Security of quantum secret sharing with two-particle entanglement against individual attacks

Security is the most important criterion to evaluate cryptography protocols. We inves-tigate the security of one important quantum secret sharing protocol [Phys. Rev. A59, 162 (1999)] (KKI protocol). By discriminating two mixed states, we derive the op-timal relationship between the induced error rate (QBER) and the maximal amount ofinformation gained by a dishonest participant. For a specific amount of eavesdropper'sknowledge on the shared secret that we consider, the disturbance on the quantum statein terms of QBER is actually larger for the hybrid protocol than the KKI protocol.Therefore, the hybrid protocol appears to be better able to detect eavesdroppers thanthe KKI protocol. For this reason, we do not see any reason to employ the KKI protocolagainst individual attacks.

[1]  N. Gisin,et al.  OPTIMAL EAVESDROPPING IN QUANTUM CRYPTOGRAPHY. I. INFORMATION BOUND AND OPTIMAL STRATEGY , 1997 .

[2]  Yeshaiahu Fainman,et al.  Security of quantum cryptography against individual attacks , 1998 .

[3]  Jian-Wei Pan,et al.  Efficient multiparty quantum-secret-sharing schemes , 2004, quant-ph/0405179.

[4]  Fuguo Deng,et al.  Improving the security of multiparty quantum secret sharing against Trojan horse attack , 2005, quant-ph/0506194.

[5]  Adam D. Smith.  Quantum secret sharing for general access structures , 2000 .

[6]  Guang-Can Guo,et al.  Quantum secret sharing without entanglement , 2002 .

[7]  R. Cleve,et al.  HOW TO SHARE A QUANTUM SECRET , 1999, quant-ph/9901025.

[8]  Yeshaiahu Fainman,et al.  Security of quantum cryptography against individual attacks , 1998, Other Conferences.

[9]  Fei Gao,et al.  A simple participant attack on the brádler-dušek protocol , 2007, Quantum Inf. Comput..

[10]  D. Gottesman.  Theory of quantum secret sharing , 1999, quant-ph/9910067.

[11]  N. Gisin,et al.  Experimental demonstration of quantum secret sharing , 2001 .

[12]  V. Buzek,et al.  Quantum secret sharing , 1998, quant-ph/9806063.

[13]  D. Bruß.  Optimal Eavesdropping in Quantum Cryptography with Six States , 1998, quant-ph/9805019.

[14]  H. Yuen.  Quantum detection and estimation theory , 1978, Proceedings of the IEEE.

[15]  D. Bruß,et al.  Optimal eavesdropping in cryptography with three-dimensional quantum states. , 2001, Physical review letters.

[16]  M. Koashi,et al.  Quantum entanglement for secret sharing and secret splitting , 1999 .

[17]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[18]  Pérès,et al.  Quantum-state disturbance versus information gain: Uncertainty relations for quantum information. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[19]  G. R. Blakley,et al.  Safeguarding cryptographic keys , 1899, 1979 International Workshop on Managing Requirements Knowledge (MARK).

[20]  Qiaoyan Wen,et al.  Improving the security of multiparty quantum secret sharing against an attack with a fake signal , 2006 .

[21]  L. Hsu,et al.  Quantum secret sharing using product states , 2005 .