Cryptanalysis of a new circular quantum secret sharing protocol for remote agents

In a recent paper (Lin and Hwang in Quantum Inf Process, 2012. doi:10.1007/s11128-012-0413-8), a new circular quantum secret sharing (QSS) protocol for remote agents was presented. The protocol is designed with entangling a Bell state and several single photons to form a multi-particle GHZ state. For each shared bit among n party, the qubit efficiency has reached 1/2n + 1 which is the best among the current circular QSS protocol. They claim that the protocol is more suitable for a remote agents’ environment as that the newly generated photons are powerful enough to reach to the next receiver. However, we show that the protocol is not secure as the first agent and the last agent in the protocol can illegally obtain all the secret messages without introducing any error.

[1]  Run-hua Shi,et al.  Quantum secret sharing between multiparty and multiparty with Bell states and Bell measurements , 2010 .

[2]  Zhang Yu-qing,et al.  Cryptanalysis and Improvement of a Quantum Secret Sharing Protocol between Multiparty and Multiparty with Single Photons and Unitary Transformations , 2010 .

[3]  Tzonelih Hwang,et al.  An enhancement on Shi et al.'s multiparty quantum secret sharing protocol , 2011 .

[4]  Zhan-Jun Zhang,et al.  Multiparty quantum secret sharing of secure direct communication , 2005 .

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

[6]  Qiaoyan Wen,et al.  Cryptanalysis of the Hillery-Buzek-Berthiaume quantum secret-sharing protocol , 2007, 0801.2418.

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

[8]  Louis Salvail,et al.  Quantum Oblivious Mutual Identification , 1995, EUROCRYPT.

[9]  Fuguo Deng,et al.  Circular quantum secret sharing , 2006, quant-ph/0612018.

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

[11]  Tzonelih Hwang,et al.  New circular quantum secret sharing for remote agents , 2013, Quantum Inf. Process..

[12]  Anmin Fu,et al.  Comment on “Reply to Comment on ‘Efficient High-Capacity Quantum Secret Sharing with Two-Photon Entanglement’ ” , 2011 .

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

[14]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

[15]  Xiu-Bo Chen,et al.  An efficient and secure multiparty quantum secret sharing scheme based on single photons , 2008 .

[16]  Yuguang Yang,et al.  Three-party quantum secret sharing against collective noise , 2010, Quantum Information Processing.

[17]  张玉清,et al.  Cryptanalysis and improvement of a quantum secret sharing scheme based on χ-type entangled states , 2012 .

[18]  Hong-Yu Zhou,et al.  An efficient quantum secret sharing scheme with Einstein–Podolsky–Rosen pairs , 2005 .

[19]  Ping Zhou,et al.  Multiparty quantum secret sharing with pure entangled states and decoy photons , 2007 .

[20]  Liang Lin-Mei,et al.  Quantum Secret Sharing with Two-Particle Entangled States , 2006 .

[21]  Chun-Wei Yang,et al.  Thwarting intercept-and-resend attack on Zhang’s quantum secret sharing using collective rotation noises , 2012, Quantum Inf. Process..

[22]  Stephen Wiesner,et al.  Conjugate coding , 1983, SIGA.

[23]  Zhan-jun Zhang,et al.  Multiparty quantum secret sharing , 2004, quant-ph/0412203.

[24]  K. Peng,et al.  Multiparty secret sharing of quantum information based on entanglement swapping , 2004 .

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

[26]  Xiu-Bo Chen,et al.  Multiparty quantum secret sharing based on Bell measurement , 2009 .

[27]  Xin Wang,et al.  Multiparty quantum secret sharing based on the improved Boström–Felbinger protocol , 2007 .

[28]  Guihua Zeng,et al.  Arbitrated quantum-signature scheme , 2001, quant-ph/0109007.

[29]  L. Hsu.  Quantum secret-sharing protocol based on Grover's algorithm , 2003 .

[30]  Yi-Min Liu,et al.  Multiparty quantum secret sharing of secure direct communication using single photons , 2008 .

[31]  Xue Fei,et al.  High-capacity three-party quantum secret sharing with superdense coding , 2009 .

[32]  Yuqing Zhang,et al.  Efficient quantum secret sharing scheme with two-particle entangled states , 2011 .

[33]  Deng Fu-Guo,et al.  Erratum: Improving the security of multiparty quantum secret sharing against Trojan horse attack [Phys. Rev. A 72, 044302 (2005)] , 2006 .

[34]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[35]  Fuguo Deng,et al.  Efficient high-capacity quantum secret sharing with two-photon entanglement , 2006, quant-ph/0602160.

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

[37]  Z. Man,et al.  Multiparty quantum secret sharing of classical messages based on entanglement swapping , 2004, quant-ph/0406103.