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Bicorn: An Optimistically Efficient Distributed Randomness Beacon

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Financial Cryptography and Data Security (FC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13950))

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Abstract

We introduce Bicorn, an optimistically efficient distributed randomness protocol with strong robustness under a dishonest majority. Bicorn is a “commit-reveal-recover” protocol. Each participant commits to a random value, which are combined to produce a random output. If any participants fail to open their commitment, recovery is possible via a single time-lock puzzle which can be solved by any party. In the optimistic case, Bicorn is a simple and efficient two-round protocol with no time-lock puzzle. In either case, Bicorn supports open, flexible participation, requires only a public bulletin board and no group-specific setup or PKI, and is guaranteed to produce random output assuming any single participant is honest. All communication and computation costs are (at most) linear in the number of participants with low concrete overhead.

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Notes

  1. 1.

    The original Unicorn proposal used modular square roots in a prime-order group. We consider using a modern VDF instead.

  2. 2.

    Verifying “hash-to-prime” involves testing the primality of a number on-chain using Pocklington certificates. This costs between 2.3–4 million gas, depending on the size of the certificate. Table 2 reports costs with the smallest possible certificate.

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Acknowledgments

Kevin Choi, Arasu Arun and Joseph Bonneau were supported by DARPA under Agreement No. HR00112020022. Nirvan Tyagi was supported via a Facebook Graduate Fellowship, and part of this work was done while he was a visiting student at Stanford University. Joseph Bonneau and Arasu Arun were also supported by a16z crypto research. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Government, DARPA, a16z, Facebook or any other supporting organization.

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Authors and Affiliations

  1. New York University, New York City, USA

    Kevin Choi, Arasu Arun & Joseph Bonneau

  2. Cornell University, Ithaca, USA

    Nirvan Tyagi

  3. a16z crypto research, Ithaca, USA

    Joseph Bonneau

Authors
  1. Kevin Choi
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  2. Arasu Arun
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  3. Nirvan Tyagi
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  4. Joseph Bonneau
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Corresponding author

Correspondence to Kevin Choi .

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Editors and Affiliations

  1. George Mason University, Fairfax, VA, USA

    Foteini Baldimtsi

  2. University of Bern, Bern, Switzerland

    Christian Cachin

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© 2024 International Financial Cryptography Association

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Choi, K., Arun, A., Tyagi, N., Bonneau, J. (2024). Bicorn: An Optimistically Efficient Distributed Randomness Beacon. In: Baldimtsi, F., Cachin, C. (eds) Financial Cryptography and Data Security. FC 2023. Lecture Notes in Computer Science, vol 13950. Springer, Cham. https://doi.org/10.1007/978-3-031-47754-6_14

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  • DOI: https://doi.org/10.1007/978-3-031-47754-6_14

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  • Online ISBN: 978-3-031-47754-6

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