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混沌映射与比特重组的图像加密

平萍, 李健华, 毛莺池, 戚荣志(河海大学计算机与信息学院, 南京 210098)

摘 要
目的 当前很多图像加密都采用基于比特的加密算法。针对这种比较流行的加密算法所存在的安全缺陷问题,提出一种能够解决比特面0比特和1比特置乱时的位置限制的图像加密算法,实现比特的全局重组。方法 首先利用Tent混沌映射生成一个伪随机序列,然后利用生成的伪随机序列对比特明文图像进行整行以及整列的置乱,将置乱后的比特像素矩阵分块分别进行Henon映射的置乱,最后经过扩散操作得到最后的密文图像。结果 加密后明文图像的像素值的分布由不均匀变成了均匀分布,明文图像的各像素间的相关性被打破,使得原图没有了统计特性,像素变化率(NPCR)以及归一化平均变化强度(UACI)皆接近理想值,算法能够抵抗穷举攻击和差分攻击,并且在能保证加密安全的同时能有较低计算复杂度。结论 本文所提出的图像加密算法具有加密后像素相关性低、密钥空间大,以及对明文图像和密钥高度敏感等特点,本文算法在进行比特级的置乱时,又加入了与明文相关的特性,增强了加密算法的明文敏感性,同时也加强了加密算法的扩散性,可有效地保障密文图像的安全。
关键词
Image encryption algorithm based on chaotic maps and bit reconstruction

Ping Ping, Li Jianhua, Mao Yingchi, Qi Rongzhi(School of Computer and Information, Hohai University, Nanjing 210098, China)

Abstract
Objective Many of the current image encryption algorithms are based on bit level,whichhave security flaws.Many bit-based image encryption algorithms divide the plain-text image into eight-bit planesaccording the eight binary pixels,and then scramble the eight bit planes,which results in 0 bits and 1 bits of each bit plane to not change,onlymakingthe position change of the 0bit and 1bit in each into bit plane,so that there are security flaws.In this paper,a new image encryption algorithm was proposed according to the existing problems of security flaws in these popular encryption algorithms.The proposed algorithm can resist the chosen-plaintext and the chosen-ciphertext attacks,and solve the position restriction of 0bit and 1bit in the bit plane to bring about global reconstruction.Method The scrambling of the image encryption algorithm is divided into two stages:the first stage of the scrambling is to be transformed into a binary pixel matrix for global scrambling;the second stage of the scrambling is to block the pixel matrix after the global scrambling and scramblefor each bit plane.First,the Tent chaotic map is used to generate a pseudo-random sequence.Then,each pixel of the plain-text image is converted into binary bits,andpseudo-random numbers are sorted in ascending order to generate a new set of sequences.For example,in any sequence {0.3,0.7,0.5,0.4,0.8,0.2},the sequence is sorted in ascending order to obtain the ordered sequence {0.2,0.3,0.4,0.5,0.7,0.8},and then the corresponding position sequence is {6,1,4,3,2,5}.The new sequence is used to carry out the whole row and column scrambling.The pixel matrix is divided into eight blocks to perform the Henon map scrambling,and then the final cipher image is obtained by the diffusion operation.Result The distribution of the pixel value of the plain-text image after encryption changes from non-uniform to uniform distribution,and the correlation between the pixels of the plain-text image is broken.Thus,the original image has no statistical characteristics,the number of pixels change rate(NPCR) and the unified average changing intensity(UACI) is close to the ideal values,and the algorithm can resist the differential attack.Experimental results show that when the algorithm key changes little,more than 99% of the pixels in the resulting cipher images are changed.This algorithm belongs to the symmetric encryption algorithm,anddecryption algorithm is also used in the same key so thatthe decryption key also has the same conclusion.Thus,the encryption algorithm is sensitive to the key.The key space of the algorithm must be large enough to resist the exhaustive attack.The key of the encryption algorithm is composed of two parts,which are the keys used to generate the chaotic sequence and the parameters needed in the diffusion phase.The key space of the algorithm is 2192,which can resist the exhaustive attack.The algorithm can guarantee the security of encryption and have lower computational complexity.The cipher image obtained by the encryption algorithm of the plain-text image can be obtained by the information entropy formula.The information entropy of the cipher image is 7.996 2,which is very close to the ideal value of 8.Experimental results show that the encryption algorithm can avoid the information leakage duringimage encryption,and the image encryption algorithm has good anti-entropy analysis attack.The algorithm of image encryption proposed in this paper mainly includes two steps:scrambling and diffusion.The complexity of the algorithm is mainly reflected in the scrambling process.The running time of this algorithm is shorter than that of other image encryption algorithms,and the diffusion process is added to the algorithm.Therefore,the algorithm is more secure than other image encryption algorithms and is more resistant to differential attacks.Conclusion The proposed algorithm is also a relatively classic "scrambling-diffusion" structure.Compared with other encryption algorithms with the same structure,this algorithm is based on bits to scramble.When 1bit in a certain pixel and 1bit of another pixel change in position,the changes not only include the position of the pixel but also the value of the pixel.Experimental results show that the proposed image encryption scheme has numerous characteristics,including large key space,low correlation of adjacent cipher pixels,and high sensitivity to the plain-text and key,which can effectivelyprotect the security of the encrypted image.In this algorithm,the global bits of the plain-text are first scrambled to avoid the scrambling of the bits in the same bit plane,which results in the weight of the 0bit and 1bit tonot change.The scrambling sequence used in the scrambling process is related to the plain-text image,so it shows partial diffusion effect.The experimental results also show that the algorithm is safe and practical and has good application prospects in image encryption and other applications.In the future work,we will continue to explore the new image encryption algorithm,and now compared with the popular encryption algorithm to improve the efficiency of the encryption algorithm while ensuring the security and practicality of the algorithm.
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