Abstract
Based on the quantum public-key cryptosystem, a transferable quantum cheque scheme is proposed. In our scheme, the bank is a trusted third party who acts as a key generation center and issues quantum blank cheque. The payer makes a payment to the payee by signing the quantum cheque with the private key, and the payee can verify the cheque with the payer’s public key locally. The cheque can be transferred many times between different customers. The transfer and verification phases do not require the help of the bank. Hence, the cheque needs to be cleared only once, which reduces the workload on the bank. Security analysis results show that the proposed quantum cheque scheme is impossible to forge, double spend and repudiate.
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References
D’Ariano, G.M., Yuen, H.P.: Impossibility of measuring the wave function of a single quantum system. Phys. Rev. Lett. 76(16), 2832 (1996)
Wooters, W.K., Zurek, W.K.: Quantum no-cloning theorem. Nature. 299(802), 16–23 (1982)
Wiesner, S.: Conjugate coding. ACM Sigact News. 15(1), 78–88 (1983)
Lutomirski, A.: An online attack against Wiesner’s quantum money. arXiv preprint arXiv:1010.0256 (2010)
Molina, A., Vidick, T., Watrous, J.: Optimal counterfeiting attacks and generalizations for Wiesner’s quantum money. In: Conference on Quantum Computation. Communication, and Cryptography, pp. 45–64. Springer, Berlin (2012)
Nagaj, D., Sattath, O., Brodutch, A., Unruh, D.: An adaptive attack on Wiesner’s quantum money. Quantum Inf. Comput. 16(11&12), 1048–1070 (2016)
Bennett, C.H., Brassard, G., Breidbart, S., Wiesner, S.: Quantum cryptography, or unforgeable subway tokens. In Advances in Cryptology, pp.267-275. Springer, Boston (1983)
Gavinsky, D.: Quantum money with classical verification. In 2012 IEEE 27th Conference on Computational Complexity, pp. 42-52. IEEE (2012)
Kumar, N.: Practically feasible robust quantum money with classical verification. Cryptography. 3(4), 26 (2019)
Aaronson, S.: Quantum copy-protection and quantum money. In 2009 24th Annual IEEE Conference on Computational Complexity, pp. 229-242. IEEE (2009)
Mosca, M., Stebila, D.: Quantum coins. Error-correcting codes, finite geometries and cryptography. 523, 35–47 (2010)
Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S., Yang, K.: On the (im) possibility of obfuscating programs. In Annual international cryptology conference, pp. 1-18. Springer, Berlin (2001)
Barak, B.: How to go beyond the black-box simulation barrier. In Proceedings 42nd IEEE Symposium on Foundations of Computer Science, pp. 106-115, IEEE (2001)
Childs, A. M.: Secure assisted quantum computation. arXiv preprint quant-ph/0111046 (2001)
Broadbent, A., Fitzsimons, J., Kashefi, E.: Universal blind quantum computation. In 2009 50th Annual IEEE Symposium on Foundations of Computer Science, pp. 517-526. IEEE (2009)
Farhi, E., Gosset, D., Hassidim, A., Lutomirski, A., Shor, P.: Quantum money from knots. In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, pp. 276-289 (2012)
Aaronson, S., Christiano, P.: Quantum money from hidden subspaces. In Proceedings of the forty-fourth annual ACM symposium on Theory of computing, pp. 41-60 (2012)
Behera, A., Sattath, O.: Almost Public Quantum Coins. arXiv preprint arXiv:2002.12438 (2020)
Al-Daoud, E.: Unconditionally secure quantum payment system. In Proc of World Academy of Science, Engineering and Technology 20(4), 64–67 (2007)
Moulick, S.R., Panigrahi, P.K.: Quantum cheques. Quantum Inf. Process. 15(6), 2475–2486 (2016)
Behera, B.K., Banerjee, A., Panigrahi, P.K.: Experimental realization of quantum cheque using a five-qubit quantum computer. Quantum Inf. Process. 16(12), 1–12 (2017)
Ngoc, D. D., Van, M. N.: Quantum E-Cheques. arXiv preprint arXiv:1705.10083 (2017)
Do NgocC, D.I.E.P.: Transfering quantum e-cheques in nonsecured channels. System. 2(10), 01 (2017)
Kashefi, E., Kerenidis, I.: Statistical Zero Knowledge and quantum one-way functions. Theor. Comput. Sci. 378(1), 101 (2007)
Hosoyamada, A., Yasuda, K.: Building quantum-one-way functions from block ciphers: Davies-Meyer and Merkle-Damgard constructions. In: International conference on the theory and application of cryptology and information security, pp. 275-304. Springer, Cham (2018)
Gottesman, D., Chuang, I.: Quantum digital signatures. arXiv:quantph/0105032 (2001)
Buhrman, H., Cleve, R., Watrous, J., De Wolf, R.: Quantum fingerprinting. Phys. Rev. Lett. 87(16), 167902 (2001)
Behera, A., Paul, G.: Quantum to classical one-way function and its applications in quantum money authentication. Quantum Inf. Process. 17(8), 200 (2018)
Luo, M.X., Chen, X.B., Yun, D., Yang, Y.X.: Quantum public-key cryptosystem. Int. J. Theor. Phys. 51(3), 912 (2012)
Shang, T., Tang, Y., Chen, R., Liu, J.: Full quantum one-way function for quantum cryptography. Quantum Eng. 2(1), e32 (2020)
Holevo, A.S.: Problems in the mathematical theory of quantum communication channels. Reports Math. Phys. 12(2), 273 (1977)
Luo, M.X., Chen, X.B., Yun, D., Yang, Y.X.: Quantum signature scheme with weak arbitrator. Int. J. Theor. Phys. 51(7), 2135 (2012)
Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67(6), 661 (1991)
Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68(21), 3121 (1992)
Ljunggren, D., Bourennane, M., Karlsson, A.: Authority-based user authentication in quantum key distribution. Phys. Rev. A. 62(2), 022305 (2000)
Funding
This work is supported by National Natural Science Foundation of China (Grant Nos. 61772134, 61701553), National Social Science Foundation of China (21BZZ108), National Defense Science and Technology Innovation Special Zone Project (No. 18-163-11-ZT-002-045-04) and the Open Foundation of State key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications) (SKLNST-2018-1-03).
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Chen, HM., Jia, HY., Wu, X. et al. Transferable Quantum Cheque Scheme Based on Quantum Public-Key Cryptography. Int J Theor Phys 61, 210 (2022). https://doi.org/10.1007/s10773-022-05195-7
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DOI: https://doi.org/10.1007/s10773-022-05195-7