基于Diophantus模型与动态S盒的图像加密算法

Image encryption algorithm based on linear Diophantus model and dynamic S-boxes

为解决当前S盒加密算法主要是借助固定S盒进行像素扩散,且S盒的生成与明文无关,导致其安全性不佳的不足,提出一种基于线性Diophantus模型与循环移位动态S盒的图像加密算法。从Logistic映射迭代生成的混沌数组中选择两个元素,计算Diophantus模型的系数,获取两个解集合,定义位置排序法,形成置乱密钥;借助外部密钥,生成2DLogistic映射的初始条件,输出随机整数序列,基于等尺度变换,拓展2D Arnold映射,形成矩形变换机制,获取系数矩阵;基于有限域理论,设计循环移位动态S盒,构建像素扩散模型;利用改进的引力模型,定义密文深度增强机制,优化密文的NPCR(number of pixels change rate)与UACI(unified average changed intensity)值。实验结果表明,与基于固定S盒的加密技术相比,所提算法的安全性与加密效率更高。

To solve the defect of low security caused by that the generated S boxes are independent on plaintext in current S boxes encryption algorithm,the image encryption algorithm based on linear Diophantus model and cyclic shift dynamic S-boxes was proposed.A chaotic number was generated by introducing the 1D Logistic map,and the coefficients of the Diophantus model were calculated by randomly selecting two elements from the chaotic numbers.The scrambling key was obtained by computing the two solution sets of Diophantus model according to the coefficients and defining the position sorting method.The cyclic dynamic S box was designed through finite field theory,and the pixel diffusion model was designed by combining the coefficient matrix of the rectangular transformation mechanism.Depth diffusion mechanism was constructed based on the improved gravity model to maximize the NPCR and UACI.Experimental results show that the proposed algorithm has higher security and efficiency compared with the current image encryption technology.