Image Self-encoding And Hiding Based On Fractional Fourier Transform

Since Fourier analysis was proposed by scientist Fourier in 1807,Fourier transform has played an important role in almost all fields of scientific research and engineering technology.However,with the continuous expansion of the research field,the limitations of the Fourier transform in processing non-stationary signals have gradually become apparent.To solve these problems,the fractional Fourier transform emerged as a generalized Fourier transform.The fractional Fourier transform not only has all the good properties of the Fourier transform,but also has some unique characteristics.The study found that these new features have better results in signal processing,image processing,and optics.With the rapid development of Internet technology,a large amount of information can be quickly and easily published and disseminated on the Internet,but it also brings about information security risks.Therefore,how to protect the data of unauthorized users is one of the most important issues today.Because image information is vivid and is widely used by humans as one of the important means of human information expression,image encryption has become a key point of information security.The early image encryption technology is mainly single-image encryption.With the rapid development of information technology,single-image encryption can no longer meet the actual needs.Therefore,researchers have made further investigations on dual image and multiple-image encryption techniques.In addition,these early technologies belong to the symmetric cryptosystem,and the keys used in the encryption process are also used in the decryption process,which makes the system vulnerable to potential attacks.To improve the robustness of the system,a safer approach is to use pixel scrambling or chaotic mapping in the encryption process.This paper uses phase truncation and phase extraction in the encryption process to break the linearity of the system and improve the robustness of the system.Although the use of non-linear encryption systems improves the security of the system,however,almost all the above algorithms encrypt the original image into meaningless ciphertext or white noise,that undoubtedly will imply the importance of data transmission,and arouse the hackers' curiosity,in fact,on the other hand,it makes more likely that the encrypted data will be destroyed.To solve this problem,this paper conducts in-depth research based on domestic research status,improves and proposes a new type of encryption algorithm,and completes the corresponding simulation experiments,including:(1)In-depth analysis of the classical double-random phase encoding method,as well as the phase-truncation double random phase encoding technique developed on this basis,and simulation implementation.(2)The cascaded phase retrieval algorithm based on the double random phase encoding algorithm is introduced in detail.The algorithm can encrypt the image into the target image we set in advance and use the computer to perform the relevant simulation.(3)On the basis of the previous analysis,the self-encoding and hiding of the double images based on the phase truncation and phase retrieval fractional Fourier transform are proposed and simulated to verify the feasibility and security of the algorithm.(4)Further research based on double images,proposes multiple-image selfencoding and hiding based on cascaded fractional Fourier transform and phase retrieval,and performs simulation experiments to verify the feasibility and safety of the algorithm.