Abstract
This work proposes two fault-tolerant quantum blind signature protocols based on the entanglement swapping of logical Bell states, which are robust against two kinds of collective noises: the collective-dephasing noise and the collective-rotation noise, respectively. Both of the quantum blind signature protocols are constructed from four-qubit decoherence-free (DF) states, i.e., logical Bell qubits. The initial message is encoded on the logical Bell qubits with logical unitary operations, which will not destroy the anti-noise trait of the logical Bell qubits. Based on the fundamental property of quantum entanglement swapping, the receiver simply performs two Bell-state measurements (rather than four-qubit joint measurements) on the logical Bell qubits to verify the signature, which makes the protocols more convenient in a practical application. Different from the existing quantum signature protocols, our protocols can offer the high fidelity of quantum communication with the employment of logical qubits. Moreover, we hereinafter prove the security of the protocols against some individual eavesdropping attacks, and we show that our protocols have the characteristics of unforgeability, undeniability and blindness.
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References
Diffie, W., Hellman, M.: New directions in cryptography. IEEE. Trans. Inf. Theory 22, 644–654 (1976)
Chaum, D.: Blind signature for untraceable payments. In: Proceedings of CRYPTO’82, pp. 199–203 (1982)
Harn, L.: Cryptanalysis of the blind signature based on the discrete logarithm problem. Electron. Lett. 31, 1136–1137 (1995)
Fan, C.I., Lei, C.L.: Efficient blind signature scheme based on quadratic residues. Electron. Lett. 32, 811–813 (1996)
Mohammed, E., Emarah, A.E., El-Shennawy, K.: Elliptic curve cryptosystems on smart cards. In: Proceedings of 35th Annual International Carnahan Conference on Security Technology, pp. 213–222 (2001)
Chien, H., Jan, J., Tseng, Y.: RSA-based partially blind signature with low computation. In: Proceedings of 8th International Conference on Parallel and Distributed Systems (ICPADS), pp. 385–389 (2001)
Clarke, P.J., Collins, R.J., Dunjko, V., et al.: Experimental demonstration of quantum digital signatures using phase-encoded coherent states of light. Nat. Commun. 3, 1174 (2012)
Gottesman, D., Chuang, I.: Quantum digital signatures. arXiv:quant-ph/0105032 (2001)
Zeng, G.H., Keitel, C.H.: Arbitrated quantum-signature scheme. Phys. Rev. A 65, 042312 (2002)
Li, Q., Chan, W.H., Long, D.Y.: Arbitrated quantum signature scheme using Bell states. Phys. Rev. A 79, 054307 (2009)
Andersson, E., Curty, M., Jex, I.: Experimentally realizable quantum comparison of coherent states and its applications. Phys. Rev. A 74, 022304 (2006)
Dunjko, V., Wallden, P., Andersson, E.: Quantum digital signatures without quantum memory. Phys. Rev. Lett. 112, 040502 (2014)
Collins, R.J., Donaldson, R.J., Dunjko, V., et al.: Realization of quantum digital signatures without the requirement of quantum memory. Phys. Rev. Lett. 113, 040502 (2014)
Wallden, P., Dunjko, V., Kent, A., et al.: Quantum digital signatures with quantum-key-distribution components. Phys. Rev. A 91, 042304 (2015)
Lee, H., Hong, C., Kim, H., et al.: Arbitrated quantum signature scheme with message recovery. Phys. Lett. A 321, 295–300 (2004)
Wen, X.J., Liu, Y., Sun, Y.: Quantum multi-signature protocol based on teleportation. Z. Naturforsch. A 62, 147–151 (2007)
Zeng, G.H., Lee, M.H., Guo, Y., et al.: Continuous variable quantum signature algorithm. Int. J. Quantum Inf. 5, 553–573 (2007)
Wen, X.J., Niu, X.M., Ji, L.P., et al.: A weak blind signature scheme based on quantum cryptography. Opt. Commun. 282, 666–669 (2008)
Su, Q., Huang, Z., Wen, Q.Y., et al.: Quantum blind signature based on two-state vector formalism. Opt. Commun. 283, 4408–4410 (2010)
Wang, T.Y., Wen, Q.Y.: Fair quantum blind signatures. Chin. Phys. B 19, 060307 (2010)
Yin, X.R., Ma, W.P., Liu, W.Y.: A blind quantum signature scheme with \(\chi \)-type entangled states. Int. J. Theor. Phys. 51, 455–461 (2012)
Wang, M.M., Chen, X.B., Niu, X.X., et al.: Re-examining the security of blind quantum signature protocols. Phys. Scr. 86, 055006 (2012)
Khodambashi, S., Zakerolhosseini, A.: A sessional blind signature based on quantum cryptography. Quantum Inf. Process. 13, 121–130 (2014)
Zhang, M.H., Li, H.F.: Weak blind quantum signature protocol based on entanglement swapping. Photon. Res. 3, 324–328 (2015)
Tian, Y., Chen, H., Ji, S.F., et al.: A broadcasting multiple blind signature scheme based on quantum teleportation. Opt. Quant. Electron. 46, 769–777 (2014)
Ribeiro, J.: Quantum blind signature with an offline repository. Int. J. Quantum Inf. 13, 1550016 (2015)
Kurtsiefer, C., Zarda, P., Halder, M., et al.: A step towards global key distribution. Nature 419, 450–450 (2002)
Stucki, D., Ginsin, N., Guinnard, O., et al.: Quantum key distribution over 67 km with a plug & play system. New J. Phys. 4, 41 (2002)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995)
Li, X.H., Deng, F.G., Zhou, H.Y.: Faithful qubit transmission against collective noise without ancillary qubits. Appl. Phys. Lett. 91, 144101 (2007)
Yamamoto, T., Shimamura, J., Ozdemir, S.K., et al.: Faithful qubit distribution assisted by one additional qubit against collective noise. Phys. Rev. Lett. 95, 040503 (2005)
Bennett, C.H., Brassard, G., Popescu, S., et al.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996)
Pan, J.W., Simon, C., Brukner, C., et al.: Entanglement purification for quantum communication. Nature 410, 1067–1070 (2001)
Kwiat, P.G., Berglund, A.J., Altepeter, J.B., et al.: Experimental verification of decoherence-free subspaces. Science 290, 498–501 (2000)
Kempe, J., Bacon, D., Lidar, D.A., et al.: Theory of decoherence-free fault tolerant universal quantum computation. Phys. Rev. A 63, 042307 (2001)
Walton, Z.D., Abouraddy, A.F., Sergienko, A.V., et al.: Decoherence-free subspaces in quantum key distribution. Phys. Rev. Lett. 91, 087901 (2003)
Boileau, J.C., Gottesman, D., Laflamme, R., et al.: Robust polarization-based quantum key distribution over a collective-noise channel. Phys. Rev. Lett. 92, 017901 (2004)
Wang, X.B.: Fault tolerant quantum key distribution protocol with collective random unitary noise. Phys. Rev. A 72, 050304 (2005)
Li, X.H., Deng, F.G., Zhou, H.Y.: Efficient quantum key distribution over a collective noise channel. Phys. Rev. A 78, 022321 (2008)
Li, X.H., Zhao, B.K., Sheng, Y.B., et al.: Fault tolerant quantum key distribution based on quantum dense coding with collective noise. Int. J. Quantum Inf. 8, 1479–1489 (2009)
Xiu, X.M., Dong, L., Gao, Y.J., et al.: Quantum key distribution protocols with six-photon states against collective noise. Opt. Commun. 282, 4171–4174 (2009)
Sun, Y., Wen, Q.Y., Gao, F., et al.: Robust variations of the Bennett-Brassard 1984 protocol against collective noise. Phys. Rev. A 80, 032321 (2009)
Lidar, D.A., Bacon, D., Kempe, J., et al.: Protecting quantum information encoded in decoherence-free states against exchange errors. Phys. Rev. A 61, 052307 (2000)
Bourennane, M., Eibl, M., Gaertner, S., et al.: Decoherence-free quantum information processing with four-photon entangled states. Phys. Rev. Lett. 92, 107901 (2004)
Ge, H., Liu, W.Y.: A new quantum secure direct communication protocol using decoherence-free subspace. Chin. Phys. Lett. 24, 2727–2729 (2007)
Qin, S.J., Wen, Q.Y., Meng, L.M., et al.: Quantum secure direct communication over the collective amplitude damping channel. Sci. China-Phys. Mech. Astron. 52, 1208–1212 (2009)
Gu, B., Zhang, C.Y., Cheng, G.S., et al.: Robust quantum secure direct communication with a quantum one-time pad over a collective-noise channel. Sci. China-Phys. Mech. Astron. 54, 942–947 (2011)
Yang, C.W., Tsai, C.W., Hwang, T.: Fault tolerant two-step quantum secure direct communication protocol against collective noises. Sci. China-Phys. Mech. Astron. 54, 496–501 (2011)
Chang, Y., Zhang, S.B., Li, J., et al.: Robust EPR-pairs-based quantum secure communication with authentication resisting collective noise. Sci. China-Phys. Mech. Astron. 57, 1907–1912 (2014)
Zhang, Z.J.: Robust multiparty quantum secret key sharing over two collective-noise channels. Phys. A 361, 233–238 (2006)
Gu, B., Mu, L., Ding, L., et al.: Fault tolerant three-party quantum secret sharing against collective noise. Opt. Commun. 283, 3099–3103 (2010)
Lin, J., Hwang, T.: Bell state entanglement swappings over collective noises and their applications on quantum cryptography. Quantum Inf. Process. 12, 1089–1107 (2013)
Yang, C.W., Hwang, T.: Quantum dialogue protocols immune to collective noise. Quantum Inf. Process. 12, 2131–2142 (2013)
Ye, T.Y.: Information leakage resistant quantum dialogue against collective noise. Sci. China-Phys. Mech. Astron. 57, 2266–2275 (2014)
Ye, T.Y.: Robust quantum dialogue based on the entanglement swapping between any two logical Bell states and the shared auxiliary logical Bell state. Quantum Inf. Process. 14, 1469–1486 (2015)
Gu, B., Pei, S.X., Song, B., et al.: Deterministic secure quantum communication over a collective-noise channel. Sci. China-Phys. Mech. Astron. 52, 1913–1918 (2009)
Shor, P., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85, 441–444 (2000)
Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, pp. 175–179 (1984)
Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68, 042317 (2003)
Bostrom, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002)
Deng, F.G., Long, G.L.: Bidirectional quantum key distribution protocol with practical faint laser pulses. Phys. Rev. A 70, 012311 (2004)
Deng, F.G., Zhou, H.Y., Long, G.L.: Circular quantum secret sharing. J. Phys. A-Math. Gen. 39, 14089–14099 (2006)
Hoeffding, W.: Probability-inequalities for sums of bounded random-variables. J. Am. Stat. Assoc. 58, 13–30 (1963)
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant No. 61273250) and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (Grant No. CX201618).
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Zhang, MH., Li, HF. Fault-tolerant quantum blind signature protocols against collective noise. Quantum Inf Process 15, 4283–4301 (2016). https://doi.org/10.1007/s11128-016-1383-z
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DOI: https://doi.org/10.1007/s11128-016-1383-z