Abstract: The classical Logistic map suffers from the limited range of system parameters and the uneven distribution of chaotic sequences.In this paper,the Logistic map is improved and applied to image encryption,and on this basis an image encryption algorithm is proposed based on simultaneous scrambling and diffusion operations.Modular operations are added to the classical Logistic map to perform binary bit rearrangement on the generated sequence.Then the improved Logistic map is used to generate pseudo-random sequences with better chaotic features for scrambling and diffusion stages of the cryptosystem.On this basis,the pseudo-random matrix and plain image matrix are bitxored to realize pre-encryption of the plain image.Finally,the scrambling and diffusion operations are performed simultaneously on the pre-encrypted image to get the final encrypted image.Security analysis and experimental results show that the proposed algorithm exhibits excellent encryption performance and high security.It can resists common attacks,such as brute-force attacks and differential attacks.

Key words: image encryption, Logistic map, chaotic characteristics, scrambling, diffusion

摘要： 经典Logistic映射存在系统参数范围受限、混沌序列分布不均等问题。对Logistic映射进行改进并将其应用于图像加密中，设计一种置乱与扩散同时操作的图像加密算法。对经典Logistic映射增加模运算并对其所生成序列进行二进制比特重排，利用改进Logistic映射生成具有更好混沌特性的伪随机序列并用于加密系统的置乱和扩散阶段。将所生成的伪随机矩阵与明文图像矩阵进行异或操作以实现明文图像预加密。在此基础上，采取置乱与扩散同时操作的策略以置乱和扩散预加密后的图像从而得到密文图像。安全性分析及实验结果表明，该算法具有良好的加密性能和安全性，可以抵抗暴力攻击、差分攻击等常见攻击。

关键词: 图像加密, Logistic映射, 混沌特性, 置乱, 扩散

CLC Number: 

• TP309.7