Fixed point theory and image integrity authentication

Li Xu (1, 2) , Xingming Sun (3) , Quansheng Liu (4)

1 CSUST - Changsha University of Science and Technology
2 Hunan University
3 NUIST - Nanjing University of Information Science and Technology
4 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

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.

Domaines: Probabilités [math.PR]; Traitement du signal et de l'image [eess.SP]; Théorie de l'information et codage [math.IT]

Li Xu, Xingming Sun, Quansheng Liu. Fixed point theory and image integrity authentication. IEEE Transactions on Image Processing, 2015, 24 (2), pp.632-645. ⟨10.1109/TIP.2014.2372473⟩. ⟨hal-01095072⟩