基于分数阶Logistic映射的彩色图像加密

曲靖师范学院学报 ›› 2018, Vol. 37 ›› Issue (3): 30-35.

基于分数阶Logistic映射的彩色图像加密

秦智伟¹, 汪马玲¹, 吴国成^1,2

1. 内江师范学院数学与信息科学学院,四川内江 641100;
2. 四川省数据恢复重点实验室,四川内江 641100

收稿日期:2018-03-24 出版日期:2018-05-26
通讯作者: 吴国成,内江师范学院数学与信息科学学院,四川省数据恢复重点实验室副教授,西南大学应用数学博士后,主要从事分数阶差分方程与图像处理研究.
作者简介:秦智伟,内江师范学院数学与信息科学学院本科生,主要从事图像处理研究.
基金资助:
中国博士后科学基金面上项目“分数阶离散系统的稳定性理论及其应用”(2016M602632)|四川省大学生创新创业训练计划项目“区间映射在混沌加密中的应用”(X201652).

Color Image Encryption Based on the Fractional Logistic Map

Qin Zhiwei¹, Wang Maling¹, Wu Guocheng^{1, 2}

1. College of Mathematics and Information Science, Neijiang Normal University,Neijiang Sichuan 641100, China;
2. Data Recovery Key Laboratory of Sichuan Province, Neijiang Sichuan 641100, China

Received:2018-03-24 Published:2018-05-26

摘要/Abstract

摘要： 分数阶Logistic混沌映射具有模型简单、动力学行为复杂,且易计算机编程的优点.基于分数阶Logistic混沌映射,结合DNA编码,提出了一种分数阶图像加密算法.利用分数阶Logistic混沌产生密钥链和DNA编码序列,再对彩色图像的三个像素层进行像素置乱,改变像素位置,将加密结果像素层组成一张灰度图.结果分析表明,分数阶图像加密不仅改变了原有图像的大小,还改变了图像的类型.通过对该算法从密钥敏感性分析、统计分析和相关性分析,分数阶图像加密算法鲁棒性、密钥敏感性强,极大地提升了密钥空间.

关键词: 混沌, 分数阶Logistic映射, 图像加密, DNA序列

Abstract: The fractional Logistic chaotic map has a simple form but holds complex dynamic behavior and can be readily generated on computer. In this paper, an image encryption algorithm is proposed by using the map and DNA coding. The fractional chaotic map generates a key chain. Each pixel layer of the RGB image is encrypted through changing pixel locations. A gray scale image is obtained by combination of the three encryption results. The encrypted image not only changes the size of the original image but the type. Through the security analysis including key sensitivity, statistics and correlation analysis, the results show that the algorithm has good robustness, key sensitivity and enhanced the key space and leads to high security.

Key words: Chaos, Fractional Logistic map, Image encryption, DNA sequence

中图分类号:

TP309

秦智伟, 汪马玲, 吴国成. 基于分数阶Logistic映射的彩色图像加密[J]. 曲靖师范学院学报, 2018, 37(3): 30-35.

Qin Zhiwei, Wang Maling, Wu Guocheng. Color Image Encryption Based on the Fractional Logistic Map[J]. JOURNAL OF QUJING NORMAL UNIVERSITY, 2018, 37(3): 30-35.

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