基于改进分段Logistic映射的PRNG算法  

PRNG Algorithm Based on Improved Piecewise Logistic Mapping

作　　者：华漫[1] 李锦长 李燕玲 HUA Man;LI Jingchang;LI Yanling(School of Computer,Civil Aviation Flight University of China,Deyang 618000,China;School of Science,Civil Aviation Flight University of China,Deyang 618000,China)

机构地区：[1]中国民用航空飞行学院计算机学院,四川德阳618000 [2]中国民用航空飞行学院理学院,四川德阳618000

出　　处：《计算机与现代化》2025年第3期113-118,126,共7页Computer and Modernization

基　　金：四川省自然科学基金资助项目(2023YFG0170)。

摘　　要：分段Logistic映射的提出改善了经典Logistic映射的一些缺点,由于其复杂性高、安全性好等特点为混沌流密码设计领域提供了一种新的研究课题。为了改善分段Logistic混沌映射存在混沌序列均匀分布特性较差、密钥空间过小等安全隐患,提出一种基于初始值和控制参数反馈调整的分段Logistic映射改进方法。该方法通过引入动态系统参数映射函数使输出的状态值分布的概率密度更均匀。基于优化后的分段Logistic混沌映射重新设计PRNG算法和分析比特级数字图像加密实验。实验结果表明本文算法产生的序列混沌特性更显著,分布更均匀,且具有更好的随机性,在流密码算法设计中具有广泛的应用前景。The proposed piecewise Logistic mapping improves some limitations of the classical Logistic mapping and presents a new avenue for research in chaotic flow cryptographic design due to its high complexity and strong security.In order to improve the security risks of piecewise Logistic chaotic mapping,such as non-uniform distribution of chaotic sequences and small key space,an improved method of piecewise Logistic mapping based on feedback adjustment of initial values and control parameters is proposed.This method incorporates a dynamic system parameter mapping function to achieve a more uniform probability den⁃sity of output state value distribution.Based on the optimized piecewise Logistic chaotic mapping,the PRNG algorithm is rede⁃signed,and the Bit-level digital image encryption experiment is analyzed.The experimental results show that the chaotic se⁃quence generated by the algorithm is more prominent,more evenly distributed,and has better randomness,which has a wide ap⁃plication prospect in stream cipher algorithm design.

关 键 词：混沌系统 流密码 分段Logistic映射 图像加密 PRNG 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]