Image Encryption Based On A Reality-preserving Fractional Discrete Cosine Transform And Chaos

Under the circumstances of informatization, the rapid development of Internettechnology has brought a great convenience for people, as well as hidden securityproblems. Because of its vivid and intuitive features, image is now an importantmeans of information expression, and also is a way that people are the most willingto accept and use. Consequently, how to ensure security of image informationinteraction and how to prevent images from being attacked illegally by a third partyhave become a research focus. Image encryption is an effective means，which canconvert the meaningful plaintext into the unrecognized and disorganized image, toassure the security of image. Because of its fractional order sensitivity, the fractionalorder transform is introduced into the field of image encryption, and a series ofalgorithms based on the fractional transform have been put forward for imageencryption. However, the outputs of most typical image encryption systems basedon the fractional transforms are complex‐valued, which contain both the amplitudeand the phase information, and are inconvenient for display, transmission andstorage. Besides, the low sensitivity and the periodicity of fractional orders limit thekey space of the encryption system. To solve this problem, a reality‐preservingfractional discrete cosine transform (RPFrDCT) is introduced to image encryption inthis dissertation. As a reality‐preserving transform, the output of the RPFrDCT is realfor real input, which ensures the ciphertext is real. Furthermore, a generatingsequence (GS) is introduced as the main key, which ensures the security of thealgorithm. Specific research work is summarized as follows:An image encryption algorithm based on the reality‐preserving fractionaldiscrete cosine transform is proposed. The significance of the algorithm is to makefull use of the reality‐preserving and the de‐correlation of RFrDCT, that is, theencrypted image is real‐valued, disordered and diffused enough and there is muchlower correlation between adjacent pixels. The GS is generated by the2D Logisticmap, in which the initial values’ and system parameters’ high sensitivity provides ahigh security. Simulation results show that images can be encrypted effectively using the proposed algorithm, which has a large key space and good robustness.A single‐channel color image encryption algorithm based on YCbCr space andthe reality‐preserving fractional discrete cosine transform is proposed. In YCbCrspace, the human eyes are more sensitive to the Y component than to the others.Therefore, with the help of the spectrum truncating, a new component is combinedwith the discrete cosine transform spectrum of the three components and istransformed by the RFrDCT. In order to overcome the hidden security risks of linearencryption system, chaotic scrambling is introduced to achieve double encryption ofthe image. The output of the encryption system is a gray image, which can bewilderothers to some extent. Simulations show that the algorithm satisfies the needs of animage encryption system, such as strong anti‐attack capability, high key sensitivity.In addition, the algorithm can also implement the encryption of three gray images.Triple‐color image encryption algorithm based on the reality‐preservingfractional discrete cosine transform and scrambling is proposed. In thepreprocessing stage, the three color images are first converted into their indexedcolor versions, which are treated as three components of a color image. Encryptionstage includes three steps: the chaos‐based cyclic shift, the RPFrDCT and Arnoldtransform, in which the RPFrDCT determines the security and the output of thesystem. The algorithm is a kind of encryption with secrecy of pixels’ values andpixels’ positions simultaneously. Numerical simulations show that the algorithm hasgood performance to encrypt three color images, as well as certain robustness.