Skip to main content
SpringerLink
Log in

Threshold Ring Signature Scheme from Cryptographic Group Action

  • Conference paper
  • First Online:
Provable and Practical Security (ProvSec 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14217))

Included in the following conference series:

  • 387 Accesses

Abstract

A threshold ring signature (t-out-of-N) is an extension of ring signatures that allow t users jointly sign a message on the behalf of N users, selected in an arbitrary manner, while keeping their identities anonymous. This paper presents a construction of threshold ring signature from cryptographic group action, based on the OR proof of group action and the idea of creating a threshold ring signature scheme from a ring signature scheme. We instantiate the proposed protocols in both isogeny and lattice settings. The signature size of our isogeny-based construction is smaller than the existing threshold ring signature scheme (e.g. 65 KB signatures compared to 187 KB for the same ring size).

This work is partially funded by the Australian Research Council (ARC) Linkage Project LP220100332, Discovery Project DP220100003 and the RevITAlise (RITA) Research Grant 2021.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aguilar Melchor, C., Cayrel, P.-L., Gaborit, P.: A new efficient threshold ring signature scheme based on coding theory. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 1–16. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88403-3_1

    Chapter  Google Scholar 

  2. Alagic, G., et al.: Status report on the third round of the nist post-quantum cryptography standardization process (2022)

    Google Scholar 

  3. Alamati, N., De Feo, L., Montgomery, H., Patranabis, S.: Cryptographic group actions and applications. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12492, pp. 411–439. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64834-3_14

    Chapter  Google Scholar 

  4. Alberto Torres, W.A., et al.: Post-Quantum one-time linkable ring signature and application to ring confidential transactions in blockchain (Lattice RingCT v1.0). In: Susilo, W., Yang, G. (eds.) ACISP 2018. LNCS, vol. 10946, pp. 558–576. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93638-3_32

    Chapter  Google Scholar 

  5. Aranha, D.F., Hall-Andersen, M., Nitulescu, A., Pagnin, E., Yakoubov, S.: Count me in! extendability for threshold ring signatures. In: PKC 2022, pp. 379–406 (2022)

    Google Scholar 

  6. Assidi, H., Ayebie, E.B., Souidi, E.M.: An efficient code-based threshold ring signature scheme. J. Inf. Secur. Appl. 45(C), 52–60 (2019)

    Google Scholar 

  7. Atapoor, S., Baghery, K., Cozzo, D., Pedersen, R.: CSI-shark: CSI-FiSh with sharing-friendly Keys. ePrint 2022/1189 (2022)

    Google Scholar 

  8. Bettaieb, S., Schrek, J.: Improved lattice-based threshold ring signature scheme. In: Gaborit, P. (ed.) PQCrypto 2013. LNCS, vol. 7932, pp. 34–51. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38616-9_3

    Chapter  Google Scholar 

  9. Beullens, W., Katsumata, S., Pintore, F.: Calamari and falafl: logarithmic (linkable) ring signatures from isogenies and lattices. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12492, pp. 464–492. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64834-3_16

    Chapter  Google Scholar 

  10. Beullens, W., Kleinjung, T., Vercauteren, F.: CSI-FiSh: efficient isogeny based signatures through class group computations. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11921, pp. 227–247. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34578-5_9

    Chapter  Google Scholar 

  11. Bonnetain, X., Schrottenloher, A.: Quantum security analysis of CSIDH. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 493–522. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_17

    Chapter  Google Scholar 

  12. Branco, P., Mateus, P.: A code-based linkable ring signature scheme. In: Baek, J., Susilo, W., Kim, J. (eds.) ProvSec 2018. LNCS, vol. 11192, pp. 203–219. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01446-9_12

    Chapter  Google Scholar 

  13. Bresson, E., Stern, J., Szydlo, M.: Threshold ring signatures and applications to ad-hoc groups. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 465–480. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45708-9_30

    Chapter  Google Scholar 

  14. Castryck, W., Decru, T.: An efficient key recovery attack on sidh (preliminary version). Cryptology ePrint Archive, Paper 2022/975 (2022)

    Google Scholar 

  15. 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. LNCS, vol. 11274, pp. 395–427. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03332-3_15

    Chapter  Google Scholar 

  16. Cayrel, P.-L., El Yousfi Alaoui, S.M., Hoffmann, G., Véron, P.: An improved threshold ring signature scheme based on error correcting codes. In: Özbudak, F., Rodríguez-Henríquez, F. (eds.) WAIFI 2012. LNCS, vol. 7369, pp. 45–63. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31662-3_4

    Chapter  Google Scholar 

  17. Cayrel, P.-L., Lindner, R., Rückert, M., Silva, R.: A lattice-based threshold ring signature scheme. In: Abdalla, M., Barreto, P.S.L.M. (eds.) LATINCRYPT 2010. LNCS, vol. 6212, pp. 255–272. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14712-8_16

    Chapter  Google Scholar 

  18. Couveignes, J.-M.: Hard homogeneous spaces. ePrint 2006/291 (2006)

    Google Scholar 

  19. Cozzo, D., Smart, N.P.: Sashimi: cutting up CSI-FiSh secret keys to produce an actively secure distributed signing protocol. In: Ding, J., Tillich, J.-P. (eds.) PQCrypto 2020. LNCS, vol. 12100, pp. 169–186. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-44223-1_10

    Chapter  Google Scholar 

  20. De Feo, L., Galbraith, S.D.: SeaSign: compact isogeny signatures from class group actions. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11478, pp. 759–789. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_26

    Chapter  Google Scholar 

  21. De Feo, L., Meyer, M.: Threshold schemes from isogeny assumptions. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12111, pp. 187–212. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45388-6_7

    Chapter  Google Scholar 

  22. 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_15

    Chapter  Google Scholar 

  23. Ducas, L., et al.: Crystals-dilithium: a lattice-based digital signature scheme. In: TCHES, pp. 238–268 (2018)

    Google Scholar 

  24. Duong, D.H., Tran, H.T., Susilo, W., Luyen, L.V.: An efficient multivariate threshold ring signature scheme. Comput. Stand. Interfaces 74, 103489 (2021)

    Article  Google Scholar 

  25. Groth, J., Kohlweiss, M.: One-out-of-many proofs: or how to leak a secret and spend a coin. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 253–280. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_9

    Chapter  Google Scholar 

  26. Haque, A., Krenn, S., Slamanig, D., Striecks, C.: Logarithmic-size (linkable) threshold ring signatures in the plain model. In: PKC 2022, pp. 437–467 (2022)

    Google Scholar 

  27. Haque, A., Scafuro, A.: Threshold ring signatures: new definitions and post-quantum security. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12111, pp. 423–452. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45388-6_15

    Chapter  Google Scholar 

  28. Langlois, A., Stehlé, D.: Worst-case to average-case reductions for module lattices. Des. Codes Cryptogr. 75(3), 565–599 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  29. Li, L., Xu, M.: Ripplesign: isogeny-based threshold ring signatures with combinatorial methods. In: CSP 2022, pp. 11–15 (2022)

    Google Scholar 

  30. Liu, J.K., Wong, D.S.: On the security models of (threshold) ring signature schemes. In: Park, C., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 204–217. Springer, Heidelberg (2005). https://doi.org/10.1007/11496618_16

    Chapter  Google Scholar 

  31. Lu, X., Au, M.H., Zhang, Z.: Raptor: a practical lattice-based (linkable) ring signature. In: Deng, R.H., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds.) ACNS 2019. LNCS, vol. 11464, pp. 110–130. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21568-2_6

    Chapter  Google Scholar 

  32. Meyer, M., Reith, S.: A faster way to the CSIDH. ePrint 2018/782 (2018)

    Google Scholar 

  33. Okamoto, T., Tso, R., Yamaguchi, M., Okamoto, E.: A k-out-of-n ring signature with flexible participation for signers. ePrint 2018/728 (2018)

    Google Scholar 

  34. Peikert, C.: He gives C-Sieves on the CSIDH. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 463–492. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_16

    Chapter  Google Scholar 

  35. Petzoldt, A., Bulygin, S., Buchmann, J.: A multivariate based threshold ring signature scheme. ePrint 2012/194 (2012)

    Google Scholar 

  36. Stolbunov, A.: Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves. Adv. Math. Commun. 4(2), 215–235 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  37. Stolbunov, A.: Cryptographic schemes based on isogenies (2012)

    Google Scholar 

  38. Tang, G., Duong, D.H., Joux, A., Plantard, T., Qiao, Y., Susilo, W.: Practical post-quantum signature schemes from isomorphism problems of trilinear forms. In: EUROCRYPT 2022, pp. 582–612. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-07082-2_21

  39. Tsang, P.P., Wei, V.K.: Short linkable ring signatures for E-Voting, E-Cash and attestation. In: Deng, R.H., Bao, F., Pang, H.H., Zhou, J. (eds.) ISPEC 2005. LNCS, vol. 3439, pp. 48–60. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31979-5_5

    Chapter  Google Scholar 

  40. Tsang, P.P., Wei, V.K., Chan, T.K., Au, M.H., Liu, J.K., Wong, D.S.: Separable linkable threshold ring signatures. In: Canteaut, A., Viswanathan, K. (eds.) INDOCRYPT 2004. LNCS, vol. 3348, pp. 384–398. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30556-9_30

    Chapter  Google Scholar 

  41. Yuen, T.H., Liu, J.K., Au, M.H., Susilo, W., Zhou, J.: Threshold ring signature without random oracles. In: ASIACCS 2011, pp. 261–267 (2011)

    Google Scholar 

  42. Zhang, X., Liu, J.K., Steinfeld, R., Kuchta, V., Yu, J.: Revocable and linkable ring signature. In: Liu, Z., Yung, M. (eds.) Inscrypt 2019. LNCS, vol. 12020, pp. 3–27. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-42921-8_1

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Cybersecurity and Cryptology, School of Computing and Information Technology, University of Wollongong, Northfields Avenue, Wollongong, NSW, 2522, Australia

    Minh Thuy Truc Pham, Dung Hoang Duong, Yannan Li & Willy Susilo

Authors
  1. Minh Thuy Truc Pham
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dung Hoang Duong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yannan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Willy Susilo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Dung Hoang Duong , Yannan Li or Willy Susilo .

Editor information

Editors and Affiliations

  1. Hubei University of Technology, Wuhan, China

    Mingwu Zhang

  2. Hong Kong Polytechnic University, Kowloon, Hong Kong

    Man Ho Au

  3. University of Wollongong, Wollongong, NSW, Australia

    Yudi Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Pham, M.T.T., Duong, D.H., Li, Y., Susilo, W. (2023). Threshold Ring Signature Scheme from Cryptographic Group Action. In: Zhang, M., Au, M.H., Zhang, Y. (eds) Provable and Practical Security. ProvSec 2023. Lecture Notes in Computer Science, vol 14217. Springer, Cham. https://doi.org/10.1007/978-3-031-45513-1_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-45513-1_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-45512-4

  • Online ISBN: 978-3-031-45513-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation