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Quantum Secret Sharing Based on Quantum Search Algorithm

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Abstract

Quantum secret sharing (QSS) and quantum search algorithm (QSA) are considered as two important but different research topics in quantum information science. This paper recognizes an important feature in the well-known Grover’s QSA and then applies it to propose a QSS protocol. In contrast to the existing QSA-based QSS protocols, the newly proposed protocol has the following two advantages: (1) no quantum memory is required by the agents, whereas the agents in the existing QSA-based QSS protocols need long-term quantum memories to store their secret shadows; (2) the agents can cooperate to recover the boss’s secret by using shadows in classical bits, whereas, the others have to combine their shadows in photons and perform a unitary operation on the retained photons. The proposed QSS protocol is also shown to be secure against eavesdroppers or malicious agents.

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References

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

    Google Scholar 

  2. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67(6), 661–663 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bell’s theorem. Phys. Rev. Lett. 68(5), 557 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. 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(4), 042317 (2003)

    Article  ADS  Google Scholar 

  5. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Long, G.-L., Li, X., Sun, Y.: Phase matching condition for quantum search with a generalized initial state. Phys. Lett. A 294(3–4), 143–152 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. 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(3), 496–501 (2011)

    Article  ADS  Google Scholar 

  8. Hwang, T., Yang, C.-W., Tsai, C.-W.: Revisiting Deng et al.’s multiparty quantum secret sharing protocol. Int. J. Theor. Phys. 50(9), 2790–2798 (2011)

    Article  MATH  Google Scholar 

  9. Hillery, M., Buek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  10. Li, Y.-M., Zhang, K., Peng, K.: Multiparty secret sharing of quantum information based on entanglement swapping. Phys. Lett. A 324(5–6), 420–424 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Xiao, L., Long, G.-L., Deng, F.-G., Pan, J.-W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69(5), 052307 (2004)

    Article  ADS  Google Scholar 

  12. Deng, F.-G., Long, G.-L., Zhou, H.-Y.: An efficient quantum secret sharing scheme with Einstein-Podolsky-Rosen pairs. Phys. Lett. A 340(1–4), 43–50 (2005)

    Article  ADS  MATH  Google Scholar 

  13. Gao, F.-Z., Guo, Q.-Y., Wen, F.-C.Z: Comment on “Quantum secret sharing based on reusable Greenberger-Horne-Zeilinger states as secure carriers”. Phys. Rev. A 72(3), 036302 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  14. Hsu, L.-Y., Li, C.-M.: Quantum secret sharing using product states. Phys. Rev. A 71(2), 022321 (2005)

    Article  ADS  Google Scholar 

  15. Li, C.-M., Chang, C.-C., Hwang, T.: Comment on “Quantum secret sharing between multiparty and multiparty without entanglement”. Phys. Rev. A 73(1), 016301 (2006)

    Article  ADS  Google Scholar 

  16. Deng, F.G., Li, X.-H., Zhou, H.-Y.: Efficient high-capacity quantum secret sharing with two-photon entanglement. Phys. Lett. A 372(12), 1957–1962 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Chen, J.-H., Lee, K.-C., Hwang, T.: The enhancement of Zhou et al.’s quantum secret sharing protocol. Int. J. Mod. Phys. C 20(10), 1531–1535 (2009)

    Article  ADS  MATH  Google Scholar 

  18. Hsieh, C.-R., Tasi, C.-W., Hwang, T.: Quantum secret sharing using GHZ-like state. Commun. Theor. Phys. 54(6), 1019 (2010)

    Article  MATH  Google Scholar 

  19. Tsai, C.-W., Wang, S.-H., Hwang, T.: Comment on “N quantum channel are sufficient for multi-user quantum key distribution protocol between N users”. Opt. Commun. 283(24), 5285–5286 (2010)

    Article  ADS  Google Scholar 

  20. Wang, S.-H., Chong, S.-K., Hwang, T.: On “multiparty quantum secret sharing with Bell states and Bell measurements”. Opt. Commun. 283(21), 4405–4407 (2010)

    Article  ADS  Google Scholar 

  21. Lin, J., Hwang, T.: An enhancement on Shi et al.’s multiparty quantum secret sharing protocol. Opt. Commun. 284(5), 1468–1471 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  22. Hwang, T., Hwang, C.-C.: Revisiting Deng et al.’s multiparty quantum secret sharing protocol. Int. J. Theor. Phys. 50(9), 2790–2798 (2011)

    Article  MATH  Google Scholar 

  23. Hwang, T., Hwang, C.-C., Li, C.-M.: Multiparty quantum secret sharing based on GHZ states. Phys. Scr. 83(4), 045004 (2011)

    Article  ADS  Google Scholar 

  24. Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325 (1997)

    Article  ADS  Google Scholar 

  25. Hsu, L.-Y.: Quantum secret-sharing protocol based on Grover’s algorithm. Phys. Rev. A 68(2), 022306 (2003)

    Article  ADS  Google Scholar 

  26. Hao, L., Li, J.-L., Long, G.-L.: Eavesdropping in a quantum secret sharing protocol based on Grover algorithm and its solution. Sci. China, Phys. Mech. Astron. 53(3), 491–495 (2010)

    Article  ADS  Google Scholar 

  27. Wang, C., Hao, L., Song, S.-Y., Long, G.-L.: Quantum direct communication based on quantum search algorithm. Int. J. Quantum Inf. 8(3), 443–450 (2010)

    Article  MATH  Google Scholar 

  28. Lin, J., Tseng, H.-Y., Hwang, T.: Intercept-resend attacks on Chen et al.’s quantum private comparison protocol and the improvements. Opt. Commun. 284(9), 2412–2414 (2011)

    Article  ADS  Google Scholar 

  29. Yang, C.-W., Tsai, C.-W., Hwang, T.: Thwarting intercept-and-resend attack on Zhang’s quantum secret sharing using collective rotation noises. Quantum Information Processing, 1–10 (2011)

  30. Tsai, C.-W., Wang, S.-H., Hwang, T.: Comment on “N quantum channel are sufficient for multi-user quantum key distribution protocol between N users”. Opt. Commun. 283(24), 5285–5286 (2010)

    Article  ADS  Google Scholar 

  31. Beveratos, A., Brouri, R., Gacoin, T., Villing, A., Poizat, J.-P., Grangier, P.: Single photon quantum cryptography. Phys. Rev. Lett. 89(18), 187901 (2002)

    Article  ADS  Google Scholar 

  32. Gobby, C., Yuan, Z., Shields, A.: Quantum key distribution over 122 km of standard telecom fiber. Appl. Phys. Lett. 84, 3762 (2004)

    Article  ADS  Google Scholar 

  33. Tsai, C.-W., Hwang, T.: New deterministic quantum communication via symmetric W state. Opt. Commun. 283(21), 4397–4400 (2010)

    Article  ADS  Google Scholar 

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Acknowledgements

The authors would like to thank the National Science Council of Republic of China and the Research Center of Quantum Communication and Security, National Cheng Kung University, Taiwan, R.O.C. for financial support of this research under Contract No. NSC 100-2221-E-471-003- and D100-36002, respectively.

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  1. No. 1, University Road, Tainan City, 701, Taiwan (R.O.C.)

    Hsin-Yi Tseng, Chia-Wei Tsai, Tzonelih Hwang & Chuan-Ming Li

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  1. Hsin-Yi Tseng
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  2. Chia-Wei Tsai
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  3. Tzonelih Hwang
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  4. Chuan-Ming Li
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Correspondence to Tzonelih Hwang.

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Tseng, HY., Tsai, CW., Hwang, T. et al. Quantum Secret Sharing Based on Quantum Search Algorithm. Int J Theor Phys 51, 3101–3108 (2012). https://doi.org/10.1007/s10773-012-1191-x

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  • DOI: https://doi.org/10.1007/s10773-012-1191-x

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