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Cornucopia: Distributed Randomness at Scale

Authors Miranda Christ , Kevin Choi , Joseph Bonneau

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Author Details

Miranda Christ
  • Columbia University, New York, NY, USA
Kevin Choi
  • New York University, NY, USA
Joseph Bonneau
  • New York University, NY, USA
  • a16z crypto research, New York, NY, USA

Funding

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, Andreessen Horowitz, or any other supporting organization.
  • Christ, Miranda: Supported by NSF grants CCF-2107187 and CCF-2212233, by LexisNexis Risk Solutions, and by the Algorand Centres of Excellence programme managed by Algorand Foundation.
  • Choi, Kevin: Supported by DARPA Agreement HR00112020022 and NSF grant CNS-2239975.
  • Bonneau, Joseph: Supported by DARPA Agreement HR00112020022, NSF grant CNS-2239975, and a16z crypto research.

Acknowledgements

The authors thank Noemi Glaeser for suggesting the name Cornucopia.

Cite As Get BibTex

Miranda Christ, Kevin Choi, and Joseph Bonneau. Cornucopia: Distributed Randomness at Scale. In 6th Conference on Advances in Financial Technologies (AFT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 316, pp. 17:1-17:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.AFT.2024.17

Abstract

We propose Cornucopia, a protocol framework for distributed randomness beacons combining accumulators and verifiable delay functions. Cornucopia generalizes the Unicorn protocol, using an accumulator to enable efficient verification by each participant that their contribution has been included. The output is unpredictable as long as at least one participant is honest, yielding a scalable distributed randomness beacon with strong security properties. Proving this approach secure requires developing a novel property of accumulators, insertion security, which we show is both necessary and sufficient for Cornucopia-style protocols. We show that not all accumulators are insertion-secure, then prove that common constructions (Merkle trees, RSA accumulators, and bilinear accumulators) are either naturally insertion-secure or can be made so with trivial modifications.

Subject Classification

ACM Subject Classification
  • Security and privacy → Cryptography
Keywords
  • Randomness beacons
  • accumulators

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References

  1. Marcin Andrychowicz, Stefan Dziembowski, Daniel Malinowski, and Lukasz Mazurek. Secure Multiparty Computations on Bitcoin. In IEEE Security & Privacy, 2014. Google Scholar
  2. Renas Bacho, Christoph Lenzen, Julian Loss, Simon Ochsenreither, and Dimitrios Papachristoudis. GRandLine: First Adaptively Secure DKG and Randomness Beacon with (Almost) Quadratic Communication Complexity. Cryptology ePrint Archive, Paper 2023/1887, 2023. Google Scholar
  3. Michael Ben-Or and Nathan Linial. Collective coin flipping, robust voting schemes and minima of banzhaf values. In FOCS, 1985. Google Scholar
  4. Michael Ben-Or and Nathan Linial. Collective coin flipping. Advances in Computing Research, 1989. Google Scholar
  5. Josh Benaloh and Michael De Mare. One-way accumulators: A decentralized alternative to digital signatures. In Eurocrypt, 1993. Google Scholar
  6. Adithya Bhat, Aniket Kate, Kartik Nayak, and Nibesh Shrestha. OptRand: Optimistically responsive distributed random beacons. Cryptology ePrint Archive, Paper 2022/193, 2022. Google Scholar
  7. Adithya Bhat, Nibesh Shrestha, Aniket Kate, and Kartik Nayak. RandPiper - Reconfiguration-Friendly Random Beacons with Quadratic Communication. Cryptology ePrint Archive, Paper 2020/1590, 2020. Google Scholar
  8. Manuel Blum. Coin flipping by telephone a protocol for solving impossible problems. ACM SIGACT News, 1983. Google Scholar
  9. Dan Boneh, Joseph Bonneau, Benedikt Bünz, and Ben Fisch. Verifiable Delay Functions. In CRYPTO, 2018. Google Scholar
  10. Dan Boneh, Benedikt Bünz, and Ben Fisch. A Survey of Two Verifiable Delay Functions. Cryptology ePrint Archive, Paper 2018/712, 2018. Google Scholar
  11. Dan Boneh, Manu Drijvers, and Gregory Neven. Compact multi-signatures for smaller blockchains. In Asiacrypt, 2018. Google Scholar
  12. Johannes Buchmann and Safuat Hamdy. A survey on IQ cryptography. In Public-Key Cryptography and Computational Number Theory, 2011. Google Scholar
  13. Jan Camenisch and Anna Lysyanskaya. Dynamic accumulators and application to efficient revocation of anonymous credentials. In CRYPTO, 2002. Google Scholar
  14. Ignacio Cascudo and Bernardo David. Albatross: publicly attestable batched randomness based on secret sharing. In Asiacrypt, 2020. Google Scholar
  15. Dario Catalano and Dario Fiore. Vector commitments and their applications. In PKC, 2013. Google Scholar
  16. Megan Chen, Carmit Hazay, Yuval Ishai, Yuriy Kashnikov, Daniele Micciancio, Tarik Riviere, Abhi Shelat, Muthu Venkitasubramaniam, and Ruihan Wang. Diogenes: Lightweight Scalable RSA Modulus Generation with a Dishonest Majority. In IEEE Security & Privacy, 2021. Google Scholar
  17. Alisa Cherniaeva, Ilia Shirobokov, and Omer Shlomovits. Homomorphic encryption random beacon. Cryptology ePrint Archive, Paper 2019/1320, 2019. Google Scholar
  18. Kevin Choi, Arasu Arun, Nirvan Tyagi, and Joseph Bonneau. Bicorn: An optimistically efficient distributed randomness beacon. In Financial Crypto, 2023. Google Scholar
  19. Kevin Choi, Aathira Manoj, and Joseph Bonneau. Sok: Distributed randomness beacons. In IEEE Security & Privacy, 2023. Google Scholar
  20. Miranda Christ, Kevin Choi, and Joseph Bonneau. Cornucopia: Distributed randomness beacons at scale. Cryptology ePrint Archive, 2023. Google Scholar
  21. Richard Cleve. Limits on the security of coin flips when half the processors are faulty. In TOC, 1986. Google Scholar
  22. Sourav Das, Vinith Krishnan, Irene Miriam Isaac, and Ling Ren. Spurt: Scalable distributed randomness beacon with transparent setup. In IEEE Security & Privacy, 2022. Google Scholar
  23. Yevgeniy Dodis. Impossibility of black-box reduction from non-adaptively to adaptively secure coin-flipping. In ECCC, 2000. Google Scholar
  24. Drand. URL: https://drand.love/.
  25. Dankrad Feist. RSA Assumptions. rsa.cash/rsa-assumptions/, 2022.
  26. FileCoin. Trusted setup complete!, 2020. URL: https://filecoin.io/blog/posts/trusted-setup-complete/.
  27. Ethereum Foundation. Proto-danksharding, 2023. URL: https://www.eip4844.com/.
  28. Georg Fuchsbauer, Eike Kiltz, and Julian Loss. The algebraic group model and its applications. In CRYPTO, 2018. Google Scholar
  29. Ariel Gabizon, Zachary J. Williamson, and Oana Ciobotaru. PLONK: Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge. Cryptology ePrint Archive, Paper 2019/953, 2019. Google Scholar
  30. David Galindo, Jia Liu, Mihai Ordean, and Jin-Mann Wong. Fully distributed verifiable random functions and their application to decentralised random beacons. In Euro S&P, 2021. Google Scholar
  31. Shafi Goldwasser, Yael Tauman Kalai, and Sunoo Park. Adaptively secure coin-flipping, revisited. In ICALP, 2015. Google Scholar
  32. Zhaozhong Guo, Liucheng Shi, and Maozhi Xu. SecRand: A Secure Distributed Randomness Generation Protocol With High Practicality and Scalability. IEEE Access, 2020. Google Scholar
  33. Iftach Haitner and Yonatan Karidi-Heller. A tight lower bound on adaptively secure full-information coin flip. In FOCS, 2020. Google Scholar
  34. Yael Tauman Kalai, Ilan Komargodski, and Ran Raz. A lower bound for adaptively-secure collective coin flipping protocols. Combinatorica, 41(1), 2021. Google Scholar
  35. Alireza Kavousi, Zhipeng Wang, and Philipp Jovanovic. SoK: Public Randomness. Cryptology ePrint Archive, Paper 2023/1121, 2023. Google Scholar
  36. Thomas Kerber, Aggelos Kiayias, and Markulf Kohlweiss. Mining for Privacy: How to Bootstrap a Snarky Blockchain. In Financial Crypto, 2021. Google Scholar
  37. Hsun Lee, Yuming Hsu, Jing-Jie Wang, Hao Cheng Yang, Yu-Heng Chen, Yih-Chun Hu, and Hsu-Chun Hsiao. HeadStart: Efficiently Verifiable and Low-Latency Participatory Randomness Generation at Scale. In NDSS, 2022. Google Scholar
  38. Arjen K. Lenstra and Benjamin Wesolowski. A random zoo: sloth, unicorn, and trx. Cryptology ePrint Archive, Paper 2015/366, 2015. Google Scholar
  39. Jiangtao Li, Ninghui Li, and Rui Xue. Universal accumulators with efficient nonmembership proofs. In ACNS, 2007. Google Scholar
  40. Helger Lipmaa. Secure accumulators from Euclidean rings without trusted setup. In ACNS, 2012. Google Scholar
  41. Lipa Long. Binary quadratic forms. https://github. com/Chia-Network/vdf-competition/blob/master/classgroups. pdf, 2018.
  42. Lan Nguyen. Accumulators from bilinear pairings and applications. In CT-RSA, 2005. Google Scholar
  43. Valeria Nikolaenko, Sam Ragsdale, Joseph Bonneau, and Dan Boneh. Powers-of-tau to the people: Decentralizing setup ceremonies. In ACNS, 2024. Google Scholar
  44. Charalampos Papamanthou. Cryptography for efficiency: new directions in authenticated data structures. PhD thesis, Brown University, 2011. Google Scholar
  45. Krzysztof Pietrzak. Simple Verifiable Delay Functions. In ITCS, 2018. Google Scholar
  46. Youcai Qian. Randao: Verifiable random number generation. randao.org/whitepaper/Randao_v0.85_en.pdf, 2017.
  47. Michael O. Rabin. Transaction protection by beacons. Journal of Computer and System Sciences, 1983. Google Scholar
  48. Mayank Raikwar and Danilo Gligoroski. SoK: Decentralized randomness beacon protocols. In Australasian Conference on Information Security and Privacy, 2022. Google Scholar
  49. Mark Ryan. Enhanced Certificate Transparency and End-to-End Encrypted Mail. In NDSS, 2014. Google Scholar
  50. Philipp Schindler, Aljosha Judmayer, Markus Hittmeir, Nicholas Stifter, and Edgar Weippl. RandRunner: Distributed Randomness from Trapdoor VDFs with Strong Uniqueness. In NDSS, 2023. Google Scholar
  51. Philipp Schindler, Aljosha Judmayer, Nicholas Stifter, and Edgar Weippl. Hydrand: Efficient continuous distributed randomness. In IEEE Security & Privacy, 2020. Google Scholar
  52. Shravan Srinivasan, Alexander Chepurnoy, Charalampos Papamanthou, Alin Tomescu, and Yupeng Zhang. Hyperproofs: Aggregating and maintaining proofs in vector commitments. In USENIX Security, 2022. Google Scholar
  53. Shravan Srinivasan, Ioanna Karantaidou, Foteini Baldimtsi, and Charalampos Papamanthou. Batching, aggregation, and zero-knowledge proofs in bilinear accumulators. In ACM CCS, 2022. Google Scholar
  54. Ewa Syta, Philipp Jovanovic, Eleftherios Kokoris Kogias, Nicolas Gailly, Linus Gasser, Ismail Khoffi, Michael J Fischer, and Bryan Ford. Scalable bias-resistant distributed randomness. In IEEE Security & Privacy, 2017. Google Scholar
  55. Weijie Wang, Annie Ulichney, and Charalampos Papamanthou. BalanceProofs: Maintainable Vector Commitments with Fast Aggregation. In USENIX Security, 2023. Google Scholar
  56. Benjamin Wesolowski. Efficient Verifiable Delay Functions. In Eurocrypt, 2019. Google Scholar
  57. David Yakira, Avi Asayag, Ido Grayevsky, and Idit Keidar. Economically viable randomness. CoRR, 2020. Google Scholar
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