Advertisement

Traceable Ring Signatures with Post-quantum Security

  • Hanwen Feng
  • Jianwei Liu
  • Qianhong WuEmail author
  • Ya-Nan Li
Conference paper
  • 8 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12006)

Abstract

Traceable ring signature (TRS), a variant of ring signature, allows a signer to sign a message anonymously labeled with a tag on behalf of a group of users, but may reveal the signer’s identity if he creates two signatures with the same tag. TRS provides accountable anonymity for users, and serves as an important role in e-voting systems and e-coupon services. However, current TRS schemes are built on hard problems in number theory that cannot resist quantum attackers. To address this issue, first, we propose a general framework of TRS, by using a non-interactive zero-knowledge proof of knowledge, a collision-resistant hash function, and a pseudorandom function with some additional properties. Then, we construct an efficient TRS scheme in the quantum random oracle model, by instantiating the framework with appropriate lattice-based building blocks. Moreover, the signature size of the lattice-based TRS is logarithmic in the ring size.

Notes

Acknowledgement

This paper is supported by the National Key R&D Program of China through project 2017YFB0802502, by the National Cryptography Development Fund through project MMJJ20170106, by the foundation of Science and Technology on Information Assurance Laboratory through project 1421120305162112006, the Natural Science Foundation of China through projects 61972019, 61932011, 61772538, 61672083, 61532021, 61472429, 91646203 and 61402029. We thank all the anonymous reviewers whose comments have greatly improved this paper.

References

  1. 1.
    Ajtai, M.: Generating hard instances of lattice problems (extended abstract). In: STOC 1996, pp. 99–108. ACM (1996)Google Scholar
  2. 2.
    Ambainis, A., Rosmanis, A., Unruh, D.: Quantum attacks on classical proof systems: the hardness of quantum rewinding. In: FOCS 2014, pp. 474–483. IEEE Computer Society (2014)Google Scholar
  3. 3.
    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)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Banerjee, A., Peikert, C., Rosen, A.: Pseudorandom functions and lattices. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 719–737. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-29011-4_42CrossRefGoogle Scholar
  5. 5.
    Baum, C., Lin, H., Oechsner, S.: Towards practical lattice-based one-time linkable ring signatures. In: Naccache, D., et al. (eds.) ICICS 2018. LNCS, vol. 11149, pp. 303–322. Springer, Cham (2018).  https://doi.org/10.1007/978-3-030-01950-1_18CrossRefGoogle Scholar
  6. 6.
    Bellare, M., Goldwasser, S.: New paradigms for digital signatures and message authentication based on non-interactive zero knowledge proofs. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 194–211. Springer, New York (1990).  https://doi.org/10.1007/0-387-34805-0_19CrossRefGoogle Scholar
  7. 7.
    Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudorandom bits. SIAM J. Comput. 13(4), 850–864 (1984)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Boneh, D., Dagdelen, Ö., Fischlin, M., Lehmann, A., Schaffner, C., Zhandry, M.: Random oracles in a quantum world. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 41–69. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-25385-0_3CrossRefzbMATHGoogle Scholar
  9. 9.
    Boneh, D., Lewi, K., Montgomery, H., Raghunathan, A.: Key homomorphic PRFs and their applications. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 410–428. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40041-4_23CrossRefGoogle Scholar
  10. 10.
    Branco, P., Mateus, P.: A traceable ring signature scheme based on coding theory. In: Ding, J., Steinwandt, R. (eds.) PQCrypto 2019. LNCS, vol. 11505, pp. 387–403. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-25510-7_21CrossRefGoogle Scholar
  11. 11.
    Camenisch, J., Hohenberger, S., Lysyanskaya, A.: Compact e-cash. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 302–321. Springer, Heidelberg (2005).  https://doi.org/10.1007/11426639_18CrossRefGoogle Scholar
  12. 12.
    Canetti, R., et al.: Fiat-shamir: from practice to theory. In: STOC 2019, pp. 1082–1090. ACM (2019)Google Scholar
  13. 13.
    Chow, S.S.M., Liu, J.K., Wong, D.S.: Robust receipt-free election system with ballot secrecy and verifiability. In: NDSS 2008. The Internet Society (2008)Google Scholar
  14. 14.
    Cramer, R., Damgård, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994).  https://doi.org/10.1007/3-540-48658-5_19CrossRefGoogle Scholar
  15. 15.
    Feige, U., Lapidot, D., Shamir, A.: Multiple non-interactive zero knowledge proofs based on a single random string (extended abstract). In: FOCS 1990, pp. 308–317. IEEE Computer Society (1990)Google Scholar
  16. 16.
    Feng, H., Liu, J., Wu, Q.: Secure Stern signatures in quantum random oracle model. In: Lin, Z., Papamanthou, C., Polychronakis, M. (eds.) ISC 2019. LNCS, vol. 11723, pp. 425–444. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-30215-3_21CrossRefGoogle Scholar
  17. 17.
    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_12CrossRefGoogle Scholar
  18. 18.
    Franklin, M.K., Zhang, H.: A framework for unique ring signatures. IACR Cryptology ePrint Archive 2012, 577 (2012)Google Scholar
  19. 19.
    Fujisaki, E.: Sub-linear size traceable ring signatures without random oracles. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 393–415. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-19074-2_25CrossRefGoogle Scholar
  20. 20.
    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_13CrossRefGoogle Scholar
  21. 21.
    Garay, J.A., MacKenzie, P., Yang, K.: Strengthening zero-knowledge protocols using signatures. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 177–194. Springer, Heidelberg (2003).  https://doi.org/10.1007/3-540-39200-9_11CrossRefGoogle Scholar
  22. 22.
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC 2009, pp. 169–178. ACM (2009)Google Scholar
  23. 23.
    Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions (extended abstract). In: FOCS 1984, pp. 464–479. IEEE Computer Society (1984)Google Scholar
  24. 24.
    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_9CrossRefGoogle Scholar
  25. 25.
    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_1CrossRefGoogle Scholar
  26. 26.
    Libert, B., Ling, S., Nguyen, K., Wang, H.: Zero-knowledge arguments for lattice-based PRFs and applications to e-cash. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10626, pp. 304–335. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-70700-6_11CrossRefGoogle Scholar
  27. 27.
    Ling, S., Nguyen, K., Stehlé, D., Wang, H.: Improved zero-knowledge proofs of knowledge for the ISIS problem, and applications. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 107–124. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-36362-7_8CrossRefGoogle Scholar
  28. 28.
    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_28CrossRefGoogle Scholar
  29. 29.
    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_6CrossRefGoogle Scholar
  30. 30.
    Peikert, C., Shiehian, S.: Noninteractive zero knowledge for NP from (plain) learning with errors. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11692, pp. 89–114. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-26948-7_4CrossRefGoogle Scholar
  31. 31.
    Rackoff, C., Simon, D.R.: Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 433–444. Springer, Heidelberg (1992).  https://doi.org/10.1007/3-540-46766-1_35CrossRefGoogle Scholar
  32. 32.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC 2005, pp. 84–93. ACM (2005)Google Scholar
  33. 33.
    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_32CrossRefGoogle Scholar
  34. 34.
    Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: FOCS 1994, pp. 124–134. IEEE Computer Society (1994)Google Scholar
  35. 35.
    Stern, J.: A new paradigm for public key identification. IEEE Trans. Inf. Theory 42(6), 1757–1768 (1996)MathSciNetCrossRefGoogle Scholar
  36. 36.
    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_32CrossRefGoogle Scholar
  37. 37.
    Unruh, D.: Non-interactive zero-knowledge proofs in the quantum random oracle model. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 755–784. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46803-6_25CrossRefzbMATHGoogle Scholar
  38. 38.
    Wang, X., Chen, Y., Ma, X.: Adding linkability to ring signatures with one-time signatures. In: Lin, Z., Papamanthou, C., Polychronakis, M. (eds.) ISC 2019. LNCS, vol. 11723, pp. 445–464. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-30215-3_22CrossRefGoogle Scholar
  39. 39.
    Yang, R., Au, M.H., 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. IACR Cryptology ePrint Archive 2017, 781 (2017)Google Scholar
  40. 40.
    Zhandry, M.: How to construct quantum random functions. In: FOCS 2012, pp. 679–687. IEEE Computer Society (2012)Google Scholar
  41. 41.
    Zhandry, M.: Secure identity-based encryption in the quantum random oracle model. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 758–775. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32009-5_44CrossRefzbMATHGoogle Scholar
  42. 42.
    Zhang, H., Zhang, F., Tian, H., Au, M.H.: Anonymous post-quantum cryptocash. IACR Cryptology ePrint Archive 2017, 716 (2017)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Hanwen Feng
    • 1
    • 2
  • Jianwei Liu
    • 1
  • Qianhong Wu
    • 1
    Email author
  • Ya-Nan Li
    • 3
  1. 1.Key Laboratory of Aerospace Network Security, Ministry of Industry and Information Technology, School of Cyber Science and TechnologyBeihang UniversityBeijingChina
  2. 2.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  3. 3.New Jersey Institute of TechnologyNewarkUSA

Personalised recommendations