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Quantum asymmetric cryptography with symmetric keys

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Abstract

Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use symmetric keys in such a scheme, which is quite different from that in conventional public-key cryptography. The security of our scheme is analyzed and some features are discussed. Furthermore, the state-estimation attack to a prior QPKC scheme is demonstrated.

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References

  1. Diffie W, Hellman M. New directions in cryptography. IEEE Trans Inform Theor, 1976, 22: 644–654

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. Schneier B. Applied Cryptography: Protocols, Algorithms and Source Code in C. 2nd ed. New York: John Wiley and Sons, 1996. 24–29

    MATH  Google Scholar 

  4. Shor P W. Algorithms for quantum computation: Discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on the Foundations of Computer Science. Los Alamitos: IEEE, 1994. 124–134

    Chapter  Google Scholar 

  5. Grover L K. A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing. New York: ACM, 1996. 212–219

    Google Scholar 

  6. Zeng G H. Quantum Cryptography (in Chinese). Beijing: Science Press, 2006. 147–153

    Google Scholar 

  7. Chen W, Han Z F, Mo X F, et al. Active phase compensation of quantum key distribution system. Chin Sci Bull, 2008, 53: 1310–1314

    Article  Google Scholar 

  8. Gao F, Guo F Z, Wen Q Y, et al. Comparing the efficiencies of different detect strategies in the ping-pong protocol. Sci China Ser G-Phys Mech Astron, 2008, 51: 1853–1860

    Article  ADS  Google Scholar 

  9. Gao F, Guo F Z, Wen Q Y, et al. Revisiting the security of quantum dialogue and bidirectional quantum secure direct communication. Sci China Ser G-Phys Mech Astrom, 2008, 51: 559–566

    Article  ADS  Google Scholar 

  10. Okamoto T, Tanaka K, Uchiyama S. Quantum public-key cryptosystems. In: Advances in Cryptology: Crypto 2000 Proceedings. Berlin: Springer, 2000. LNCS, 1880: 147–165

    Google Scholar 

  11. Kawachi A, Koshiba T, Nishimura H, et al. Computational indistinguishability between quantum states and its cryptographic application. In: Advances in Cryptology: Eurocrypt 2005 Proceedings. Berlin: Springer, 2005. LNCS, 3494: 268–284

    Google Scholar 

  12. Yang L. Quantum public-key cryptosystem based on classical NP-complete problem. arXiv: quant-ph/0310076

  13. Koshiba T. Security notions for quantum public-key cryptography. arXiv: quant-ph/0702183

  14. Nikolopoulos G M. Applications of single-qubit rotations in quantum public-key cryptography. Phys Rev A, 2008, 77: 032348

    Article  MathSciNet  ADS  Google Scholar 

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

  16. Zhang Y S, Li C F, Guo G C. Quantum key distribution via quantum encryption. Phys Rev A, 2001, 64: 024302

    Article  MathSciNet  ADS  Google Scholar 

  17. Zeng G H. Encrypting binary bits via quantum cryptography. Chin J Electr, 2004, 13: 651–653

    Google Scholar 

  18. Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2000. 531–533

    MATH  Google Scholar 

  19. Massar S, Popescu S. Optimal extraction of information from finite quantum ensembles. Phys Rev Lett, 1995, 74: 1259–1263

    Article  MATH  MathSciNet  ADS  Google Scholar 

  20. Derka R, Buzek V, Ekert A K. Universal algorithm for optimal estimation of quantum states from finite ensembles via realizable generalized measurement. Phys Rev Lett, 1998, 80: 1571–1575

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. Bagan E, Baig M, Munoz-Tapia R. Optimal scheme for estimating a pure qubit state via local measurements. Phys Rev Lett, 2002, 89: 277904

    Article  ADS  Google Scholar 

  22. Nikolopoulos G M. Erratum: Applications of single-qubit rotations in quantum public-key cryptography. Phys Rev A, 2008, 78: 019903

    Article  MathSciNet  ADS  Google Scholar 

  23. Dusek M, Haderka O, Hendrych M, et al. Quantum identification system. Phys Rev A, 1999, 60: 149–156

    Article  ADS  Google Scholar 

  24. Zeng G H, Zhang W P. Identity verification in quantum key distribution. Phys Rev A, 2000, 61: 022303

    Article  ADS  Google Scholar 

  25. Leung D W. Quantum Vernam cipher. Quantum Inf Comput, 2002, 2: 14–34

    MathSciNet  Google Scholar 

  26. Vernam G S. Cipher printing telegraph systems for secret wire and radio telegraphic communications. J Am Inst Elect Eng, 1926, 55: 109–115

    Google Scholar 

  27. Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature (London), 1982, 299: 802–803

    Article  ADS  Google Scholar 

  28. Cai Q Y. The “Ping-Pong” protocol can be attacked without eavesdropping. Phys Rev Lett, 2003, 91: 109801

    Article  ADS  Google Scholar 

  29. Gao F, Guo F Z, Wen Q Y, et al. Consistency of shared reference frames should be reexamined. Phys Rev A, 2008, 77: 014302

    Article  ADS  Google Scholar 

  30. 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

    Article  ADS  Google Scholar 

  31. Pan J W, Gasparoni S, Ursin R, et al. Experimental entanglement purification of arbitrary unknown states. Nature (London), 2003, 423: 417–422

    Article  ADS  Google Scholar 

  32. Deutsch D, Ekert A, Jozsa R, et al. Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys Rev Lett, 1996, 77: 2818–2821

    Article  ADS  Google Scholar 

  33. Lo H K, Chau H F. Unconditional security of quantum key distribution over arbitrarily long distances. Science, 1999, 283: 2050–2056

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  35. Gao F, Guo F Z, Wen Q Y, et al. Comment on “Quantum key distribution for d-level systems with generalized Bell states”. Phys Rev A, 2005, 72: 066301

    Article  ADS  Google Scholar 

  36. Bennett C H, Brassard G, Mermin N D. Quantum cryptography without Bell theorem. Phys Rev Lett, 1992, 68: 557–559

    Article  MATH  MathSciNet  ADS  Google Scholar 

  37. Waks E, Zeevi A, Yamamoto Y. Security of quantum key distribution with entangled photons against individual attacks. Phys Rev A, 2002, 65: 052310

    Article  ADS  Google Scholar 

  38. Deng F G, Long G L. Secure direct communication with a quantum one-time pad. Phys Rev A, 2004, 69: 052319

    Article  ADS  Google Scholar 

  39. 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

    Article  ADS  Google Scholar 

  40. Bennett C H, Brassard G, Robert J. Privacy amplification by public discussion. SIAM J Comput, 1988, 17: 210–229

    Article  MathSciNet  Google Scholar 

  41. Zeng G H, Keitel C H. Arbitrated quantum-signature scheme. Phys Rev A, 2002, 65: 042312

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Fei Gao, QiaoYan Wen & SuJuan Qin

  2. National Laboratory for Modern Communications, Chengdu, 610041, China

    FuChen Zhu

Authors
  1. Fei Gao
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  2. QiaoYan Wen
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  3. SuJuan Qin
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  4. FuChen Zhu
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Corresponding author

Correspondence to Fei Gao.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 60873191, 60821001 and 60903152), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 200800131016), Beijing Nova Program (Grant No. 2008B51), Key Project of Chinese Ministry of Education (Grant No. 109014), Beijing Municipal Natural Science Foundation (Grant No. 4072020) and China Postdoctoral Science Foundation (Grant No. 20090450018)

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Gao, F., Wen, Q., Qin, S. et al. Quantum asymmetric cryptography with symmetric keys. Sci. China Ser. G-Phys. Mech. Astron. 52, 1925–1931 (2009). https://doi.org/10.1007/s11433-009-0299-3

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  • DOI: https://doi.org/10.1007/s11433-009-0299-3

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