Annotations for symmetric probabilistic encryption algorithm based on chaotic attractors of neural networks

Abstract

The security of the symmetric probabilistic encryption scheme based on chaotic attractors of neural networks is analyzed and discussed. Firstly, the key uniqueness is proved by analyzing the rotation transform matrix to avoid the attack of the equivalent key. Secondly, the distributed uniformity of the numbers “0” and “1” in the corresponding attracting domain for every chaotic attractor is analyzed by the statistics method. It is testified that the distributed uniformity can be kept if the synaptic matrix of the neural network is changed by a standard permutation matrix. Two annotations based on the results above are proposed to improve the application security of the encryption algorithm.

Keywords

Rotation Matrix / Chaotic Attractor / Encryption Algorithm / Attraction Domain / Permutation Matrix

References

[1] HopfieldJ. J.. Proceedings of the National Academy of Science, USA, 1982, 79: 2554

[2] LiJ., FengY., YangX.-q.. Journal of Optoelectronics · Laser, 2009, 20: 78

[3] GuoD., ChengL.M., ChengL. L.. Applied Intelligence, 1999, 10: 71

[4] GuoD.-H., HeX.-j., ChenC.-s.. Chinese Journal of Computers, 2000, 23: 1230

[5] QiR., ZhangD., YanP.. Journal of Tsinghua University, 2001, 41: 89

[6] ZhangX.. Matrix Analysis and Applications, 2004, Beijing, Tsinghua University Press: 133

[7] HuB.-x., LiN., LvJ.. Journal of System Simulation, 2004, 11: 2432

[8] XuS.-p., JiangS.-l., XiongY.-h.. Journal of Optoelectronics·Laser, 2009, 20: 89

[9] LiX., TuN.. Lottery Combination Number-Rotation Matrix, 2001, Beijing, China Price Press: 1

[10] LiuN.-s., GuoD.-h.. Optoelectronics·Letters, 2009, 5: 227

[11] GardnerE.. Europhys. Lett., 1987, 4: 481