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Universally Composable \(\varSigma \)-protocols in the Global Random-Oracle Model

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Theory of Cryptography (TCC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13747))

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Abstract

Numerous cryptographic applications require efficient non-interactive zero-knowledge proofs of knowledge (NIZKPoK) as a building block. Typically they rely on the Fiat-Shamir heuristic to do so, as security in the random-oracle model is considered good enough in practice. However, there is a troubling disconnect between the stand-alone security of such a protocol and its security as part of a larger, more complex system where several protocols may be running at the same time. Provable security in the general universal composition model (GUC model) of Canetti et al. is the best guarantee that nothing will go wrong when a system is part of a larger whole, even when all parties share a common random oracle. In this paper, we prove the minimal necessary properties of generally universally composable (GUC) NIZKPoK in any global random-oracle model, and show how to achieve efficient and GUC NIZKPoK in both the restricted programmable and restricted observable (non-programmable) global random-oracle models.

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Notes

  1. 1.

    For a full discussion of the subtle differences between observation and programming privileges in the global ROM(s), see Appendix A.2 in the full version [37].

  2. 2.

    As discussed by Camenish et al. [10], the challenger in such a hybrid experiment can make use of techniques like programming and rewinding that are otherwise ā€œillegalā€ for the simulator to employ in the GUC model.

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Acknowledgements

Many thanks to Yashvanth Kondi and abhi shelat for crucial security analysis of our original OR-protocol construction, and to Jack Doerner for insightful discussions about \(\mathcal {F}_{\texttt{NIZK}}\) that inspired our results in Sect. 3.5. This research was supported by NSF grant 2154170, and by grants from Meta.

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  1. Brown University, Providence, RI, 02906, USA

    Anna Lysyanskaya & Leah Namisa Rosenbloom

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  1. Anna Lysyanskaya
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  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

  2. Massachusetts Institute of Technology, Cambridge, MA, USA

    Vinod Vaikuntanathan

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Lysyanskaya, A., Rosenbloom, L.N. (2022). Universally Composable \(\varSigma \)-protocols in the Global Random-Oracle Model. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13747. Springer, Cham. https://doi.org/10.1007/978-3-031-22318-1_8

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