Entangled Fractional Fourier Transform And The Application To Optical Information Security

Optical transforms are indispensable tools in optical information security systems,among which fractional Fourier transform is most frequently used.Fractional Fourier transform as a generalized form of Fourier transform not only inherits the merits of optic Fourier transform in optical information processing but also developes a better time-frequency expression,hence it is widely studied and applied to optical information processing and security systems.However,encryption systems based on fractional Fourier transform have security flaws and safety loopholes such as security-risk key problems.Therefore,it is of great significance to propose a novel type of fractional Fourier transform that can overcome inherent security flaws of classical fractional Fourier transform.Through in-depth analysis of classical fractional Fourier transform and its security flaws,this paper proposes a novel type of fractional Fourier transform named entangled fractional Fourier transform,studies inherent properties and the security of the transform,and based on such twisty transform proposes two types of optical image information security techniques satisfying two different security demands in order to provide new tool,method and theoretical basis for the furthur development of optical information security.First,this paper proposes entangled fractional Fourier transform and points out that the transform is equipped with the dimension-parallel-processing pattern fitting for optical image processing which transforms both horizontal and vertical information of the input signal simultaneously.The transform has nonseperability,nonperiodicity and multiplicity.Through analysis on the security properties of the entangled fractional Fourier transform,it is found that the inherent nonperiodicity,nonseparability and multiplicity are the theoretical assurances and technical supports of range expansion and dimension escalation of key space of information security systems based on the entangled fractional Fourier transform.Second,to achieve two different goals of information hiding,this paper establishes the double random phase optical image encryption technique in entangled fractional Fourier transform domain and the encryption-watermarking technique in entangled fractional Fourier transform domain.The double random phase optical image encryption technique transforms the original image to the entangled fractional Fourier transform domain and reassigns image greyscale values distribution to hide the secret information by utilizing entangled fractional Fourier transform.The nonperiodicity,nonseparability and multiplicity of the transform prevents the decryption process from safety risk of more-solution-to-one-key problem,expands the key space range,increases the key space dimension,therefore remarkably enhances the security level of the system.The simulation and security performance comparision results show that the proposed double random phase optical image encryption system in entangled fractional Fourier transform domain has good security level,and imply that such system has higher security level and better reconstructed images than the systems based on classical fractional Fourier transform.The entangled phase retrieval algorithm is proposed based on entangled fractional Fourier transform.It is pointed out that entangled fractional Fourier transform guarantees and enhances the convergence and the degree of freedom of the algorithm.Based on the entangled phase retrieval algorithm and Chirikov map an optical encryption-watermarking technique is proposed named encryption-watermarking technique in entangled fractional Fourier transform domain.Through comparing and analyzing differences between such technique and classical watermarking techniques,it is indicated that this encryption-watermarking technique uses two kinds of keys to retrieve watermark,has properties of nondistorted host image and high tolerance of watermark.Therefore the technique therefore has bigger key space and higher security level than traditional watermarking techniques.The simulation results show the validity and security of the proposed encryption-watermarking technique.Finally,double-image authentication technique in image entangled fractional Fourier transform domain is proposed which pioneerly accomplishes the one-enryption-two-authentication pattern.Such technique is constructed based on double image encryption method in entangled fractional Fourier transform domain,part-phase-information-recovery technique and nonlinear optics correlator verification technique which satisfies high security demands and low operation cost demands of verification systems.Through theoretical analysis,it is concluded that such double-image verification technique remarkably reduces the storage and transmission cost of verification systems,the one-enryption-two-authentication pattern decreases the time and storage cost.The simulation results show the validity and security of the proposed double-image verification technique.