Robust variations of secret sharing through noisy quantum channel

In this paper, the perfect secret sharing in quantum cryptography is investigated. On one hand, the security of a recent protocol [Adhikari et al. Quantum Inform. & Comput. 12 (2012) 0253-0261] is re-examined. We find that it violates the requirement of information theoretic security in the secret sharing and suffers from the information leakage. The cryptanalysis including several specific attack strategies are given, which shows that a dishonest participant can steal half or all of the secrets without being detected. On the other hand, we design a new quantum secret sharing protocol. The security of protocol is rigorously proved. It meets the fundamental requirement of information theoretic security. Furthermore, the security analysis including both the outside attacks and participant attacks is given in details. It is shown that our proposed protocol can achieve perfect secret sharing.

[1]  Mitsuru Ito,et al.  Secret sharing scheme realizing general access structure , 1989 .

[2]  Gan Gao,et al.  Cryptanalysis of multiparty quantum secret sharing with collective eavesdropping-check , 2010 .

[3]  Yuan Su,et al.  Cryptanalysis on the improved multiparty quantum secret sharing protocol based on the GHZ state , 2012, Physica Scripta.

[4]  Lo,et al.  Unconditional security of quantum key distribution over arbitrarily long distances , 1999, Science.

[5]  Qiaoyan Wen,et al.  Robust variations of the Bennett-Brassard 1984 protocol against collective noise , 2009 .

[6]  Gilles Brassard,et al.  Quantum Cryptography , 2005, Encyclopedia of Cryptography and Security.

[7]  Tzonelih Hwang,et al.  Multiparty quantum secret sharing based on GHZ states , 2011 .

[8]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[9]  Josh Benaloh,et al.  Generalized Secret Sharing and Monotone Functions , 1990, CRYPTO.

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

[11]  Yixian Yang,et al.  Multi-party quantum secret sharing with the single-particle quantum state to encode the information , 2013, Quantum Inf. Process..

[12]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

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

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

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

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

[17]  Sudhir Kumar Singh,et al.  Generalized quantum secret sharing , 2003, quant-ph/0307200.

[18]  Jeroen van de Graaf,et al.  Cryptographic Distinguishability Measures for Quantum-Mechanical States , 1997, IEEE Trans. Inf. Theory.

[19]  Xiao-Fen Liu,et al.  Cryptanalysis of quantum secret sharing based on GHZ states , 2011 .

[20]  Adan Cabello,et al.  Six-qubit permutation-based decoherence-free orthogonal basis , 2007, quant-ph/0702118.

[21]  Pankaj Agrawal,et al.  Probabilistic secret sharing through noisy quantum channel , 2012, Quantum Inf. Comput..

[22]  Fei Gao,et al.  Improving the security of multiparty quantum secret sharing based on the improved Boström–Felbinger protocol , 2008 .