Abstract
Aiming at the problems of large key size and low computation efficiency of linkable ring signature (LRS) schemes from lattice, we construct a LRS scheme based on the RLWE (learning with errors from ring) commitment scheme and further apply the proposed LRS scheme to blockchain to construct an anonymous post-quantum cryptocurrency model. Concretely, we first prove through setting parameters reasonably, we can make a RLWE-based commitment scheme to have homomorphism; Then use the RLWE-based homomorphic commitment scheme, combined with the Σ-protocol and Fiat-Shamir heuristic to construct a LRS scheme; Finally, by combining the proposed LRS scheme with blockchain we present an anonymous post-quantum cryptocurrency model. Analysis shows that compared with the previous LRS schemes, since the proposed LRS scheme is constructed based on the intractability of RLWE problem which can be reduced to SVP (shortest vector problem) on lattice, it can both resist the quantum computer attacks and have smaller key size, signature size and higher computational efficiency. The proposed cryptocurrency model uses the proposed LRS scheme to ensure the sender’s anonymity and the one-time stealth address to guarantee the recipient’s anonymity, which can both protect users’ identities and resist quantum attacks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Nakamoto, S.: Bitcoin: A Peer-to-Peer Electronic Cash System (2008)
Barber, S., Boyen, X., Shi, E., Uzun, E.: Bitter to better—how to make bitcoin a better currency. In: Keromytis, A.D. (ed.) FC 2012. LNCS, vol. 7397, pp. 399–414. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32946-3_29
Reid, F., Harrigan, M.: An analysis of anonymity in the bitcoin system. In: Altshuler, Y., Elovici, Y., Cremers, A., Aharony, N., Pentland, A. (eds.) Security and Privacy in Social Networks, pp. 197–223. Springer, New York (2013). https://doi.org/10.1007/978-1-4614-4139-7_10
Ober, M., Katzenbeisser, S., Hamacher, K.: Structure and anonymity of the bitcoin transaction graph. Fut. Internet 5(2), 237–250 (2013)
Ron, D., Shamir, A.: Quantitative analysis of the full bitcoin transaction graph. In: Sadeghi, A.-R. (ed.) FC 2013. LNCS, vol. 7859, pp. 6–24. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39884-1_2
Maxwell, G.: CoinJoin: bitcoin privacy for the real world (2013). https://bitcointalk.org/index.php?topic=279249.0
Bonneau, J., Narayanan, A., Miller, A., et al.: Mixcoin: anonymity for bitcoin with accountable mixes. In: International Conference on Financial Cryptography and Data Security (FC 2014), pp. 486–504 (2014)
Bergan, T., Anderson, O., Devietti, J., et al.: CryptoNote v 2.0 (2013). https://cryptonote.org/whitepaper.pdf
Miers, I., Garman, C., Green, M., Rubin, A.D.: Zerocoin: anonymous distributede-cash from bitcoin. In: Symposium on Security and Privacy SP2013, pp. 397–411, May 2013. https://doi.org/10.1109/sp.2013.34
Sasson, E.B., Chiesa, A., Garman, C., et al.: Zerocash: decentralized anonymous payments from Bitcoin. In: Security and Privacy (SP 2014), pp. 459–474 (2014)
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
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
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: CRYPTO. Lecture Notes in Computer Science, vol. 576, pp. 129–140 (1991)
Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: CRYPTO. Lecture Notes in Computer Science, vol. 263, pp. 186–194 (1986)
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
Liu, J.K., Wong, D.S.: Linkable ring signatures: security models and new schemes. In: Gervasi, O., et al. (eds.) ICCSA 2005. LNCS, vol. 3481, pp. 614–623. Springer, Heidelberg (2005). https://doi.org/10.1007/11424826_65
Wang, F.H., Hu, Y.P., Wang, C.X.: A lattice-based ring signature scheme from bonsai trees. J. Electron. Inf. Technol. 32(2), 2400–2403 (2010)
Tian, M.M., Huang, L.S., Yang, W.: Efficient lattice-based ring signature scheme. Jisuanji Xuebao (Chin. J. Comput.) 35(4), 712–718 (2012)
Wang, S., Zhao, R.: Lattice-Based Ring Signature Scheme under the Random Oracle Model. Eprint Arxiv (2014)
Yang, R., Au, M.H., Lai, J., et al.: Lattice-based techniques for accountable anonymity: composition of abstract stern’s protocols and weak PRF with efficient protocols from LWR. IACR Cryptology ePrint Archive, p. 781 (2017)
Zhang, H., Zhang, F., Tian, H., Au, M.H.: Anonymous post-quantum cryptocash. In: Meiklejohn, S., Sako, K. (eds.) FC 2018. LNCS, vol. 10957, pp. 461–479. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-662-58387-6_25
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_18
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
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
Benhamouda, F., Krenn, S., Lyubashevsky, V., Pietrzak, K.: Efficient zero-knowledge proofs for commitments from learning with errors over rings. In: Pernul, G., Ryan, P.Y.A., Weippl, E. (eds.) ESORICS 2015. LNCS, vol. 9326, pp. 1–14. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24174-6_16
Liu, J.K., Au, M.H., Susilo, W., et al.: Linkable ring signature with unconditional anonymity. IEEE Trans. Knowl. Data Eng. 26(1), 157–165 (2013)
Acknowledgments
This work was supported by the National Natural Science Foundation of China (61802117), the ‘13th Five-Year’ National Crypto Development Foundation (MMJJ20170122), the Projects of Henan Provincial Department of Science and Technology under Grant (182102310923,192102210280), Key Research Projects of Henan Higher Education Institutions (18A413001,19A520025), Natural Science Foundation of Henan Polytechnic University (T2018-1), Young Backbone Teacher Funded Project of Henan Polytechnic University (2018XQG-10).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Ye, Q. et al. (2020). RLWE Commitment-Based Linkable Ring Signature Scheme and Its Application in Blockchain. In: Zheng, Z., Dai, HN., Tang, M., Chen, X. (eds) Blockchain and Trustworthy Systems. BlockSys 2019. Communications in Computer and Information Science, vol 1156. Springer, Singapore. https://doi.org/10.1007/978-981-15-2777-7_2
Download citation
DOI: https://doi.org/10.1007/978-981-15-2777-7_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-2776-0
Online ISBN: 978-981-15-2777-7
eBook Packages: Computer ScienceComputer Science (R0)