Research On Image Encryption Based On Chaotic System And Threshold Scheme

With the rapid development of computational intelligence,the security of the information carried by the image is getting more and more attention.Therefore,the image encryption algorithm has gradually become a hot topic in the field of information security.In recent years,the digital image encryption based on chaos has been more and more perfect.When the parameters of the nonlinear system take a specific value,the dynamic behaviors highly depend on the changes of the initial value,and the iterative orbit cannot be accurately predicted.Thus,this feature can be better applied to the diffusion and confusion process in cryptography.In addition,the mathematical equation of the chaotic system is determined.The chaotic sequence can be reconstructed by protecting the security of the parameters and the initial value.There are two main methods for image protection.One is to use the chaotic sequence with pseudo-random property to permute the image pixels position and change the image pixels value.The other is the image sharing technology based on threshold scheme.In this scheme,the original image can be restored by multi-cooperation,and even if some shares of image are lost,the original image can be reconstructed as well.In this dissertation,image encoding and decoding based on piecewise linear function(PWLF)are studied in detail.We discuss the process of constructing PWLF and analyze the chaotic characteristics.Combining the compression coding based on PWLF with the Chinese residual theorem(CRT),the size of the shadow image can be effectively reduce,and the data expansion of the shadow image can be improved.Firstly,the original image is divided into several blocks.The frequencies of different pixels are counted in each block image and converted into probability distribution.Then,the PWLF and the corresponding interval are constructed by using probability.The PWLF and its inverse function correspond to the decoding and encoding process,respectively.Because each image block has different encoding length.Therefore,the codes are divided into several groups and each group contains the same length binary bits.The corresponding decimal value can be obtained as the secret value for sharing.In order to improve the sensitivity of the shadow image to the change of original image pixels,the chaotic sequences are used to permute the secret sequences.Due to the change of pixels in block image,the corresponding entropy will be changed as well.If it does not change,one small random number will be superimposed on the entropy.The set consists of entropy of all blocks and the variance of this set is used as the initial value of Logistic map after entering chaotic status.Thus,we can get completely different iteration orbits,and then reorder the secret value sequence to achieve better resistance to the differential attacks.Secondly,the threshold sharing scheme is constructed by using CRT,and the secret value sequences are transformed into several shadow images,which are distributed to a number of legal members.Moreover,the changes in the number of participating members have been analyzed.In other words,the authorized subset contains new members.The improved algorithm can ensure that the shares of the original participants will be unchanged.The secret value can also be restored through their cooperation.In order to protect the security of the sharing scheme and avoid cheating behaviors,in this dissertation,the identity authentication scheme based on public key cryptography has been designed.The participants restore the secret value by cooperation after passing verification.The experimental results are in line with the theoretical requirements by combining the computer numerical simulation and the relevant evaluation criteria of the security,which prove that our proposed scheme satisfies the security and the effectiveness for secret image sharing.