Abstract
This paper proposes an orderly identity-based quantum multi-signature scheme exploring the concept of locally indistinguishable orthogonal product states. In the developed scheme, the classic message is converted into a quantum bit string with indistinguishable orthogonal product states that cannot be precisely distinguished by local operations and classical communication (LOCC). The private key generator (PKG) generates keys by the signer’s ID and shares them with the signers, which are used in sequence permutation. Moreover, the verifier Bob generates keys shared with the signers, and the latter sign the message with both keys and their ID. Given that a signature verifier can verify the signature with ID, the proposed scheme has the advantages of the classic identity-based signature scheme. Additionally, it avoids the PKG decoding message from the signature, ensuring the security of non-reputation and unforgeability. Moreover, our method does not require long-term quantum memory, making it more secure and efficient.
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References
Rivest, R.L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 26(2), 96–99 (1978)
Miller V.S.: Use of elliptic curves in cryptography. In: Conference on the Theory and Application of Cryptographic Techniques, Springer, Berlin, Heidelberg, pp. 417–426 (1985)
Koblitz, N.: Elliptic curve cryptosystems. Math. Comput. 48(177), 203–209 (1987)
NIST: A proposed federal information processing standard for digital signature standard (DSS). Fed. Regist. 56(169), 42980–42982 (1991)
Gottesman, D., Chuang, I.: Quantum digital signatures. arXiv preprint quant-ph/0105032 (2001)
Zeng, G., Keitel, C.H.: Arbitrated quantum-signature scheme. Phys. Rev. A 65(4), 042312 (2002)
Yang, Y.G., Lei, H., Liu, Z.C., et al.: Arbitrated quantum signature scheme based on cluster states. Quantum Inf. Process. 15(6), 2487–2497 (2016)
Yang, Y.G., Zhou, Z., Teng, Y.W., et al.: Arbitrated quantum signature with an untrusted arbitrator. Eur. Phys. J. D 61(3), 773–778 (2011)
Luo, M.X., Chen, X.B., Yun, D., et al.: Quantum signature scheme with weak arbitrator. Int. J. Theor. Phys. 51(7), 2135–2142 (2012)
Fatahi, N., Naseri, M., Gong, L.H., et al.: High-efficient arbitrated quantum signature scheme based on cluster states. Int. J. Theor. Phys. 56(2), 609–616 (2017)
Shi, R., Ding, W., Shi, J.: Arbitrated quantum signature with Hamiltonian algorithm based on blind quantum computation. Int. J. Theor. Phys. 57(7), 1961–1973 (2018)
Zhang, Y., Zeng, J.: An improved arbitrated quantum scheme with Bell states. Int. J. Theor. Phys. 57(4), 994–1003 (2018)
Jiang, D.H., Xu, Y.L., Xu, G.B.: Arbitrary quantum signature based on local indistinguishability of orthogonal product states. Int. J. Theor. Phys. 58(9), 1036–1045 (2019)
Wang, T.Y., Wei, Z.L.: One-time proxy signature based on quantum cryptography. Quantum Inf. Process. 11(2), 455–463 (2012)
Zhang, K.J., Zhang, W.W., Li, D.: Improving the security of arbitrated quantum signature against the forgery attack. Quantum Inf. Process. 12(8), 2655–2669 (2013)
Su, Q., Li, W.M.: Improved quantum signature scheme with weak arbitrator. Int. J. Theor. Phys. 52(9), 3343–3352 (2013)
Kang, M.S., Hong, C.H., Heo, J., et al.: Quantum signature scheme using a single qubit rotation operator. Int. J. Theor. Phys. 54(2), 614–629 (2015)
Guo, Y., Feng, Y., Huang, D., et al.: Arbitrated quantum signature scheme with continuous-variable coherent states. Int. J. Theor. Phys. 55(4), 2290–2302 (2016)
Wang, T.Y., Ma, J.F., Cai, X.Q.: The postprocessing of quantum digital signatures. Quantum Inf. Process. 16(19), 1–10 (2017)
Ma, H., Li, F., Mao, N., et al.: Network-based arbitrated quantum signature scheme with graph state. Int. J. Theor. Phys. 56(8), 2551–2561 (2017)
Zhang, C.H., Zhou, X.Y., Ding, H.J., et al.: Proof-of-principle demonstration of passive decoy-state quantum digital signatures over 200 km. Phys. Rev. A 10(3), 034033 (2018)
Ding, H.J., Chen, J.J., Ji, L., et al.: 280-km experimental demonstration of a quantum digital signature with one decoy state. Opt. Lett. 45(7), 1711–1714 (2020)
Zhang, C.H., Zhou, X., Zhang, C.M., et al.: Twin-field quantum digital signatures. Opt. Lett. 46(15), 3757–3760 (2021)
Gao, F., Qin, S.J., Guo, F.Z., et al.: Cryptanalysis of the arbitrated quantum signature protocols. Phys. Rev. A 84(2), 022344 (2011)
Liu, F., Zhang, K., Cao, T.: Security weaknesses in arbitrated quantum signature protocols. Int. J. Theor. Phys. 53(1), 277–288 (2014)
Li, Q., Chan, W.H., Wu, C., et al.: On the existence of quantum signature for quantum messages. Int. J. Theor. Phys. 52(12), 4335–4341 (2013)
Zhang, K.J., Qin, S.J., Sun, Y., et al.: Reexamination of arbitrated quantum signature: the impossible and the possible. Quantum Inf. Process. 12(9), 3127–3141 (2013)
Kang, M.S., Hong, C.H., Heo, J., et al.: Comment on “Quantum signature scheme with weak arbitrator.” Int. J. Theor. Phys. 53(6), 1862–1866 (2014)
Zou, X., Qiu, D., Yu, F., et al.: Security problems in the quantum signature scheme with a weak arbitrator. Int. J. Theor. Phys. 53(2), 603–611 (2014)
Li, Q., Li, C., Wen, Z., et al.: On the security of arbitrated quantum signature schemes. J. Phys. A: Math. Theor. 46(1), 015307 (2012)
Shamir, A.: Identity-based cryptosystems and signature schemes. In: Advances in Cryptology: Proceedings of CRYPTO 84(4), pp. 47–53. Springer Berlin Heidelberg (1985)
Chen, F.L., Liu, W.F., Chen, S.G., et al.: Public-key quantum digital signature scheme with one-time pad private-key. Quantum Inf. Process. 17(1), 1–14 (2018)
Buhrman, H., Cleve, R., Watrous, J., et al.: Quantum fingerprinting. Phys. Rev. Lett. 87(16), 167902 (2001)
Itakura, K., Nakamura, K.: A public-key cryptosystem suitable for digital multisignatures. NEC Res. Dev. 71(71), 1–8 (1983)
Jiang, D.H., Hu, Q.Z., Liang, X.Q., et al.: A novel quantum multi-signature protocol based on locally indistinguishable orthogonal product states. Quantum Inf. Process. 18(9), 1–14 (2019)
Shannon, C.E.: Communication theory of secrecy systems. The Bell System Technical Journal 28(4), 656–715 (1949)
Kahn, D.: The codebreakers: The story of secret writing. Am. Hist. Rev. 74(2), 537–538 (1968)
Yu, S., Oh, C.H.: Detecting the local indistinguishability of maximally entangled states. arXiv preprint arXiv:1502.01274 (2015)
Walgate, J., Hardy, L.: Nonlocality, asymmetry, and distinguishing bipartite states. Phys. Rev. Lett. 89(14), 147901 (2002)
Wang, Y.L., Li, M.S., Zheng, Z.J., et al.: Nonlocality of orthogonal product-basis quantum states. Phys. Rev. A 92(3), 032313 (2015)
Zhang, Z.C., Gao, F., Cao, Y., et al.: Local indistinguishability of orthogonal product states. Phys. Rev. A 93(1), 012314 (2016)
Xu, G.B., Wen, Q.Y., Qin, S.J., et al.: Quantum nonlocality of multipartite orthogonal product states. Phys. Rev. A 93(3), 032341 (2016)
Xu, G.B., Yang, Y.H., Wen, Q.Y., et al.: Locally indistinguishable orthogonal product bases in arbitrary bipartite quantum system. Sci. Rep. 6(1), 1–6 (2016)
Xu, G.B., Wen, Q.Y., Gao, F., et al.: Local indistinguishability of multipartite orthogonal product bases. Quantum Inf. Process. 16(11), 1–19 (2017)
Guo, G.P., Li, C.F., Shi, B.S., et al.: Quantum key distribution scheme with orthogonal product states. Phys. Rev. A 64(4), 042301 (2001)
Jiang, D.H., Xu, G.B.: Multiparty quantum key agreement protocol based on locally indistinguishable orthogonal product states. Quantum Inf. Process. 17(7), 1–17 (2018)
Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. arXiv preprint arXiv:2003.06557 (2020)
Weng, C.X., Lu, Y.S., Gao, R.Q., Xie, Y.M., Gu, J., Li, C.L., Li, B.H., Yin, H.L., Chen, Z.B.: Secure and practical multiparty quantum digital signatures. Opt. Express 29(11), 27661–27673 (2021)
Ruan, X., Zhang, H., Zhao, W., Jin, D., Wang, Z., Guo, Y.: Orbital angular momentum-encoded quantum digital signature over atmospheric channel. Quantum Inf. Process. 21(5), 191 (2022)
Cai, X.Q., Wang, T.Y., Wei, C.Y., Gao, F.: Cryptanalysis of quantum digital signature for the access control of sensitive data. Physica A 593, 126949 (2022)
Acknowledgements
This work is supported by “the Fundamental Research Funds for the Central Universities” (Grant Nos. 3282023015; 3282023051), National first-class undergraduate program construction site of “Information Security”, the Research on Digital Identity Trust System for Massive Heterogeneous Terminals in Road Traffic System (Grant No. 2022YFB3104402).
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Liu, A., Chen, Xb., Wang, Z. et al. An orderly quantum multi-signature based on orthogonal product states for the multi-party transaction blockchain. Quantum Inf Process 22, 417 (2023). https://doi.org/10.1007/s11128-023-04169-w
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DOI: https://doi.org/10.1007/s11128-023-04169-w