Image Encryption and Decryption Systems Using the Jigsaw Transform and the Iterative Finite Field Cosine Transform

Abstract

We propose the use of the Jigsaw transform (JT) and the iterative cosine transform over a finite field in order to encrypt and decrypt images. The JT is a nonlinear operation that allows one to increase the security over the encrypted images by adding new keys to the encryption and decryption systems. The finite field is a finite set of integer numbers where the basic mathematical operations are performed using modular arithmetic. The finite field used in the encryption and decryption systems has an order given by the Fermat prime number 257. The iterative finite field cosine transform (FFCT) was used in our work with the purpose of obtaining images that had an uniform random distribution. We used a security key given by an image randomly generated and uniformly distributed. The JT and iterative FFCT was utilized twice in the encryption and decryption systems. The encrypted images presented a uniformly distributed histogram and the decrypted images were the same original images used as inputs in the encryption system. The resulting decrypted images had a high level of image quality in comparison to the image quality of the decrypted images obtained by the actual optical decryption systems. The proposed encryption and decryption systems have three security keys represented by two random permutations used in the JTs and one random image. The key space of the proposed encryption and decryption systems is larger. The previous features of the security system allow a better protection of the encrypted image against brute force and statistical analysis attacks.