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Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2021: Advances in Cryptology – EUROCRYPT 2021 pp 278–308Cite as

Towards Accountability in CRS Generation

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12698))

Abstract

It is well known that several cryptographic primitives cannot be achieved without a common reference string (CRS). Those include, for instance, non-interactive zero-knowledge for NP, or maliciously secure computation in fewer than four rounds. The security of those primitives heavily relies upon on the assumption that the trusted authority, who generates the CRS, does not misuse the randomness used in the CRS generation. However, we argue that there is no such thing as an unconditionally trusted authority and every authority must be held accountable for any trust to be well-founded. Indeed, a malicious authority can, for instance, recover private inputs of honest parties given transcripts of the protocols executed with respect to the CRS it has generated.

While eliminating trust in the trusted authority may not be entirely feasible, can we at least move towards achieving some notion of accountability? We propose a new notion in which, if the CRS authority releases the private inputs of protocol executions to others, we can then provide a publicly-verifiable proof that certifies that the authority misbehaved. We study the feasibility of this notion in the context of non-interactive zero knowledge and two-round secure two-party computation.

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Notes

  1. 1.

    We stress that this extractor interacts with the malicious authority online without being able to rewind the authority. This is because, if we want to implicate the authority in the real world then we would not have the ability to rewind such an authority.

  2. 2.

    An indistinguishability obfuscator [5, 19] is a compiler that on input circuit C outputs a functionally equivalent circuit \(\widehat{C}\). Moreover, it gurantees that the obfuscations of two functionally equivalent circuits (of the same size) are computationally indistinguishable.

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Acknowledgements

The authors thank the anonymous reviewers of EUROCRYPT 2021 for many helpful comments.

Gilad Asharov is sponsored by the Israel Science Foundation (grant No. 2439/20), and by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 891234. Hila Dahari is a fellow of the Ariane de Rothschild Women Doctoral Program and supported in part by grants from the Israel Science Foundation (No. 950/15 and 2686/20) and by the Simons Foundation Collaboration on the Theory of Algorithmic Fairness. Vipul Goyal is supported in part by the NSF award 1916939, DARPA SIEVE program, a gift from Ripple, a DoE NETL award, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award.

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Authors and Affiliations

  1. University of California, Santa Barbara, Santa Barbara, USA

    Prabhanjan Ananth

  2. Bar-Ilan University, Ramat Gan, Israel

    Gilad Asharov

  3. Weizmann Institute, Rehovot, Israel

    Hila Dahari

  4. NTT Research and Carnegie Mellon University, Pittsburgh, USA

    Vipul Goyal

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  1. Prabhanjan Ananth
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Correspondence to Prabhanjan Ananth .

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  1. Inria, Paris, France

    Anne Canteaut

  2. UCLouvain, Louvain-la-Neuve, Belgium

    François-Xavier Standaert

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Ananth, P., Asharov, G., Dahari, H., Goyal, V. (2021). Towards Accountability in CRS Generation. In: Canteaut, A., Standaert, FX. (eds) Advances in Cryptology – EUROCRYPT 2021. EUROCRYPT 2021. Lecture Notes in Computer Science(), vol 12698. Springer, Cham. https://doi.org/10.1007/978-3-030-77883-5_10

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