Image Encryption Research Based On Random Fractional Discrete Cosine Transform

Because of its intuitive,comprehensiveness and vivid features,image is now an indispensable means of information expression in the network world,and also is a way that people are the most willing to accept and use.With the development of internet communication technology,the image information has became one of the major targets of attack of hackers and illegal operative,so situation of image information security is more and more serious.Therefore,in order to ensure the security of image information in the internet,researchers have proposed a lot of safe and efficient image encryption technologies.Because of the computational multiplicities of fractional powers and varieties of computation in transform domain,the fractional transform has attracted the attention of research community,and been introduced into the field of image encryption.However,the sensitivity of fractional orders themselves applied in image encryption is low,and the outputs of most typical fractional transforms are complex-valued,which increase the computer's storage burden and are inconvenient for transmission and rendition of transform results.The discrete cosine transform(DCT)and fractional discrete cosine transform(FrDCT)are analyzed in this paper,and a novel random fractional discrete cosine transform(RFrDCT)is presented and applied in image encryption domain.The proposed RFrDCT keeps many characteristics of DCT and FrDCT,such as unitarity,reality,additivity of index,uniqueness,invertibility and nonperiodicity.Besides,the randomization,irrational choice and vectorization of fractional orders and the randomization of generating sequences(GS)improves the key-sensitivity and thus enlarges the key space greatly.Specific research work is summarized as follows:(1)An image encryption algorithm based on RFrDCT is proposed.The proposed RFrDCT can overcome drawbacks of the low sensitivity of the fractional order.The randomization,irrational choice and vectorization of fractional orders by the one-dimension(1-D)Logistic mapping improve the cipher-space further.Numerical simulations and performance analysis demonstrate that the proposed image encryption algorithm can recover the original image losslessly and resist statistical attacks and robustness attacks to some extent.(2)Since the image encryption algorithm based on pure RFrDCT is not a perfect one,an image encryption algorithm based on RFrDCT with the dependent scrambling and diffusion(DSD)is proposed.After RFrDCT to the original image,DSD is adopted in transform domain and ensures the encrypted image is more confused.The random fractional vector and random GS are generated by a two-dimension(2-D)Logistic mapping instead of two 1-D Logistic maps.Compared with 1-D Logistic map,2-D Logistic map has more complex operation and higher security.In addition,a disturbance factor which is dependent on plain-image is adopted in encryption algorithm which modified every initial value and system parameter of the chaotic maps.The disturbance factor relates cryptosystem and plain-image,which ensures the non-linear of the cryptosystem,and thus the cryptosystem has the ability of resisting the known-plaintext and chosen-plaintext attacks.Numerical simulations and performance analysisof multiple gray images demonstrate that the proposed encryption algorithm is safe and effective with a high key-sensitivity and large key space,and can resist common statistical attacks and robustness attacks to some extent.