Image scrambling based on a new linear transform

A new linear transform for scrambling images is proposed in this paper. The forward transform scrambles the image and the inverse transform unscrambles the image. We define transformation matrices for both scalar and blocked cases. Recursive and non-recursive algorithms based on the new transform are also proposed. The degree of scrambling or unscrambling can be determined by the user. The experimental results show that the positions of the pixels are strongly irregularized using the proposed transform. Unscrambling using a wrong key fails and results in an unintelligible image which cannot be recognized. We also show that the new transform provides a high level of image scrambling and is robust under common attacks and noise. The proposed linear transform is very simple and its implementation as triple-matrix multiplication is straightforward.