Skip to main content

Post-Quantum One-Time Linkable Ring Signature and Application to Ring Confidential Transactions in Blockchain (Lattice RingCT v1.0)

  • Conference paper
  • First Online:
Information Security and Privacy (ACISP 2018)

Abstract

In this paper, we construct a Lattice-based one-time Linkable Ring Signature (L2RS) scheme, which enables the public to verify if two or more signatures were generated by same signatory, whilst still preserving the anonymity of the signatory. The L2RS provides unconditional anonymity and security guarantees under the Ring Short Integer Solution (Ring-SIS) lattice hardness assumption. The proposed L2RS scheme is extended to be applied in a protocol that we called Lattice Ring Confidential transaction (Lattice RingCT) v1.0, which forms the foundation of the privacy-preserving protocol in any post-quantum secure cryptocurrency such as Hcash.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Notes

  1. 1.

    The Ring-SIS and Ring-LWE refer to the Ring mathematical structure and differ from the Ring in the Ring Signature scheme.

References

  1. Rivest, R.L., Shamir, A., Tauman, Y.: How to leak a secret. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 552–565. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_32

    Chapter  Google Scholar 

  2. Chaum, D., van Heyst, E.: Group signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 257–265. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46416-6_22

    Chapter  Google Scholar 

  3. Liu, J.K., Wei, V.K., Wong, D.S.: Linkable spontaneous anonymous group signature for ad hoc groups. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) ACISP 2004. LNCS, vol. 3108, pp. 325–335. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27800-9_28

    Chapter  Google Scholar 

  4. Liu, J.K., Au, M.H., Huang, X., Susilo, W., Zhou, J., Yu, Y.: New insight to preserve online survey accuracy and privacy in big data era. In: Kutyłowski, M., Vaidya, J. (eds.) ESORICS 2014. LNCS, vol. 8713, pp. 182–199. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11212-1_11

    Chapter  Google Scholar 

  5. Noether, S.: Ring signature confidential transactions for monero. IACR Cryptology ePrint Archive, vol. 2015, p. 1098 (2015)

    Google Scholar 

  6. Elgamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory 31, 469–472 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  7. Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  8. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Micciancio, D., Regev, O.: Lattice-based cryptography. In: Bernstein, D.J., Buchmann, J., Dahmen, E. (eds.) Post-Quantum Cryptography, pp. 147–191. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-540-88702-7_5

    Chapter  MATH  Google Scholar 

  10. Ducas, L., Durmus, A., Lepoint, T., Lyubashevsky, V.: Lattice signatures and bimodal Gaussians. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 40–56. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_3

    Chapter  Google Scholar 

  11. Au, M.H., Liu, J.K., Susilo, W., Yuen, T.H.: Secure ID-based linkable and revocable-iff-linked ring signature with constant-size construction. Theor. Comput. Sci. 469, 1–14 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, J.K., Wong, D.S.: Enhanced security models and a generic construction approach for linkable ring signature. Int. J. Found. Comput. Sci. 17(6), 1403–1422 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Au, M.H., Liu, J.K., Susilo, W., Yuen, T.H.: Constant-size ID-based linkable and revocable-iff-linked ring signature. In: Barua, R., Lange, T. (eds.) INDOCRYPT 2006. LNCS, vol. 4329, pp. 364–378. Springer, Heidelberg (2006). https://doi.org/10.1007/11941378_26

    Chapter  Google Scholar 

  14. Liu, J.K., Susilo, W., Wong, D.S.: Ring signature with designated linkability. In: Yoshiura, H., Sakurai, K., Rannenberg, K., Murayama, Y., Kawamura, S. (eds.) IWSEC 2006. LNCS, vol. 4266, pp. 104–119. Springer, Heidelberg (2006). https://doi.org/10.1007/11908739_8

    Chapter  Google Scholar 

  15. Fujisaki, E., Suzuki, K.: Traceable ring signature. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 181–200. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71677-8_13

    Chapter  Google Scholar 

  16. Tsang, P.P., Au, M.H., Liu, J.K., Susilo, W., Wong, D.S.: A suite of non-pairing ID-based threshold ring signature schemes with different levels of anonymity (extended abstract). In: Heng, S.-H., Kurosawa, K. (eds.) ProvSec 2010. LNCS, vol. 6402, pp. 166–183. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16280-0_11

    Chapter  Google Scholar 

  17. Liu, J.K., Au, M.H., Susilo, W., Zhou, J.: Linkable ring signature with unconditional anonymity. IEEE Trans. Knowl. Data Eng. 26(1), 157–165 (2014)

    Article  Google Scholar 

  18. Yuen, T.H., Liu, J.K., Au, M.H., Susilo, W., Zhou, J.: Efficient linkable and/or threshold ring signature without random oracles. Comput. J. 56, 407–421 (2013)

    Article  Google Scholar 

  19. Bernstein, D.J., Lange, T.: Post-quantum cryptography. Nature 549, 188–194 (2017)

    Article  Google Scholar 

  20. Goldreich, O., Goldwasser, S., Halevi, S.: Public-key cryptosystems from lattice reduction problems. In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 112–131. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052231

    Chapter  Google Scholar 

  21. Hoffstein, J., Pipher, J., Silverman, J.H.: NSS: an NTRU lattice-based signature scheme. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 211–228. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44987-6_14

    Chapter  Google Scholar 

  22. Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Symposium on Theory of Computing - STOC 2008, pp. 197–206. ACM Press (2008)

    Google Scholar 

  23. Lyubashevsky, V.: Fiat-shamir with aborts: applications to lattice and factoring-based signatures. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 598–616. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_35

    Chapter  Google Scholar 

  24. Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_12

    Chapter  Google Scholar 

  25. Ajtai, M.: Generating hard instances of lattice problems. In: ACM Symposium on Theory of Computing, pp. 99–108. ACM (1996)

    Google Scholar 

  26. Micciancio, D.: Generalized compact knapsacks, cyclic lattices, and efficient one-way functions. Comput. Complex. 16(4), 365–411 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  27. Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1–23. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_1

    Chapter  Google Scholar 

  28. Brakerski, Z., Kalai, Y.T.: A Framework for Efficient Signatures, Ring Signatures and Identity Based Encryption in the Standard Model (2010). https://eprint.iacr.org/2010/086/

  29. Aguilar Melchor, C., Bettaieb, S., Boyen, X., Fousse, L., Gaborit, P.: Adapting lyubashevsky’s signature schemes to the ring signature setting. In: Youssef, A., Nitaj, A., Hassanien, A.E. (eds.) AFRICACRYPT 2013. LNCS, vol. 7918, pp. 1–25. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38553-7_1

    Chapter  Google Scholar 

  30. Libert, B., Ling, S., Nguyen, K., Wang, H.: Zero-knowledge arguments for lattice-based accumulators: logarithmic-size ring signatures and group signatures without trapdoors. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 1–31. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_1

    Chapter  Google Scholar 

  31. Yang, R., Ho Au, R., Lai, J., Xu, Q., Yu, Z.: Lattice-Based Techniques for Accountable Anonymity: Composition of Abstract Stern’s Protocols and Weak PRF with Efficient Protocols from LWR. https://eprint.iacr.org/2017/781/

  32. Zhang, H., Zhang, F., Tian, H., Au, M.H.: Anonymous Post-Quantum Cryptocash (Full Version). https://eprint.iacr.org/2017/716/

  33. Baum, C., Huang, L., Sabine, O.: Towards Practical Lattice-Based One-Time Linkable Ring Signatures (2018). https://eprint.iacr.org/2018/107/

  34. Lyubashevsky, V., Seiler, G.: Short, invertible elements in partially splitting cyclotomic rings and applications to lattice-based zero-knowledge proofs. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10820, pp. 204–224. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78381-9_8

    Chapter  MATH  Google Scholar 

  35. Alberto Torres, W., Steinfeld, R., Sakzad, A., Liu, J.K., Kuchta, V., Bhattacharjee, N., Au, M.H., Cheng, J.: Post-Quantum One-Time Linkable Ring Signature and Application to Ring Confidential Transactions in Blockchain (Lattice RingCT v1.0). https://eprint.iacr.org/2018/379

  36. Sun, S.-F., Au, M.H., Liu, J.K., Yuen, T.H.: RingCT 2.0: a compact accumulator-based (linkable ring signature) protocol for blockchain cryptocurrency monero. In: Foley, S.N., Gollmann, D., Snekkenes, E. (eds.) ESORICS 2017. LNCS, vol. 10493, pp. 456–474. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66399-9_25

    Chapter  Google Scholar 

  37. Chen, Y., Nguyen, P.Q.: BKZ 2.0: better lattice security estimates. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 1–20. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_1

    Chapter  Google Scholar 

Download references

Acknowledgement

The work of Ron Steinfeld and Amin Sakzad was supported in part by ARC Discovery Project grant DP150100285. This work was also supported by the Monash-HKPU-Collinstar Blockchain Research Lab.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Wilson Abel Alberto Torres , Ron Steinfeld , Amin Sakzad or Joseph K. Liu .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Alberto Torres, W.A. et al. (2018). 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) Information Security and Privacy. ACISP 2018. Lecture Notes in Computer Science(), vol 10946. Springer, Cham. https://doi.org/10.1007/978-3-319-93638-3_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-93638-3_32

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93637-6

  • Online ISBN: 978-3-319-93638-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics