.: Making groth’s zk-SNARK simulation extractable in the random oracle model. Cryptology ePrint Archive, Report 2018/187 (2018). https://eprint.iacr.org/2018/187
Fuchsbauer, G.: Subversion-zero-knowledge SNARKs. In: Abdalla, M., Dahab, R. (eds.) PKC 2018. LNCS, vol. 10769, pp. 315–347. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76578-5_11
Groth, J.: On the size of pairing-based non-interactive arguments. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 305–326. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_11
Groth, J., Maller, M.: Snarky signatures: minimal signatures of knowledge from simulation-extractable SNARKs. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 581–612. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63715-0_20
Kerber, T., Kiayias, A., Kohlweiss, M., Zikas, V.: Ouroboros crypsinous: privacy-preserving proof-of-stake. In: 2019 IEEE Symposium on Security and Privacy, pp. 157–174. IEEE Computer Society Press (2019)
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
Lipmaa, H.: Simulation-extractable SNARKs revisited. Cryptology ePrint Archive, Report 2019/612 (2019). http://eprint.iacr.org/2019/612
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
Acknowledgements
The research leading to this article was partially supported by Project RTI2018-102112-B-I00 (AEI/FEDER, UE), Defense Advanced Research Projects Agency(DARPA) under Contract No. HR001120C0085, and by Cyber Security Research Flanders with reference number VR20192203.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Baghery, K., Pindado, Z., Ràfols, C. (2020). Simulation Extractable Versions of Groth’s zk-SNARK Revisited. In: Krenn, S., Shulman, H., Vaudenay, S. (eds) Cryptology and Network Security. CANS 2020. Lecture Notes in Computer Science(), vol 12579. Springer, Cham. https://doi.org/10.1007/978-3-030-65411-5_22
Download citation
DOI: https://doi.org/10.1007/978-3-030-65411-5_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-65410-8
Online ISBN: 978-3-030-65411-5
eBook Packages: Computer ScienceComputer Science (R0)