线性分段混沌映射构造及在图像加密中的应用  

Construction of linear piecewise chaotic map and its application in image encryption

作　　者：于万波[1] 王玉新 YU Wan-bo;WANG Yu-xin(School of Information Engineering,Dalian University,Dalian 116622,China)

机构地区：[1]大连大学信息工程学院,辽宁大连116622

出　　处：《计算机工程与设计》2023年第3期707-713,共7页Computer Engineering and Design

摘　　要：参考一些经典的混沌系统例如改造或者复合后的账篷映射、调频后的正弦函数等,构建可用的混沌系统是一项重要的工作。研究发现一组计算简单、混沌特性非常好的分段线性函数,该分段线性函数族中的一类具有较好的混沌特性,其分岔图遍历特性较好,在较大的参数区间内Lyapunov指数均大于1.5,同时也可以证明其在定义区间上是Devaney混沌的。该系统具有多个可变的自由参数,各种抗攻击指标较理想,计算时间少,密钥空间大,是一种实用的混沌加密系统,同时该分段函数也是混沌研究的一个实例。It is an important work to construct usable chaotic systems by referring to some classical chaotic systems,such as modi-fied or compound tent mapping,frequency modulated sine function,etc.A family of piecewise linear functions with simple calculations and good chaotic characteristics were discovered.One of the piecewise linear functions had good chaotic characteristics,and its bifurcation diagram traversal characteristics were better.The Lyapunov exponents in the interval were all greater than 1.5,and it was verified that it was Devaney chaotic in the defined interval.The system had multiple variable free parameters,various anti-attack indicators were ideal,calculation time was small,and the key space was large.It was a practical chaotic encryption system.At the same time,the piecewise function was also an example of chaos research.

关 键 词：混沌序列 图像加密 分段线性函数 计算时间复杂度 自由参数 DEVANEY混沌 分岔图 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]