A Digital Image Encryption Algorithm Based On Arnold Transform

Today’s society is an information era, which is highly developed, the salient features of this era is the highly developed internet technology and multimedia technology. In this background, more and more information is rapidly spread through the Internet, but it also brings the problem of information security because of the innate freedom and openness of Internet. As a kind of multimedia information, digital images which are spread over the Internet is not secure enough. Therefore, how to ensure the safety of digital images in this era of Internet has become a hot topic of research all over the world.As the most effective means to protect the security of digital images, image encryption technologies mainly includes which based on pixel scrambling, secret segmentation and secret sharing, modern cryptography system, chaotic system and so on. This thesis focuses on two parts, the first part is the Arnold algorithm, which can be easily achieved and has high flexibility. The second part is the algorithm based on the Lorenz chaotic system, which is sensitive to the initial key and has huge key space. Based on the two parts abovementioned, this thesis proposes an improved scheme, which has the excellent performance of encryption. The main work has the following aspects:(1) Summarize the related theories of digital image encryption. Discuss the current situation of the development of image encryption, the basics of cryptography, the basics of chaos theory, the scrambling algorithm and the chaotic system in common.(2) Propose an image scrambling algorithm based on Arnold transform. The traditional Arnold transform has some disadvantages, such as it does not meet Kerckhoffs’ s principle and it has the characteristics of cyclicity. This algorithm is based on image blocking and the optimal round of transform of sub block, in order to improve the performance of traditional Arnold transform. Compared the performance of encryption image, which is generated by using this algorithm and the traditional Arnold algorithm, it is proposed in this thesis that the distribution of gray value is more uniform, the autocorrelation image is more smooth and the correlation coefficient is lower in the encryption image, which is generated by using this algorithm, and the algorithm meets Kerckhoffs’ s principle too.(3) In applications, we propose an image encryption algorithm based on improved Arnold transform and the Lorenz chaotic system. In this algorithm, original image is divided into small blocks and preprocessed by the improved Arnold transform, then these small blocks are encrypted by chaotic sequence, which is generated by the Lorenz system. Compared with the traditional Arnold algorithm, as a comparison object with the performance index of encrypted image in the same scrambling round, this algorithm has obvious advantage. On the one hand, the entropy is improved while the correlation coefficient is reduced, on the other hand, the gray histogram is more uniform. In addition, this algorithm has a high sensitivity to the initial key, the encrypted image also has high ability to resist the noise interference and the shear attack.