三维Arnold映射的周期及在图像加密中的应用  

Periods of the 3-Arnold Transformation and Its Application in Image Encryption

作　　者：李用江[1] 张睿哲[2] 葛建华[3] 孙志林 

机构地区：[1]广东海洋大学信息学院,广东湛江524088 [2]平顶山学院计算机科学与技术学院,河南平顶山467002 [3]西安电子科技大学综合业务网国家重点实验室,西安710071 [4]河南宇通信息技术有限公司,郑州450003

出　　处：《电子科技大学学报》2015年第2期289-294,共6页Journal of University of Electronic Science and Technology of China

基　　金：国家自然科学基金(41340049);国家863项目(B50306290182);国家发展改革委卫星应用高技术产业化专项([2009]214);河南省科技计划重点项目(102102210420)

摘　　要：具有混沌特性的Arnold映射在图像置乱、保密通信等方面都取得了很好的效果,但Arnold变换矩阵具有周期性,因此确定变换矩阵的周期是置乱变换的重要基础。为了研究三维Arnold变换矩阵的周期性,引入了孪生Fibonacci数列对概念,并阐述了4条相关性质定理。证明了三维Arnold变换矩阵的模周期是孪生Fibonacci数列对的模周期的一半,从而找到了确定变换矩阵模周期的新方法。最后提出了一种新的基于三维Arnold映射的多轮双置乱加密算法,对比二维Arnold映射置乱加密算法,仿真结果表明该算法优势比较明显,具有一定的先进性。The Arnold mapping with chaotic has achieved good results in the image scrambling and secure communication, however, the Arnold transformation matrix is periodic so that finding the cycle of the transformation matrix is the important basis of scrambling transformation. In order to study the periodicity of the 3-Arnold transform matrix, the new concept of the twin Fibonacci sequence is introduced and four related periodicity theorems are given. And then we prove that the molding cycle of 3-Arnold transform matrix is half of the molding cycle of the twin Fibonacci sequence. Accordingly, a new method to determine the molding cycle of the transformation matrix is formed. At last, a new several-rounds double-scrambling encryption algorithm based on the 3-Arnold mapping is proposed. Simulation results show the proposed algorithm outperforms the 2-Arnold mapping algorithm.

关 键 词：ARNOLD变换 图像置乱 信息隐藏 多轮置乱 孪生Fibonacci数列对 

分 类 号：TP393[自动化与计算机技术—计算机应用技术] O156[自动化与计算机技术—计算机科学与技术]