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Prover-Efficient Commit-and-Prove Zero-Knowledge SNARKs

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Progress in Cryptology – AFRICACRYPT 2016 (AFRICACRYPT 2016)

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Abstract

Zk-SNARKs (succinct non-interactive zero-knowledge arguments of knowledge) are needed in many applications. Unfortunately, all previous zk-SNARKs for interesting languages are either inefficient for the prover, or are non-adaptive and based on a commitment scheme that depends both on the prover’s input and on the language, i.e., they are not commit-and-prove (CaP) SNARKs. We propose a proof-friendly extractable commitment scheme, and use it to construct prover-efficient adaptive CaP succinct zk-SNARKs for different languages, that can all reuse committed data. In new zk-SNARKs, the prover computation is dominated by a linear number of cryptographic operations. We use batch-verification to decrease the verifier’s computation; importantly, batch-verification can be used also in QAP-based zk-SNARKs.

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Notes

  1. 1.

    Recently, [12] proposed an independent methodology to improve the prover’s computational complexity in QAP-based arguments. However, [12] does not spell out their achieved prover’s computational complexity.

  2. 2.

    We emphasize that \(\textsc {Circuit-SAT}\) is not our focus; the lines corresponding to \(\textsc {Circuit-SAT}\) are provided only for the sake of comparison. One can use proof boot-strapping [12] to decrease the length of the resulting \(\textsc {Circuit-SAT}\) argument from \(\varTheta (\log n)\), as stated in [25], to \(\varTheta (1)\); we omit further discussion.

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Acknowledgments

We would like to thank Diego Aranha, Paulo Barreto, Markulf Kohlweiss, and Prastudy Fauzi for useful comments. This work was supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 653497 (project PANORAMIX), and the Estonian Research Council.

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  1. Institute of Computer Science, University of Tartu, Tartu, Estonia

    Helger Lipmaa

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  1. Helger Lipmaa
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Correspondence to Helger Lipmaa .

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  1. Ecole Normale Supérieure, Paris, France

    David Pointcheval

  2. University of Caen, Caen, France

    Abderrahmane Nitaj

  3. Al Akhawayn University in Ifrane, Ifrane, Morocco

    Tajjeeddine Rachidi

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Lipmaa, H. (2016). Prover-Efficient Commit-and-Prove Zero-Knowledge SNARKs. In: Pointcheval, D., Nitaj, A., Rachidi, T. (eds) Progress in Cryptology – AFRICACRYPT 2016. AFRICACRYPT 2016. Lecture Notes in Computer Science(), vol 9646. Springer, Cham. https://doi.org/10.1007/978-3-319-31517-1_10

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  • DOI: https://doi.org/10.1007/978-3-319-31517-1_10

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