Computationally secure bit commitment protocol based on quantum steganography

Abstract

Abstract:

In quantum bit commitment (QBC), most existed proposals of them analyze little of communicating an innocent message over noisy quantum channels. These methods are not practical. Based on the information hiding characteristics of quantum steganography, we propose a novel QBC. An elegantly scheme is presented for disguising secret information as quantum noise, and embedding it in stego qubits which encode into a codeword of quantum error-correcting code. The method is proved secure and effectiveness in the presence of noisy quantum channel and a potential eavesdropper. The results of theoretical analysis and numerical simulation show that the proposed scheme has perfect concealing and binding properties. Theoretical analysis proved the validity. The method forms a theoretical basis for the promotion and application of quantum cryptographic protocols.

Key words: quantum information, quantum cryptography, bit commitment, quantum steganography

CLC Number:

O431.2

Cao Dong，Song Yaoliang. Computationally secure bit commitment protocol based on quantum steganography[J]. J4, 2012, 29(1): 63-68.

References

[1] Blun M. Coin flipping by telephone[C]. Proc IEEE Sprint COMPCOM, Las Vegas, 1982:133-137.
[2] Naor M. Bit commitment using pseudorandomness[J]. Journal of Cryptology, 1991, 2(2): 151-158.
[3] Damgard I and Fujisaki E. An integer commitment scheme based on groups with hidden order[C]. Advances in Cryptology –ASIACRYPT, New Zealand, 2002: 125-142.
[4] Brassard G, Crepeau C, Jozsa R and Langlois D. A quantum bit commitment scheme provably unbreakable by both parties[C]. Proceedings of 34th Annual IEEE Symposium on the Foundations of Computer Science. Palo Alto, California, USA, 1993: 362-371.
[5] Andrew C C Yao. Security of quantum protocols against coherent measurements[C]. Proceedings of 26th Annual ACM Symposium on the Theory of Computing. Las Vegas, Nevada, USA, 1995:67-75.
[6] Mayers D. Unconditional secure quantum bit commitment is impossible[J]. Phys. Rev. Lett, 1997, 78: 3414-3417.
[7] Lo H K. Insecurity of quantum secure computations[J]. Phys. Rev. A, 1997, 56:1154-1162.
[8] Ramos R V, Mendonca F A. Quantum bit commitment protocol without quantum memory. http://arxiv.org/abs/0801.0690v1, 2008.
[9] Magnin L, Magniez F, Leverrier A, Cerf N J. Strong no-go theorem for gaussian quantum bit commitment[J]. Phys. Rev. A, 2010, 81(1):010302
[10] Li Q, Li C, Long D Y, Chan W H, Wu C H. On the impossibility of non-static quantum bit commitment between two parties. http://arxiv.org/abs/1101.5684v1,2011.
[11] Chailloux A, Kerenidis I. Optimal bounds for quantum bit commitment. http://arxiv.org/abs/ 1102.1678v1 ,2011.
[12] Shaw B A, Brun T A. Quantum Steganography. http://arxiv.org/abs/1006.1934, 2010.
[13] Shaw B A, Brun T A. Hiding Quantum Information in the Perfect Code. http://arxiv.org/abs/ 1007.0793, 2010.
[14] Ben-Aroya A, Ta-Shma A. On the complexity of approximating the diamond norm. http://arxiv.org/abs/0902.3397v3, 2009.
[15] Watrous J. Semidefinite programs for completely bounded norms. http://arxiv.org/abs/0901.4 709v2, 2009.
[16] Benenti G, Strini G. Computing the distance between quantum channels: usefulness of the Fano representation[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 2010, 43(21): 215508.
[17] Nielsen M A, Chuang I L. Quantum computation and quantum information. Higher Education Press. 2003, page379.
[18] 张守林, 张盛, 王剑. 基于压缩态的连续变量量子对话协议[J]. 量子电子学报, 2011, 28(3): 335-340 Zhang S L, Zhang S, Wang J. Continuous variable quantum dialogue protocol based on squeezed state[J]. Chinese Journal of Quantum Electronics. 2011, 28(3): 335-340