An ill-posed operator for secure image authentication

Many problems in science and technology are modeled by ill-posed operators and the main difficulty in obtaining accurate solutions is caused by the high instability of such operators. The paper introduces a new schema for secure image authentication. It is based on a rather unconventional approach - the extremely high sensitivity of ill-posed operators to any change in the input data is turned into a tool to achieve fragile watermarking for secure image verification. The ill-posed operator of concern is based on a highly ill-conditioned matrix interrelating the watermark and the original image. Authentication is achieved by solving the least squares problem associated with the underlying linear operator. Regarding general requirements for secure watermark-based authentication, analytical and practical aspects of the introduced technique are discussed. It is shown that the proposed authentication schema is highly secure while providing excellent tamper localization. Several experiments were conducted to demonstrate the effectiveness of the technique when it is subjected to different attacks, including vector quantization counterfeiting and cropping.