Image Encryption Algorithms Based On Fractional Hartley Transform

The rapid development of Internet technology enables people to transmitinformation on the open communication platform anywhere at anytime. This makespeople more and more close and the world smaller. The society has come into theinformation era. The social informatization not only brings people a lot ofconveniences, but also forces people to face a lot of security problems. At present, theinformation security has been a very challenging topic. Different kinds of fractionaltransformations have been proposed, improved and applied to optical informationprocessing and digital signal processing, etc. We mainly introduce the fractionalFourier transform (FRFT) and fractional Hartley transform (FRHT) in thisdissertation. The new definition of fractional Hartley transform is the linearsuperposition of fractional Fourier transforms. It satisfies periodicity, order additivity,reversibility, energy concentration, etc like fractional Fourier transform. Theredefinition of fractional Hartley transform is broadly a generation of fractionalFourier transform. So the researches of the redefinition of fractional Hartleytransform are advantageous to promote the development of fractional Fouriertransform in the aspects of image encryption technology. Two image encryptionschemes have been designed. They are mainly based on the redefined fractionalHartley transform and some other technologies combined together. The specific workis as follows:A color image encryption algorithm synthetically applying multiplexingtechnique, logistic map and fractional Hartley transform in a single channel has beenproposed. The red, green and blue parts of the original color image are easilymultiplexed into a single channel through simple mathematical operations.Subsequently the single-channel information is encrypted by double random phaseencoding based on the redefined fractional Hartley transform. Compared with theconventional multiple-channel color image encryption system, the single-channelcolor image encryption system has confusion property to some extent. This is becausethe outputs of the proposed single-channel image encryption system are not threegrayscale images but a gray image and two corresponding phase-only keys. The results of numerical simulation and theoretical analysis declare that the proposedencryption system has high sensitive keys, huge key space and very good security.A single-channel color image encryption algorithm is proposed by combiningfractional Hartley transform with vector operation. The original color image isdecomposed into R、G and B components. The G and B components are encryptedinto two phase-only masks Gand Bwith vector operation, respectively. The R,Gand Bare transformed by FRHT and vector operation twice to obtain anamplitude, a random phase and a decryption phase key. The new amplitude combinedwith the random phase is transformed by FRHT once more and then the result isscrambled by the chaotic scrambling to strengthen the security of the algorithm. Theprivate phase key is dependent on the original image, which makes the proposedencryption algorithm more secure than the linear color image encryption algorithmbased on the double random phase encoding in FRHT. Simulation results demonstratethe security and effectiveness of the proposed algorithm.