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Efficient Threshold-Optimal ECDSA

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Cryptology and Network Security (CANS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13099))

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Abstract

This paper proposes a threshold-optimal ECDSA scheme based on the first threshold signature scheme by Gennaro et al. with efficient non-interactive signing for any \(t+1\) signers in the group, provided the total group size is more than twice the threshold t. The scheme does not require any homomorphic encryption or zero-knowledge proofs and is proven to be robust and unforgeable with identifiable aborts tolerating at most t corrupted participants. The security of the scheme is proven in a simulation-based definition, assuming DDH and that ECDSA is existentially unforgeable under chosen message attack. To evaluate the performance of the protocol, it has been implemented in C++ and the results demonstrate the non-interactive signing phase takes 0.12 ms on average meaning over 8000 signatures can be created per second. With pre-signing phase, it takes 3.35 ms in total, which is over 144 times faster than the current state of the art.

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Notes

  1. 1.

    The method can be applied to elliptic curve groups as given here, but it is understood that it may be applied to generic cyclic groups used in the standard DSA.

References

  1. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Robust threshold DSS signatures. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 354–371. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-68339-9_31

    Chapter  Google Scholar 

  2. MacKenzie, P., Reiter, M.K.: Two-party generation of DSA signatures. Int. J. Inf. Secur. 2(3–4), 218–239 (2004)

    Article  Google Scholar 

  3. Lindell, Y.: Fast secure two-party ECDSA signing. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 613–644. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63715-0_21

    Chapter  Google Scholar 

  4. Doerner, J., Kondi, Y., Lee, E., Shelat, A.: Secure two-party threshold ecdsa from ecdsa assumptions. In: 2018 IEEE Symposium on Security and Privacy (SP), pp. 980–997. IEEE (2018)

    Google Scholar 

  5. Castagnos, G., Catalano, D., Laguillaumie, F., Savasta, F., Tucker, I.: Two-party ECDSA from hash proof systems and efficient instantiations. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 191–221. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_7

    Chapter  Google Scholar 

  6. Gennaro, R., Goldfeder, S., Narayanan, A.: Threshold-optimal DSA/ECDSA signatures and an application to bitcoin wallet security. In: Manulis, M., Sadeghi, A.-R., Schneider, S. (eds.) ACNS 2016. LNCS, vol. 9696, pp. 156–174. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39555-5_9

    Chapter  MATH  Google Scholar 

  7. Gennaro, R., Goldfeder, S.: Fast multiparty threshold ecdsa with fast trustless setup. In: Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security, pp. 1179–1194 (2018)

    Google Scholar 

  8. Lindell, Y., Nof, A.: Fast secure multiparty ecdsa with practical distributed key generation and applications to cryptocurrency custody. In: Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security, pp. 1837–1854 (2018)

    Google Scholar 

  9. Doerner, J., Kondi, Y., Lee, E., Shelat, A.: Threshold ecdsa from ecdsa assumptions: the multiparty case. In: 2019 IEEE Symposium on Security and Privacy (SP), pp. 1051–1066. IEEE (2019)

    Google Scholar 

  10. Castagnos, G., Catalano, D., Laguillaumie, F., Savasta, F., Tucker, I.: Bandwidth-efficient threshold EC-DSA. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12111, pp. 266–296. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45388-6_10

    Chapter  Google Scholar 

  11. Battagliola, M., Longo, R., Meneghetti, A., Sala, M.: Threshold ecdsa with an offline recovery party. arXiv preprint arXiv:2007.04036 (2020)

  12. Gagol, A., Straszak, D.: Threshold ecdsa for decentralized asset custody (2020)

    Google Scholar 

  13. Canetti, R., Makriyannis, N., Peled, U.: Uc non-interactive, proactive, threshold ecdsa. IACR Cryptol. ePrint Arch. 2020, 492 (2020)

    Google Scholar 

  14. Gennaro, R., Goldfeder, S.: One round threshold ecdsa with identifiable abort. IACR Cryptol. ePrint Arch. 2020, 540 (2020)

    Google Scholar 

  15. Kravitz, D.W.: Digital signature algorithm (Jul 27 1993), uS Patent 5,231,668

    Google Scholar 

  16. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure distributed key generation for discrete-log based cryptosystems. J. Cryptology 20(1), 51–83 (2007)

    Article  MathSciNet  Google Scholar 

  17. Feldman, P.: A practical scheme for non-interactive verifiable secret sharing. In: 28th Annual Symposium on Foundations of Computer Science (sfcs 1987), pp. 427–438. IEEE (1987)

    Google Scholar 

  18. Damgård, I., Jakobsen, T.P., Nielsen, J.B., Pagter, J.I., Østergård, M.B.: Fast threshold ecdsa with honest majority. IACR Cryptol. ePrint Arch. 2020, 501 (2020)

    Google Scholar 

  19. Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17(2), 281–308 (1988)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The author thanks Owen Vaughan, Wei Zhang, Mehmet Sabir Kiraz, and Katharine Molloy for useful comments on the paper. The author also thanks John Murphy and Josie Wilden for implementing the scheme.

Author information

Authors and Affiliations

  1. nChain AG, Zug, Switzerland

    Michaella Pettit

Authors
  1. Michaella Pettit
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Correspondence to Michaella Pettit .

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Editors and Affiliations

  1. University of Padua, Padua, Italy

    Mauro Conti

  2. Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

    Marc Stevens

  3. AIT Austrian Institute of Technology, Vienna, Austria

    Stephan Krenn

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Pettit, M. (2021). Efficient Threshold-Optimal ECDSA. In: Conti, M., Stevens, M., Krenn, S. (eds) Cryptology and Network Security. CANS 2021. Lecture Notes in Computer Science(), vol 13099. Springer, Cham. https://doi.org/10.1007/978-3-030-92548-2_7

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  • DOI: https://doi.org/10.1007/978-3-030-92548-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92547-5

  • Online ISBN: 978-3-030-92548-2

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