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Sashimi: Cutting up CSI-FiSh Secret Keys to Produce an Actively Secure Distributed Signing Protocol

  • Daniele Cozzo
  • Nigel P. SmartEmail author
Conference paper
  • 82 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12100)

Abstract

We present the first actively secure variant of a distributed signature scheme based on isogenies. The protocol produces signatures from the recent CSI-FiSh signature scheme. Our scheme works for any access structure, as we use a replicated secret sharing scheme to define the underlying secret sharing; as such it is only practical when the number of maximally unqualified sets is relatively small. This, however, includes the important case of full threshold, and (nt)-threshold schemes when n is small.

Notes

Acknowledgments

We would like to thank Frederik Vercauteren for the numerous and useful discussions on the arithmetic of isogenies. This work has been supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by the FWO under an Odysseus project GOH9718N and by CyberSecurity Research Flanders with reference number VR20192203. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the ERC or FWO.

References

  1. 1.
    Beullens, W., Kleinjung, T., Vercauteren, F.: CSI-FiSh: efficient isogeny based signatures through class group computations. IACR Cryptology ePrint Archive 2019, 498 (2019). https://eprint.iacr.org/2019/498
  2. 2.
    Brandao, L.T.A.N., Davidson, M., Vassilev, A.: NIST 8214A (Draft): towards NIST standards for threshold schemes for cryptographic primitives: a preliminary roadmap (2019). https://nvlpubs.nist.gov/nistpubs/ir/2019/NIST.IR.8214A-draft.pdf
  3. 3.
    Castryck, W., Lange, T., Martindale, C., Panny, L., Renes, J.: CSIDH: an efficient post-quantum commutative group action. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018, Part III. LNCS, vol. 11274, pp. 395–427. Springer, Cham (2018).  https://doi.org/10.1007/978-3-030-03332-3_15CrossRefGoogle Scholar
  4. 4.
    Cogliati, B., et al.: Provable security of (tweakable) block ciphers based on substitution-permutation networks. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part I. LNCS, vol. 10991, pp. 722–753. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-96884-1_24CrossRefGoogle Scholar
  5. 5.
    Couveignes, J.M.: Hard homogeneous spaces. Cryptology ePrint Archive, Report 2006/291 (2006). http://eprint.iacr.org/2006/291
  6. 6.
    Cozzo, D., Smart, N.P.: Sharing the LUOV: threshold post-quantum signatures. IACR Cryptology ePrint Archive 2019, 1060 (2019). https://eprint.iacr.org/2019/1060
  7. 7.
    Cramer, R., Damgård, I., Ishai, Y.: Share conversion, pseudorandom secret-sharing and applications to secure computation. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 342–362. Springer, Heidelberg (2005).  https://doi.org/10.1007/978-3-540-30576-7_19CrossRefGoogle Scholar
  8. 8.
    Damgård, I., Koprowski, M.: Practical threshold RSA signatures without a trusted dealer. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 152–165. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-44987-6_10CrossRefGoogle Scholar
  9. 9.
    De Feo, L., Galbraith, S.D.: SeaSign: compact isogeny signatures from class group actions. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019, Part III. LNCS, vol. 11478, pp. 759–789. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-17659-4_26CrossRefGoogle Scholar
  10. 10.
    Decru, T., Panny, L., Vercauteren, F.: Faster SeaSign signatures through improved rejection sampling. In: Ding, J., Steinwandt, R. (eds.) PQCrypto 2019. LNCS, vol. 11505, pp. 271–285. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-25510-7_15CrossRefGoogle Scholar
  11. 11.
    Doerner, J., Kondi, Y., Lee, E., Shelat, A.: Secure two-party threshold ECDSA from ECDSA assumptions. In: 2018 IEEE Symposium on Security and Privacy, pp. 980–997. IEEE Computer Society Press, May 2018Google Scholar
  12. 12.
    Feo, L.D., Meyer, M.: Threshold schemes from isogeny assumptions. IACR Cryptology ePrint Archive 2019, 1288 (2019). https://eprint.iacr.org/2019/1288
  13. 13.
    Gennaro, R., Goldfeder, S.: Fast multiparty threshold ECDSA with fast trustless setup. In: Lie, D., Mannan, M., Backes, M., Wang, X. (eds.) ACM CCS 2018, pp. 1179–1194. ACM Press, October 2018Google Scholar
  14. 14.
    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_9CrossRefzbMATHGoogle Scholar
  15. 15.
    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_31CrossRefGoogle Scholar
  16. 16.
    Lindell, Y.: Fast secure two-party ECDSA signing. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part II. LNCS, vol. 10402, pp. 613–644. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63715-0_21CrossRefGoogle Scholar
  17. 17.
    Lindell, Y., Nof, A.: Fast secure multiparty ECDSA with practical distributed key generation and applications to cryptocurrency custody. In: Lie, D., Mannan, M., Backes, M., Wang, X. (eds.) ACM CCS 2018, pp. 1837–1854. ACM Press, October 2018Google Scholar
  18. 18.
    Lindell, Y., Nof, A., Ranellucci, S.: Fast secure multiparty ECDSA with practical distributed key generation and applications to cryptocurrency custody. IACR Cryptology ePrint Archive 2018, 987 (2018). https://eprint.iacr.org/2018/987
  19. 19.
    MacKenzie, P., Reiter, M.K.: Two-party generation of DSA signatures. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 137–154. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-44647-8_8CrossRefGoogle Scholar
  20. 20.
    Rostovtsev, A., Stolbunov, A.: Public-key cryptosystem based on isogenies. Cryptology ePrint Archive, Report 2006/145 (2006). http://eprint.iacr.org/2006/145
  21. 21.
    Shoup, V.: Practical threshold signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000).  https://doi.org/10.1007/3-540-45539-6_15CrossRefGoogle Scholar
  22. 22.
    Stolbunov, A.: Cryptographic schemes based on isogenies. Ph.D. thesis, NTNU (2012)Google Scholar
  23. 23.
    Vélu, J.: Isogènies entre courbes elliptiques. C.R. Acad. Sc. Paris, Série 273, 238–241 (1971)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.imec-COSICKU LeuvenLeuvenBelgium
  2. 2.University of BristolBristolUK

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