三维复合混沌系统及其在图像加密的应用

Three-Dimensional Composite Chaotic System for Image Encryption

混沌是非线性学的一个重要学科,在信息安全、物理学和经济学等领域得到了广泛应用,持续构造新的混沌系统是有意义的。针对这一情况,构造了一类包含迭代次数t的三维三角函数复合混沌系统,对系统的动力学行为进行测试和分析,通过对系统分岔图、Lyapunov指数、周期点导数、谱熵等进行分析,确定其具有较强的混沌特性和较大的混沌区间,同时证明了混沌系统满足Devaney混沌定义,通过对系统随机生成的混沌序列进行0-1测试和NIST测试确定其混沌序列质量良好。因此基于该系统的混沌序列对图像进行加密,实现简单,加密速度快,同时对加密结果的各项指标系数进行了计算和分析,测试结果均非常接近理论最优值。其中,密钥空间很大,可达10252。与最近的其他方法进行对比,结果表明,基于该系统的加密方案可以具有较强的安全性和可靠性。

Chaos is an important subject of nonlinearity,which has been widely used in information security,physics and economics.It is meaningful to construct new chaotic systems continuously.In view of this situation,a class of threedimensional trigonometric complex chaotic system containing the number of iteration t is constructed.The dynamic behavior of the system is tested and analyzed.By analyzing the bifurcation diagram,Lyapunov,derivative of periodic points and spectral entropy of the system,it is determined that it has strong chaotic characteristics and large chaotic interval.At the same time,it is proved that the chaotic system satisfies the Devaney definition of chaos.Through 0-1 test and NIST test,the chaotic sequence randomly generated by the system is determined to have good quality.Based on this system,an efficient image encryption scheme is constructed,which is simple to implement and fast to encrypt.And further through the simulation test,index coefficients of encryption results are calculated and analyzed,and the results are very close to the theoretical optimal value.Among them,the key space is huge,up to 10252.The results are compared with other methods proposed recently,which can prove that the image encryption algorithm has strong security and reliability.