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              <p>Based on the fixed point theory, this paper proposes a new scheme for image integrity authentication,which is very different from Digital Signature and Fragile Watermarking. By the new scheme, the sender transformsan original image into a fixed point image (very close to the original one) of a well chosen transform, and send thefixed point image (instead of the original one) to the receiver; using the same transform, the receiver checks theintegrity of the received image by testing whether it is a fixed point image, and locate the tampered areas if theimage has been modified during the transmission. A realization of the new scheme is based on a GaussianConvolution and Deconvolution (GCD) transform, for which an existence theorem of fixed points is proved. Thesemi-fragility is analyzed via commutativity of transforms, and three commutativity theorems are found for theGCD transform. Three iterative algorithms are presented for finding a fixed point image with few numbers ofiterations, and for the whole procedure of image integrity authentication; a fragile authentication system and asemi-fragile one are separately built. Experiments show that both systems have good performance in transparence,fragility, security and tampering localization. In particular, the semi-fragile system can perfectly resist the rotationby a multiple of 90o, flipping and brightness attacks.</p>
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