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Subversion-Resistant Quasi-adaptive NIZK and Applications to Modular Zk-SNARKs

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Book cover Cryptology and Network Security (CANS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13099))

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Abstract

Quasi-adaptive non-interactive zero-knowledge (QA-NIZK) arguments are NIZK arguments where the common reference string (CRS) is allowed to depend on the language and they can be very efficient for specific languages. Thus, they are for instance used within the modular LegoSNARK toolbox by Campanelli et al. (ACM CCS’19) as succinct NIZKs (aka zkSNARKs) for linear subspace languages. Such modular frameworks are interesting, as they provide gadgets for a flexible design of privacy-preserving blockchain applications. Recently, there has been an increasing interest to reduce the trust required in the generator of the CRS. One important line of work in this direction is subversion zero-knowledge by Bellare et al. (ASIACRYPT’16), where the zero-knowledge property even holds when the CRS is generated maliciously.

In this paper, we firstly analyze the security of the most efficient QA-NIZK constructions of Kiltz and Wee (EUROCRYPT’15) and the asymmetric QA-NIZKs by González et al. (ASIACRYPT’15) when the CRS is subverted and propose subversion versions of them. Secondly, for the first time, we construct unbounded (strong) true-simulation extractable (tSE) variants of them. Thirdly, we show how to integrate our subversion QA-NIZKs into the LegoSNARK toolbox, which so far does not consider subversion resistance. Our results together with existing results on (SE) subversion zk-SNARKS represent an important step towards a subversion variant of the LegoSNARK toolbox.

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Notes

  1. 1.

    ZKProof (https://zkproof.org/) being the most notable industry and academic initiative towards a common framework and standards has been founded in 2018.

  2. 2.

    Zero-knowledge proofs are on the rise, cf. https://www.gartner.com/en/documents/3947373/hype-cycle-for-privacy-2019.

  3. 3.

    We note that there are some tasks, such as fitting existing subversion (SE) zk-SNARKs into the commit-prove framework remaining that need to be worked out in detail. However, we do not expect that one faces significant problems there.

  4. 4.

    Compared to the one independently introduced by Baghery et al. [9] we use non-black box extraction and guarantee only tSE.

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Acknowledgements

We would like to thank Antonio Faonio for helpful discussion. This work received funding from the European Union’s Horizon 2020 ECSEL Joint Undertaking under grant agreement n\(^{\circ }\) 783119 (Secredas), from the European Union’s Horizon 2020 research and innovation programme under grant agreement n\(^{\circ }\)871473 (Kraken), and by the Austrian Science Fund (FWF) and netidee SCIENCE under grant agreement P31621-N38 (Profet). This work is supported by the German Federal Ministry of Education and Research BMBF (grant 16K15K042, project 6GEM).

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Authors and Affiliations

  1. Max Planck Institute for Security and Privacy, Bochum, Germany

    Behzad Abdolmaleki

  2. AIT Austrian Institute of Technology, Vienna, Austria

    Daniel Slamanig

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  1. Behzad Abdolmaleki
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Correspondence to Behzad Abdolmaleki .

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  1. University of Padua, Padua, Italy

    Mauro Conti

  2. Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

    Marc Stevens

  3. AIT Austrian Institute of Technology, Vienna, Austria

    Stephan Krenn

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Abdolmaleki, B., Slamanig, D. (2021). Subversion-Resistant Quasi-adaptive NIZK and Applications to Modular Zk-SNARKs. In: Conti, M., Stevens, M., Krenn, S. (eds) Cryptology and Network Security. CANS 2021. Lecture Notes in Computer Science(), vol 13099. Springer, Cham. https://doi.org/10.1007/978-3-030-92548-2_26

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