Application Research Of Robust Chinese Remainder Theorem In Secret Image Sharing And Data Hiding

Secret Image Sharing(SIS)and Reversible Data Hiding in Encrypted Image(RDHEI)are two important techniques for protecting privacy data.Based on the problems of existing SIS schemes and RDH-EI methods,this dissertation uses the Robust Chinese Remainder Theorem(RCRT)on integer rings and polynomial rings as a research tool to construct two new SIS schemes and a new RDH-EI method.The details are as follows:(1)Most of the existing SIS schemes cannot reconstruct the secret image when the shadow image is disturbed by noise and causes errors.To solve this problem,this dissertation proposes an RCRT-based secret image sharing scheme.Even if small errors occur in the shadow image,the proposed scheme can reconstruct the secret image with high quality.In addition,based on this scheme,an image correction method is proposed,which can greatly improve the quality of the reconstructed secret image.(2)Although some existing SIS schemes can reconstruct the secret image when the shadow image is wrong,they require a large amount of additional data.In addition,the pixel values of the shadow images generated by most SIS schemes based on Shamir secret sharing and Chinese remainder theorem are not uniformly distributed in the range of[0,255].Aiming at these problems,this dissertation proposes a secret image sharing scheme based on RCRT over polynomial rings.Even if the shadow image is affected by noise and causes low-bit flipping of pixels,the scheme can reconstruct the secret image with high quality without additional data.Additionally,the generated shadow image pixel values are uniformly distributed between[0,255].(3)The existing secret sharing-based RDH-EI methods have low embedding rate,the cover image cannot be reconstructed without loss,and the pixel value may overflow during image encryption or data hiding.For the above problems,this dissertation proposes an RDH-EI method based on RCRT over polynomial rings.Compared with the known RDH-EI method based on secret sharing,this method has the highest maximum embedding rate of 4 bpp(i.e.,an average of 4 bits of secret data can be embedded per pixel),because the operations are performed in the polynomial ring F2[x],there is no risk of pixel value overflow during image encryption and data hiding.Compared with the RDH-EI method based on a single data hider,this method can resist internal attacks.Even if there are one or more malicious data hiders,the cover image can be losslessly restored.Compared with the RDH-EI methods based on traditional encryption algorithms,this method has a higher maximum embedding rate,and the data embedding rate does not change with the cover image.Finally,this method is separable,meaning that the image recovery and data extraction processes are independent of each other.