整数动态耦合帐篷映射优化设计与性能分析
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摘要
给出一种整数帐篷映射的等价形式,并对整数动态耦合帐篷映射模型进行了优化设计。采用耦合映象格子模型,选用整数动态帐篷映射的优化形式作为格点的非线性函数,快速生成了具有均匀分布性和独立性的伪随机序列,对模型的信息熵、互信息、差值特性、Lyapunov指数、随机性进行了仿真分析。仿真结果表明,整数动态帐篷映射与其优化模型完全等价,满足了生成伪随机序列各项性能要求,生成效率显著提高。
An equivalent form of the integer tent map is given, and the integral dynamic coupled tent map model is designed optimally. The optimal form of integer dynamic tent map is used as the nonlinear function of lattice point based the couple map lattice model, which can generate quickly the pseudo random sequence with uniform distribution and independence. The information entropy, mutual information, difference characteristic, Lyapunov exponent and randomness of the model are simulated and analyzed. The simulation results indicate that the integer dynamic tent map is completely equivalent to the optimization model, which satisfies the performance requirements of generating pseudorandom sequences,and the efficiency of generating is significantly improved.
An equivalent form of the integer tent map is given, and the integral dynamic coupled tent map model is designed optimally. The optimal form of integer dynamic tent map is used as the nonlinear function of lattice point based the couple map lattice model, which can generate quickly the pseudo random sequence with uniform distribution and independence. The information entropy, mutual information, difference characteristic, Lyapunov exponent and randomness of the model are simulated and analyzed. The simulation results indicate that the integer dynamic tent map is completely equivalent to the optimization model, which satisfies the performance requirements of generating pseudorandom sequences,and the efficiency of generating is significantly improved.
引文
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[3]胡辉辉,刘建东,商凯,张啸.基于时空混沌的伪随机序列发生器设计与分析[J].计算机工程与应用,2017,53(24):100-105.
[4]Dastgheib M A,Farhang M.A digital pseudo-random number generator based on sawtooth chaotic map with a guaranteed enhanced period[J].Nonlinear Dynamics,2017,89(1):1-10.
[5]田清,徐正光,田立.基于与Tent Map拓扑共轭系统的混沌流加密方案设计[J].工程科学学报,2015,37(1):125-131.
[6]刘建东.基于整数耦合帐篷映射的单向Hash函数及其性能分析[J].计算机研究与发展,2008(3):563-569.
[7]商凯,刘建东,张啸,等.整数非线性耦合映象格子模型及其性能分析[J].计算机科学与探索,2017,11(3):389-395.
[8]Liu H,Wang X.Color image encryption using spatial bitlevel permutation and high-dimension chaotic system[J].Optics Communications,2011,284(16):3895-3903.
[9]Wang X,Teng L,Qin X.A novel colour image encryption algorithm based on chaos[J].Signal Processing,2012,92(4):1101-1108.
[10]Liu H,Wang X.Color image encryption based on onetime keys and robust chaotic maps[J].Computers&Mathematics with Applications,2010,59(10):3320-3327.
[11]Liu H,Wang X,Kadir A.Image encryption using DNAcomplementary rule and chaotic maps[J].Applied Soft Computing Journal,2012,12(5):1457-1466.
[12]Hao Z,Wang X Y,Wang S W,et al.Application of coupled map lattice with parameter q,in image encryption[J].Optics&Lasers in Engineering,2017,88:65-74.
[13]Liu J,Wang X,Yang K,et al.A fast new cryptographic hash function based on integer tent mapping system[J].Journal of Computers,2012,7(7).
[14]Wang X,Liu L,Zhang Y.A novel chaotic block image encryption algorithm based on dynamic random growth technique[J].Optics&Lasers in Engineering,2015,66:10-18.
[15]Zhang D Z.Research on the correlation between the mutual information and Lempel-Ziv complexity of nonlinear time series[J].Acta Physica Sinica,2007,56(6):3152-3157.
[16]Yang Zhi’an,Wang Guangrui,Chen Shigang.Determination of delay time by calculating mutual information with equally distant space cells[J].Chinese Journal of Computational Physics,1995,12(4):442-448.
[17]王永.混沌加密算法和Hash函数构造研究[D].重庆:重庆大学,2007.
[18]Zhang Y Q,Wang X Y.A symmetric image encryption algorithm based on mixed linear-nonlinear coupled map lattice[J].Information Sciences,2014,273(8):329-351.
[19]Zhang Y Q,Wang X Y.A new image encryption algorithm based on non-adjacent coupled map lattices[J].Applied Soft Computing,2015,26:10-20.
[20]AmigóJ M,Kocarev L,Szczepanski J.Theory and practice of chaotic cryptography[J].Physics Letters A,2007,366(3):211-216.
[21]Rukhin A,Soto J,Nechvatal J,et al.A statistical test suite for random and pseudorandom number generators for cryptographic applications[J].Applied Physics Letters,2015,22(7):1645-1679.