Research On Image Integrity Authentication Based On Fixed Point Theory

Integrity authentication is a basic problem in the field of active-forensics,and to some degree,it determines the subsequent authentication processes,such as authenticity,tampering localization and restoration etc.The key point of integrity authentication is making the research subject to be fragile to malicious tampering,and reveals the imperfections of the subject when modifications happen.In the classical integrity authentication methods,except the fragility brought from encryption algorithms,the fragility of information digest is used in digital signature,and the fragility of embedding location is used in digital watermarking.In this paper,the fragility of fixed point(under certain conditions,almost any tampering can make a fixed point to be a non-fixed point)is used to build the authentication scheme,which is a totally new research direction and is very different to digital signature and digital watermarking;in addition,some subsequent authentication processes are preliminarily studied.For digital image,based on fixed point theory,this paper studies the building of the integrity authentication scheme,the realization of the scheme and its applications,the tampering localization and the semi-fragile problem,and makes some progress in both theory and experiment.The works of this paper can be detailed as follows.1.An image integrity authentication scheme is built based on fixed point theory.For this method,the two communicating parties agree on a image transform in advance.The sender transforms an original image into a fixed point image(very close to the original one)of a well chosen transform,and send the fixed point image(instead of the original one)to the receiver;using the same transform,the receiver checks the integrity of the received image by testing whether it is a fixed point image,and locate the tampered areas if the image has been modified during the transmission.A realization of the new scheme is proposed based on a Gaussian Convolution and Deconvolution(GCD)transform,for which an existence theorem of fixed points is given.Based on the existence theorem,three fast iterative algorithems are presented for finding fixed point images with few numbers of iterations,and for the whole procedure of image integrity authentication;Experiments show that the authentication system has good performance in transparence,fragility,security and tampering localization etc.2.The consistency between Semi-fragility and commutativity of transforms is indicated.For the authentication system with an explicit mathematical expression,the semi-fragility problem is theoretically discussed,and is translated into the commutativity problem of transforms.Especially,the commutativity theorems of the GCD transform and the rotation transform,the transposition transform and the translation transform;Experiments show that the semi-fragile system based on GCD transform can perfectly resist the rotation by a multiple of 90°,flipping and brightness attacks.3.An authentication scheme based on local fixed point pixels is proposed.The fragility of fixed point is used to build the scheme;with the local fixed point pixels method,each pixel value of a given image is calculated into a fixed point of a function(which is built from the pixel's neighbors and a secret key),and at last a new image composed of fixed point pixels is generated.In this paper,periodic function is used to constract the fixed point generation transform.The simulation results demonstrate the efficiency of our method:the image quality can be well kept,and the tampered areas can be localized precisely.4.An integrity authentication scheme for LSB(Least Significant Bits)steganography is given using GCD transform.For a LSB stego-image,with a well-chosen GCD transform,the existence of the fixed point stego-image(which has the same least significant bits as the original stego-image)is proved,and an iteration algorithm is given for calculating the fixed point stego-image.The experiments show that the fixed point stego-images perform well in fragility,transparence,security and tampering localization.Additionally,some experiments for steganalysis show that the fixed point stego-images do not decrease the invisibility of the corresponding stego-images.