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Quantum private comparison based on quantum dense coding



A serious problem in cloud computing is privacy information protection. This study proposes a new private comparison protocol using Einstein-Podolsky-Rosen (EPR) pairs. This protocol allows two parties to secretly compare their classical information. Quantum dense coding enables the comparison task to be completed with the help of a classical semi-honest center. A one-step transmission scheme and designed decoy photons can be used against various quantum attacks. The new protocol can ensure fairness, efficiency, and security. The classical semi-honest center cannot learn any information about the private inputs of the players. Moreover, this scheme can be easily generalized using the general EPR pairs in order to improve the transmission efficiency.


(1)本文设计一种新的公平、有效、安全的量子隐私对比协议。(2)与以前的诚实第三方和量子第三方不同, 本文的协议只依赖于经典的半诚实中心。(3)不像以前的协议可信第三方可能获取部分隐私信息, 本文中的经典半诚实中心不能获取对比双方的隐私消息。(4)本文的协议具有较好的扩展性, 可以拓展到基于多层量子态的隐私对比协议。

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  1. 1

    Fu Z J, Sun X M, Liu Q, et al. Achieving efficient cloud search services: multi-keyword ranked search over encrypted cloud data supporting parallel computing. IEICE Trans Commun, 2015, 98: 190–200

  2. 2

    Li J, Li X L, Yang B, et al. Segmentation-based image copy-move forgery detection scheme. IEEE Trans Inform Forens Secur, 2015, 10: 507–518

  3. 3

    Ren Y J, Shen J, Wang J, et al. Mutual verifiable provable data auditing in public cloud storage. J Internet Technol, 2015, 16: 317–324

  4. 4

    Xia Z H, Wang X H, Sun X M, et al. A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data. IEEE Trans Parall Distrib Syst, 2015, 27: 340–352

  5. 5

    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

  6. 6

    Zhou C, Bao W S, Fu X Q. Decoy-state quantum key distribution for the heralded pair coherent state photon source with intensity fluctuations. Sci China Inf Sci, 2010, 53: 2485–2494

  7. 7

    Qian X D, He G Q, Zeng G H. Realization of error correction and reconciliation of continuous quantum key distribution in detail. Sci China Ser-F: Inf Sci, 2009, 52: 1598–1604

  8. 8

    Bennett C H, Brassard G, Crepeau C, et al. Teleporting an unknown quantum state via dual classical and Einstein- Podolsky-Rosen channels. Phys Rev Lett, 1993, 70: 1895–1899

  9. 9

    Bouwmeester D, Pan J W, Mattle K, et al. Experimental quantum teleportation. Nature, 1997, 390: 575–579

  10. 10

    Furusawa A, Søensen J L, Braunstein S L, et al. Unconditional quantum teleportation. Science, 1998, 282: 706–709

  11. 11

    Bennett C H, DiVincenzo D P, Shor P Q, et al. Remote state preparation. Phys Rev Lett, 2001, 87: 077902

  12. 12

    Luo M X, Deng Y, Chen X B, et al. The faithful remote preparation of general quantum states. Quantum Inform Process, 2013, 12: 279–294

  13. 13

    Hillery M, Buzek V, Berthiaume A. Quantum secret sharing. Phys Rev A, 1999, 59: 1829–1834

  14. 14

    Cleve R, Gottesman D, Lo H K. How to share a quantum secret. Phys Rev Lett, 1999, 83: 648–651

  15. 15

    Guo G P, Guo G C. Quantum secret sharing without entanglement. Phys Lett A, 2003, 310: 247–251

  16. 16

    Xiao L, Long G L, Deng F G, et al. Efficient multiparty quantum-secret-sharing schemes. Phys Rev A, 2004, 69: 052307

  17. 17

    Qin S J, Gao F, Wen Q Y, et al. Improving the security of multiparty quantum secret sharing against an attack with a fake signal. Phys Lett A, 2006, 357: 101–103

  18. 18

    Xu J, Chen H W, Liu W J, et al. Selection of unitary operations in quantum secret sharing without entanglement. Sci China Inf Sci, 2011, 54: 1837–1842

  19. 19

    Wang T Y, Wen Q Y. Security of a kind of quantum secret sharing with single photons. Quantum Inform Comput, 2011, 11: 434–443

  20. 20

    Boström K, Felbinger T. Deterministic secure direct communication using entanglement. Phys Rev Lett, 2002, 89: 187902

  21. 21

    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, 2003, 68: 042317

  22. 22

    Wang C, Deng F-G, Li Y-S, et al. Quantum secure direct communication with high-dimension quantum superdense coding. Phys Rev A, 2005, 71: 044305

  23. 23

    Lin S, Wen Q Y, Gao F, et al. Quantum secure direct communication with χ-type entangled states. Phys Rev A, 2008, 78: 064304

  24. 24

    Liu Z H, Chen H W, Liu W J, et al. Deterministic secure quantum communication without unitary operation based on highdimensional entanglement swapping. Sci China Inf Sci, 2012, 55: 360–367

  25. 25

    Zheng C, Long G F. Quantum secure direct dialogue using Einstein-Podolsky-Rosen pairs. Sci China Phys Mech Astro, 2014, 57: 1238–1243

  26. 26

    Zou X F, Qiu D W. Three-step semiquantum secure direct communication protocol. Sci China Phys Mech Astro, 2014, 57: 1696–1702

  27. 27

    Qu Z G, Chen X B, Zhou X J, et al. Novel quantum steganography with large payload. Opt Commun, 2010, 283: 4782–4786

  28. 28

    Qu Z G, Chen X B, Luo M X, et al. A large payload of novel quantum steganography with χ-type entangled state. Opt Commun, 2011, 284: 2075–2082

  29. 29

    Xu S J, Chen X B, Niu X X, et al. High-efficiency quantum steganography based on the tensor product of Bell states. Sci China Phys Mech Astro, 2013, 56: 1745–1754

  30. 30

    Yao A C. Protocols for secure computations. In: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science, Chicago, 1982. 160–164

  31. 31

    Yao A C. How to generate and exchange secrets. In: Proceedings of the 27th Annual Symposium on Foundations of Computer Science, Toronto, 1986. 162–167

  32. 32

    Boudot F, Schoenmakers B, Traore J. A fair and efficient solution to the socialist millionaires problem. Discret Appl Math, 2001, 111: 23–36

  33. 33

    Lo H K. Insecurity of quantum secure computations. Phys Rev A, 1997, 56: 1154–1162

  34. 34

    Yang Y G, Wen Q Y. An efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement. J Phys A-Math Theor, 2009, 42: 055305

  35. 35

    Yang Y G, Cao W F, Wen Q Y. Secure quantum private comparison. Phys Scr, 2009, 80: 065002

  36. 36

    Lin J, Tseng H Y, Hwang T. Intercept-resend attacks on Chen et al.’s quantum private comparison protocol and the improvements. Opt Commun, 2011, 284: 2412–2414

  37. 37

    Chen X B, Xu G, Niu X X, et al. An efficient protocol for the private comparison of equal information based on the triplet entangled state and single-particle measurement. Opt Commun, 2010, 283: 1561–1565

  38. 38

    Liu W J, Liu C, Wang H B, et al. Secure quantum private comparison of equality based on asymmetric W state. Int J Theor Phys, 2014, 53: 1804–1813

  39. 39

    Tseng H Y, Lin J, Hwang T. New quantum private comparison protocol using EPR pairs. Quantum Inf Proc, 2012, 11: 373–384

  40. 40

    Liu W J, Liu C, Chen H W, et al. Cryptanalysis and improvement of quantum private comparison protocol based on bell entangled states. Commun Theor Phys, 2014, 62: 210–214

  41. 41

    Liu W, Wang Y B, Jiang Z T, et al. A protocol for the quantum private comparison of equality with χ-type state. Int J Theor Phys, 2012, 51: 69–77

  42. 42

    Xu G A, Chen X B, Wei Z H, et al. An efficient protocol for the quantum private comparison of equality with a four-qubit cluster state. Int J Quantum Inf, 2012, 10: 1250045

  43. 43

    Liu W, Wang Y B, Jiang Z T. An efficient protocol for the quantum private comparison of equality with W state. Opt Commun, 2011, 284: 3160–3163

  44. 44

    Liu B, Gao F, Jia H Y, et al. Efficient quantum private comparison employing single photons and collective detection. Quantum Inf Proc, 2013, 12: 887–897

  45. 45

    Li Y B, Qin S J, Yuan Z, et al. Quantum private comparison against decoherence noise. Quantum Inf Proc, 2013, 12: 2191–2205

  46. 46

    Zhang W W, Zhang K J. Cryptanalysis and improvement of the quantum private comparison protocol with semi-honest third party. Quantum Inf Proc, 2013, 12: 1981–1990

  47. 47

    Chen X B, Su Y, Niu X X, et al. Efficient and feasible quantum private comparison of equality against the collective amplitude damping noise. Quantum Inf Proc, 2013, 12: 2871–2875

  48. 48

    Zukowski M, Zeilinger A, Horne M A, et al. Event-ready-detectors Bell experiment via entanglement swapping. Phys Rev Lett, 1993, 71: 4287–4290

  49. 49

    Pan J W, Bouwmeester D, Weinfurter H, et al. Experimental entanglement swapping: entangling photons that never interacted. Phys Rev Lett, 1998, 80: 3891–3894

  50. 50

    Barencoa A, Ekerta A K. Dense coding based on quantum entanglement. J Mod Opt, 1995, 42: 1253–1259

  51. 51

    Yeo Y, Chua W K. Teleportation and dense coding with genuine multipartite entanglement. Phys Rev Lett, 2006, 96: 060502

  52. 52

    Shadman Z, Kampermann H, Macchiavello C, et al. Optimal super dense coding over noisy quantum channels. New J Phys, 2010, 12: 073042

  53. 53

    Cai Q Y. Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys Lett A, 2006, 351: 23–25

  54. 54

    Deng F G, Li X H, Zhou H Y, et al. Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys Rev A, 2006, 73: 049901

  55. 55

    Qin S J, Wen Q Y, Zhu F C. Cryptanalysis of multiparty quantum secret sharing of quantum state using entangled states. Chin Phys Lett, 2008, 25: 3551–3554

  56. 56

    Li X H, Deng F G, Zhou H Y. Improving the security of secure direct communication based on the secret transmitting order of particles. Phys Rev A, 2006, 74: 054302

  57. 57

    Yang C W, Hwang T, Luo Y P. Enhancement on quantum blind signature based on two-state vector formalism. Quantum Inf Proc, 2013, 12: 109–117

  58. 58

    Bennett C H, Brassard G, Popescu S, et al. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys Rev Lett, 1996, 76: 722–725

  59. 59

    Sheng Y B, Zhou L. Deterministic entanglement distillation for secure double-server blind quantum computation. Sci Rep, 2015, 5: 7815

  60. 60

    Sheng Y B, Zhou L. Deterministic polarization entanglement purification using time-bin entanglement. Laser Phys Lett, 2014, 11: 085203

  61. 61

    Sheng Y B, Zhou L, Long G L. Hybrid entanglement purification for quantum repeaters. Phys Rev A, 2013, 88: 022302

  62. 62

    Bennett C H, Bernstein H J, Popescu S, et al. Concentrating partial entanglement by local operations. Phys Rev A, 1996, 53: 2046–2052

  63. 63

    Zhao Z, Yang T, Chen Y A, et al. Experimental realization of entanglement concentration and a quantum repeater. Phys Rev Lett, 2003, 90: 207901

  64. 64

    Sheng Y B, Zhou L, Zhao S M, et al. Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs. Phys Rev A, 2012, 85: 012307

  65. 65

    Ren B C, Du F F, Deng F G. Hyperentanglement concentration for two-photon four-qubit systems with linear optics. Phys Rev A, 2013, 88: 012302

  66. 66

    Zhao Z, Pan J W, Zhan M S. Practical scheme for entanglement concentration. Phys Rev A, 2001, 64: 014301

  67. 67

    Sheng Y B, Deng F G, Zhou H Y. Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics. Phys Rev A, 2008, 77: 062325

  68. 68

    Shi B S, Jiang Y K, Guo G C. Optimal entanglement purification via entanglement swapping. Phys Rev A, 2000, 62: 054301

  69. 69

    Luo M X, Chen X B, Yang Y X, et al. Hyperentanglement concentration for n-photon 2n-qubit systems with linear optics. J Opt Soc Amer B-Opt Phys, 2014, 31: 67–74

  70. 70

    Luo M X, Li H R, Wang X. Efficient atomic and photonic multipartite W state concentration via photonic faraday rotation. Eur Phys J D, 2014, 68: 190

  71. 71

    Chrzanowski H M, Walk N, Assad S M, et al. Measurement-based noiseless linear amplification for quantum communication. Nat Photon, 2014, 8: 333–338

  72. 72

    Eleftheriadou E, Barnett S M, Jeffers J. Quantum optical state comparison amplifier. Phys Rev Lett, 2013, 111: 213601

  73. 73

    Kocsis S, Xiang G Y, Ralph T C, et al. Heralded noiseless amplification of a photon polarization qubit. Nat Phys, 2013, 9: 23–28

  74. 74

    Zhou L, Sheng Y B. Recyclable amplification protocol for the single-photon entangled state. Laser Phys Lett, 2015, 12: 045203

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This work was supported by National Natural Science Foundation of China (Grant Nos. 61303039, 61373131), Natural Science Foundation of Shandong Province (Grant No. ZR2015FL024), Fundamental Research Funds for the Central Universities (Grant No. 2682014CX095), PAPD and CICAEET Funds, Open Foundation of Jiangsu Engineering Center of Network Monitoring (Nanjing University of Information Science & Technology) (Grant No. KJR1502), Open Foundation of China-USA Computer Science Center (Grant No. KJR16012), and Science Foundation Ireland (SFI) under the International Strategic Cooperation Award (Grant No. SFI/13/ISCA/2845).

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Correspondence to Zhiguo Qu.

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Wang, F., Luo, M., Li, H. et al. Quantum private comparison based on quantum dense coding. Sci. China Inf. Sci. 59, 112501 (2016).

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  • private comparison
  • multiparty secure computation
  • classical semi-honesty center
  • quantum dense coding
  • general EPR pair


  • 隐私消息对比
  • 多方安全计算
  • 经典半诚实中心
  • 量子超幂编码
  • 一般EPR对