Applying projection and B-spline to image authentication and remedy

Many image authentication methods have been proposed, in recent years, to protect image authenticity and integrity, but most have ignored the dangers of counterfeit attack. In this paper, we propose a new image authentication method, using a vector projection technique, for safety and security in digital systems based on a PKI cryptographic framework. In this method, the vector projective square (VPS) pair of each block can be calculated by a vector projection technique, and we prove that an attacker cannot forge a counterfeit image with the same VPS pair as the original image. In addition to addressing counterfeit attacks, we also propose a new remedial algorithm which applying non-uniform B-spline to repair the modified image. This paper, therefore, has five goals: (1) to verify image authentication, (2) to verify the integrity of an image received, (3) to locate any parts that were illegally modified or counterfeited, (4) to provide security against counterfeit attacks and (5) to repair the illegally modified parts.