On Security Of Fractional Fourier Transform Domain Optical Image Encryption Method

This paper studied the parameters of fractional Fourier transform and multiparameter discrete fractional Fourier transform theory, multi parameter discretefractional Fourier transform domain of double random phase encoding(MPDFRFT-DRPC) optical image encryption method for safety as well as theoptical image encryption system key to the special structure and properties. In orderto theoretically strict proof in the password system several typical patterns of attackMPDFRFT-DRPC optical image encryption system of quantitative safety, this papermade a detailed research of multi parameter discrete fractional Fourier transformand MPDFRFT-DRPC linear properties of optical image encryption system, thenonlinear properties of cryptosystems encryption key is part of independent randomdynamic characteristics. This made the following achievements.First, establish and strictly proved MPDFRFT-DRPC optical image encryptionsystem nonlinear properties. Although, many parameters of fractional Fouriertransform and multi parameter discrete fractional Fourier transform is a linearoperator, however, because the MPDFRFT-DRPC optical image encryption systemin the process of encryption and decryption and encryption key special structure,ensure that the MPDFRFT-DRPC optical image encryption system is a nonlinearpassword system. This paper uses the probability theory method rigorousdemonstration of MPDFRFT-DRPC optical image encryption system probability of1is a nonlinear code system. At the same time, it points out that the [41]’s first basictheory error, namely the error that MPDFRFT-DRPC optical image encryptionsystem is linear. Thus, fundamentally denied the literature gossiping aboutMPDFRFT-DRPC optical image encryption system and the use of fractional Fouriertransform of all optical image encryption system is not secure cryptosystem recklesspride conclusion.Secondly, using the theory of probability method is strictly proved that theMPDFRFT-DRPC optical image encryption system theory safety and practicalsecurity. In a MPDFRFT-DRPC optical image encryption system, encryption keysand decryption key is formed in each component of continuous values under thecondition of password system, an attacker can attack through the optical imageencryption system the probability is0, the encryption keys and decryption key isformed in each component under the condition of discrete values, an attacker can attack to break the cipher system for optical image encryption the probabilities ofthe system while not0, but very close to0.Third, using the theory of probability method to prove that, using the chosencipher text attack, chosen-plaintext attack, known plaintext and cipher text onlyattack the4most commonly used typical cryptosystem attack mode attack cannotbreak MPDFRFT-DRPC optical image encryption system. Point out clearly at thesame time, the [41] using the known plaintext attack will break MPDFRFT-DRPCoptical image encryption system, is equivalent to solving a the existence anduniqueness of the solution of linear equations and using Gauss elimination methodfor solving, it is impossible to break the optical image encryption system, theanalysis method and conclusion of the study is completely wrong.Finally, set up and demonstrated that the MPDFRFT-DRPC optical imageencryption system with the encryption key is part of independent random dynamicproperties, and pointed out the MPDFRFT-DRPC, optical image encryptiondecryption process nonlinear system.The conclusion that the MPDFRFT-DRPC optical image encryption systeminto significant increase in implementation cost under the premise of a significantincrease in optical image encryption security. The results of these studies showedthat,[41] literature research method and the conclusion is wrong, MPDFRFT-DRPCoptical image encryption system is safe. At the same time, these studies also showthat, not only can say "based on a fractional Fourier transform optical imageencryption system is a textbook is not secure encryption method of typicalexamples" and without significantly increasing the cost under the premise of thedevelopment of this part, with independent random dynamic encryption keypassword system is to improve the optical image encryption system safety in aneffective way, is also the fractional Fourier transform domain optical imageencryption method based on domain important research direction. The researchmethods and research results, but the [41] has set a textbook example of errors inscientific research!...