The Research Of Image Encryption Algorithm Based On Fractional Fourier Transform

Information security has become an important issue which cannot be ignored,since the multimedia technique in network,the communication technique and transmission technique are developing so fast.As a kind of effective information carrier,images are widely applied in various fields due to their vivid characters.Therefore,image security is an important research direction for information security.Image encryption is thus an effective method to ensure the information security.At present,there are a series of image encryption algorithms of which the image encryption algorithm based on fractional Fourier transform(FRT)is a highlight for researchers that has aroused great concern.On the basis of FRT as well as random phase encoding and phase retrieval algorithm,this paper discusses two encryption algorithms and conducts numerical simulation for the encryption algorithm.The following is the summary of the main work of this paper:Introducing the basic theory of FRT and putting forward an image encryption algorithm based on multilevel and multi parameter discrete fractional random transform.On the basis of multi parameter discrete fractional random transform,the order is changed from two dimensional transform whereas there is only one number each in horizontal direction and vertical direction into a matrix that every line and every column includes a number,so that a multilevel and multi parameter discrete fractional random transform is constructed.Applying this transform to image encryption directly,the plaintext and cipher text are separately located in space domain and transform domain which are decided by the key.The validity is verified and the strong ability against statistical interpretation is proved by the numerical simulation.Compared with the image encryption algorithm based on multilevel and multi parameter discrete fractional random transform,the algorithm this paper has proposed contains more transformation parameters,enjoys more space for keys and the security is further improved.As a result,this method of encryption has multiple keys with high sensitivity and possesses high degree of robustness and high stability in nose conditions.Putting forward a single-channeled color image encryption algorithm based on FRT.By rotating color cube,the original color image is converted from RGB color space to the R'G'B 'space.Select R 'and G' from three new color components as amplitude and phase,adjust the phase and conduct FRT to a certain order,take the amplitude information and the new color components B' from the result,then use the double image encryption algorithm thanks to phase recovery based on the FRT,and at last conduct three dimensional scrambling to previous output,we will get the color cipher image.The parameter of space rotation,transform order,four seed parameters in three dimensional scrambling can all be used as a key for the encryption system.The results of the numerical simulation verified the feasibility,effectiveness and safety of the encryption method.Through simulation analysis of image features of FRT,including the features of energy distribution as well as the features of the amplitude and phase,it is concluded that the characters of the space and frequency of an image will be reflected in any FRT domain and these characters of the space and frequency differ with the variety of the transform order.The analysis of the change of the image characters of FTR will be helpful for using FRT in image processing.