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Secure Computation of Shared Secrets and Its Applications

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Information Security Applications (WISA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13009))

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Abstract

There has been renewed attention to threshold signature in recent years as the threshold version of the ECDSA and SM2 Elliptic Curve Cryptographic Algorithm (SM2) could be used in Bitcoin as an underlying digital signature scheme to protect users’ private keys that guarantees transactions. A (t, n) threshold signature scheme means in a set of n parties, at least t players can exercise the right of generating signatures on behalf of the group, and any less than t of the players’ cooperation cannot generate a valid signature for the message nor obtain any information about the shared secret key. Thus, it is meaningful to construct a purely (t, n) threshold SM2 signature scheme (purely (t, n) means in the whole signature scheme, the threshold value is fixed to t). We propose a robust multiplication protocol of shared secrets to resolve the “multiplication of shared secrets” problem in existing threshold signature schemes. Using the proposed multiplication protocol, we improve the existing secret reciprocal computation protocol and show how to get a purely (t, n) threshold SM2 signature scheme.

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References

  1. Béguin, P., Cresti, A.: General short computational secret sharing schemes. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol. 921, pp. 194–208. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-49264-X_16

    Chapter  Google Scholar 

  2. Blakley, G.R.: Safeguarding cryptographic keys. In: 1979 International Workshop on Managing Requirements Knowledge (MARK), pp. 313–318. IEEE (1979)

    Google Scholar 

  3. Boneh, D., Gennaro, R., Goldfeder, S.: Using level-1 homomorphic encryption to improve threshold DSA signatures for bitcoin wallet security. In: Lange, T., Dunkelman, O. (eds.) LATINCRYPT 2017. LNCS, vol. 11368, pp. 352–377. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25283-0_19

    Chapter  Google Scholar 

  4. Boyd, C.: Digital multisignatures. Cryptography and Coding, pp. 241–246 (1986)

    Google Scholar 

  5. Canetti, R., Gennaro, R., Goldfeder, S., Makriyannis, N., Peled, U.: UC non-interactive, proactive, threshold ECDSA with identifiable aborts. Cryptology ePrint Archive, Report 2021/060 (2021). https://eprint.iacr.org/2021/060

  6. 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 

  7. Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults. In: 26th Annual Symposium on Foundations of Computer Science (SFCS 1985), pp. 383–395, October 1985. https://doi.org/10.1109/SFCS.1985.64

  8. Damgård, I., Jakobsen, T.P., Nielsen, J.B., Pagter, J.I., Østergaard, M.B.: Fast threshold ECDSA with honest majority. In: Galdi, C., Kolesnikov, V. (eds.) SCN 2020. LNCS, vol. 12238, pp. 382–400. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-57990-6_19

    Chapter  Google Scholar 

  9. Davida, G.I., DeMillo, R.A., Lipton, R.J.: Protecting shared cryptographic keys. In: 1980 IEEE Symposium on Security and Privacy, p. 100. IEEE (1980)

    Google Scholar 

  10. Desmedt, Y., Frankel, Y.: Threshold cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0_28

    Chapter  Google Scholar 

  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 (SP), pp. 980–997. IEEE (2018)

    Google Scholar 

  12. 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 

  13. 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 

  14. 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 

  15. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure distributed key generation for discrete-log based cryptosystems. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 295–310. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48910-X_21

    Chapter  Google Scholar 

  16. Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and fast-track multiparty computations with applications to threshold cryptography. In: Proceedings of the Seventeenth Annual ACM Symposium on Principles of Distributed Computing, pp. 101–111 (1998)

    Google Scholar 

  17. GM/T 0003–2012: Public Key Cryptographic Algorithm SM2 Based on Elliptic Curves. China’s State Cryptography Administration, Beijing (2010)

    Google Scholar 

  18. Johnson, D., Menezes, A., Vanstone, S.: The elliptic curve digital signature algorithm (ECDSA). Int. J. Inf. Secur. 1(1), 36–63 (2001)

    Article  Google Scholar 

  19. Langford, S.K.: Threshold DSS signatures without a trusted party. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 397–409. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-44750-4_32

    Chapter  Google Scholar 

  20. 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 

  21. 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 

  22. 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_8

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  24. Pedersen, T.P.: Distributed provers with applications to undeniable signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 221–242. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46416-6_20

    Chapter  Google Scholar 

  25. Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1_9

    Chapter  Google Scholar 

  26. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  Google Scholar 

  27. Shang, M., Ma, Y., Lin, J., Jing, J.: A threshold scheme for SM2 elliptic curve cryptographic algorithm. J. Cryptol. Res. 1(2), 155 (2014). https://doi.org/10.13868/j.cnki.jcr.000015. http://www.jcr.cacrnet.org.cn/CN/abstract/abstract24.shtml. (in Chinese)

  28. Yang, J., Lu, Y., Chen, L., Ni, W.: A SM2 elliptic curve threshold signature scheme without a trusted center. TIIS 10, 897–913 (2016)

    Google Scholar 

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Authors and Affiliations

  1. Institute of Cybersecurity and Cryptology, School of Computing and Information Technology, University of Wollongong, Wollongong, Australia

    Xin Liu, Willy Susilo & Joonsang Baek

Authors
  1. Xin Liu
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  2. Willy Susilo
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  3. Joonsang Baek
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Correspondence to Xin Liu .

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Editors and Affiliations

  1. Sungkyunkwan University, Suwon-Si, Korea (Republic of)

    Hyoungshick Kim

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Liu, X., Susilo, W., Baek, J. (2021). Secure Computation of Shared Secrets and Its Applications. In: Kim, H. (eds) Information Security Applications. WISA 2021. Lecture Notes in Computer Science(), vol 13009. Springer, Cham. https://doi.org/10.1007/978-3-030-89432-0_10

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  • DOI: https://doi.org/10.1007/978-3-030-89432-0_10

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  • Online ISBN: 978-3-030-89432-0

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