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An efficient quantum blind digital signature scheme


Recently, many quantum digital signature (QDS) schemes have been proposed to authenticate the integration of a message. However, these quantum signature schemes just consider the situation for bit messages, and the signing-verifying of one-bit modality. So, their signature efficiency is very low. In this paper, we propose a scheme based on an application of Fibonacci-, Lucas- and Fibonacci-Lucas matrix coding to quantum digital signatures based on a recently proposed quantum key distribution (QKD) system. Our scheme can sign a large number of digital messages every time. Moreover, these special matrices provide a method to verify the integration of information received by the participants, to authenticate the identity of the participants, and to improve the efficiency for signing-verifying. Therefore, our signature scheme is more practical than the existing schemes.

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  1. 1

    William S. Cryptography and Network Security: Principles and Practice. 2nd ed. New Jersey: Prentice Hall, 2003. 67–68

  2. 2

    Rivest R L, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems. Commun ACM, 1978, 21: 120–126

  3. 3

    Cramer R, Shoup V. Signature schemes based on the strong RSA assumption. ACM Trans Inf Syst Secur, 2000, 3: 161–185

  4. 4

    ElGamal T. A public key cryptosystem and a signature scheme based on discrete logarithms. In: Proceedings of Workshop on the Theory and Application of Cryptographic Techniques. Berlin: Springer, 1984. 10–18

  5. 5

    Shor P W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev, 1999, 41: 303–332

  6. 6

    Amiri R, Andersson E. Unconditionally secure quantum signatures. Entropy, 2015, 17: 5635–5659

  7. 7

    Gottesman D, Chuang I. Quantum digital signatures. arXiv:quant-ph/0105032, 2001

  8. 8

    Chaum D, Heyst E V. Group signatures. In: Advances in cryptography-EUROCRYPT’91. Berlin: Springer, 1991. 257–265

  9. 9

    Zeng G H, Keitel C H. Arbitrated quantum-signature scheme. Phys Rev A, 2002, 65: 1–6

  10. 10

    Wallden P, Dunjko V, Kent A, et al. Quantum digital signatures with quantum-key-distribution components. Phys Rev A, 2015, 91: 042304

  11. 11

    Shi J J, Shi R H, Guo Y, et al. Batch proxy quantum blind signature scheme. Sci China Inf Sci, 2013, 56: 052115

  12. 12

    Dunjko V, Wallden P, Andersson E. Quantum digital signatures without quantum memory. Phys Rev Lett, 2014, 112: 040502

  13. 13

    Collins R J, Donaldson R J, Dunjko V, et al. Realization of quantum digital signatures without the requirement of quantum memory. Phys Rev Lett, 2014, 113: 040502

  14. 14

    Arrazola J M, Wallden P, Andersson E. Multiparty quantum signature schemes. Quantum Inf Comput, 2016, 6: 0435

  15. 15

    Wang T Y, Cai X Q, Ren Y L, et al. Security of quantum digital signatures for classical messages. Sci Rep, 2014, 5: 9231

  16. 16

    Wen X J, Niu X M, Ji L P, et al. A weak blind signature scheme based on quantum cryptography. Optics Commun, 2009, 282: 666–669

  17. 17

    Li F G, Shirase M, Takagi T. Cryptanalysis of efficient proxy signature schemes for mobile communication. Sci China Inf Sci, 2010, 53: 2016–2021

  18. 18

    Amiri R, Wallden P, Kent A, et al. Secure quantum signatures using insecure quantum channels. Phys Rev A, 2016, 93: 032325

  19. 19

    Yin H L, Fu Y, Chen Z B. Practical quantum digital signature. Phys Rev A, 2016, 93: 032316

  20. 20

    Donaldson R J, Collins R J, Kleczkowska K, et al. Experimental demonstration of kilometer-range quantum digital signatures. Phys Rev A, 2016, 93: 012329

  21. 21

    Simon D S, Lawrence N, Trevino J, et al. High-capacity quantum Fibonacci coding for key distribution. Phys Rev A, 2013, 87: 032312

  22. 22

    Simon D S, Fitzpatrick C A, Sergienko A V. Discrimination and synthesis of recursive quantum states in highdimensional Hilbert spaces. Phys Rev A, 2015, 91: 043806

  23. 23

    Esmaeili M, Moosavi M, Gulliver T A. A new class of Fibonacci sequence based error correcting codes. Cryptogr Commun, 2017, 9: 379–396

  24. 24

    Vajda S. Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. New York: Ellis Horwood Ltd.-Halsted Press, 1989

  25. 25

    Mishra M, Mishra P, Adhikary M C, et al. Image encryption using Fibonacci-Lucas transformation. Int J Cryptogr Inf Secur, 2012, 2: 131–141

  26. 26

    Stakhov A P. Fibonacci matrices, a generalization of the cassini formula and a new coding theory. Chaos Soliton Fract, 2006, 30: 56–66

  27. 27

    Rey A, Sanchez G. On the security of the golden cryptography. Int J Netw Secur, 2008, 7: 448450

  28. 28

    Bennett C H, Brassard G. Quantum cryptography: public-key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, 1984. 175–179

  29. 29

    Ekert A K. Quantum cryptography based on Bell’s theorem. Phys Rev Lett, 1991, 67: 661–663

  30. 30

    Vogel H. A better way to construct the sunflower head. Math Biosci, 1979, 44: 179–189

  31. 31

    Wang T Y, Cai X Q, Zhang R L. Security of a sessional blind signature based on quantum cryptograph. Quant Inf Process, 2014, 13: 1677–1685

  32. 32

    Wang T Y, Wen Q Y. Fair quantum blind signatures. Chin Phys B, 2010, 19: 060307

  33. 33

    Wen X J, Chen Y Z, Fang J B. An inter-bank E-payment protocol based on quantum proxy blind signature. Quant Inf Process, 2013, 12: 549–558

  34. 34

    Cai X Q, Zheng Y H, Zhang R L. Cryptanalysis of a batch proxy quantum blind signature scheme. Int J Theor Phys, 2014, 53: 3109–3115

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Hong LAI was supported by Fundamental Research Funds for the Central Universities (Grant No. XDJK2016C043), 1000-Plan of Chongqing by Southwest University (Grant No. SWU116007), and Doctoral Program of Higher Education (Grant No. SWU115091). Mingxing LUO was supported by Sichuan Youth Science & Technique Foundation (Grant No.2017JQ0048). Josef PIEPRZYK was supported by National Science Centre, Poland (Grant No. UMO-2014/15/B/ST6/05130). Shudong Li was supported by National Natural Science Foundation of China (Grant Nos. 61672020, 61662069, 61472433), Project Funded by China Postdoctoral Science Foundation (Grant Nos. 2013M542560, 2015T81129) and A Project of Shandong Province Higher Educational Science and Technology Program (Grant Nos. J16LN61, 2016ZH054). The paper was also supported by A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology (CICAEET).

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Correspondence to Hong Lai or Mehmet A. Orgun.

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Conflict of interest The authors declare that they have no conflict of interest.

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Lai, H., Luo, M., Pieprzyk, J. et al. An efficient quantum blind digital signature scheme. Sci. China Inf. Sci. 60, 082501 (2017).

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  • blind quantum digital signature
  • Fibonacci-
  • Lucas- and Fibonacci-Lucas matrix coding
  • digital messages
  • signing-verifying modality