Logistic映射敏感值的有限精度研究  

Finite precision of Logistic mapping sensitive values

作　　者：朱贵良[1] 朱宏飞[1] 张晓强[2] 

机构地区：[1]华北水利水电学院信息工程学院,郑州450011 [2]北京航空航天大学软件开发环境国家重点实验室,北京100191

出　　处：《计算机应用研究》2012年第2期664-666,671,共4页Application Research of Computers

基　　金：河南省科技攻关资助项目(102102210217)

摘　　要：针对一维混沌加密算法密钥空间小、安全性能低的问题,提出了基于混沌大整数化的完整解决方案,把密钥空间扩大到2392。详细阐述了用于大整数运算的分治叠加法设计思路与实现要点,包括混沌大整数化步骤在内的数字图像加密步骤。以256×256的彩色数字图像为例,验证了加密耗时和加密效果。通过对密钥空间、直方图、明文敏感性、密钥敏感性、信息熵等指标进行分析,表明了基于混沌大整数化的一维混沌加密算法,可以有效抵御穷举、统计和差分等攻击,为一维混沌加密算法走向应用开拓了更大的密钥空间。最后,对密钥的自身安全和超大数字图像处理方法,给出了成熟的解决思路和方案。As one-dimensional chaotic encryption algorithm had the small key space and low security,this paper proposed a complete solution based on big-integer chaos,which expanded the key space to 2392.It expounded the detailed design and implement points of combinative algorithm of pen-and-pencil and divide-and-conquer of big integer operations,including digital image encryption steps of the big-integer chaos.It took a color digital image with the size of 256×256 as an example to verify the encryption scheme.It analyzed the new algorithm in terms of the key space,histogram,plaintext sensitivity,key sensitivity and information entropy.The detailed analysis of simulation results show that the encryption algorithm can effectively resist brute-force,statistic and differential attacks,etc.The scheme of big-integer chaos offers larger key space for one-dimensional chaos encryption algorithm.Finally,it gave the mature ideas and solutions to solve the security of key and the large image processing methods.

关 键 词：混沌映射 密钥空间 混沌大整数化 分治叠加法 有限精度 混沌序列 敏感值 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]