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.

An Image Encryption Scheme Based on Lorenz Hyperchaotic System and RSA Algorithm

“…In cryptography, the finite field called GF (p) is an important field, where p is a prime number. It is a finite set of integers and uses mode operations to perform basic mathematical operations [52]. is study uses a finite field, GF(257) � 0, 1, .…”

Image Encryption and Decryption System through a Hybrid Approach Using the Jigsaw Transform and Langton’s Ant Applied to Retinal Fundus Images

“…For this, we encrypted 2 images, image number 6 from the healthy patients and image number 15 from the sick subset. We used subsections of 16 × 16 for the Jigsaw transform, a cyclic permutation of 2005 columns and 2007 rows, 4 9 sections for Langton's ant (placing the ants of the red channels on the first row and second column, the ants of the green channels on the second row and second column, and the ants of the blue channels on the third row and second column) and p 1 = 530, 530, p 2 = 120, 120, p 3 = 350, 350 as the parameters for the second deterministic noise. The results obtained are shown in Figures 12 and 13, respectively.…”

“…For example, if we use a 4224 × 3616 RGB picture and divide it in sections of 16 × 16 for the Jigsaw transform and into 4 9 sections for Langton's ant, then K > 1 × 10 1134190. 38 .…”

“…For example, in [8] the authors proposed a chaos-based image encryption method and imitating the Jigsaw technique as a scrambling scheme, its proposal consists of three steps, a pre-processing, encryption, and post-processing stage, in pre-processing and post-processing stages the hyperchaotic Lorenz system is used to generate the control sequences of revolving and shifting image blocks, whilst in the encryption process, the skew tent system is applied to revolving image blocks. In [9] an image encryption system using the Jigsaw transform (JT) and the iterative finite field cosine transform is presented. Hua et al [1] presented a medical image encryption scheme, it first inserts random data in the input image, then, two stages scrambling and pixel adaptive diffusion (bitwise XOR and modulo arithmetic) are applied.…”

Optical Bit-Plane-Based 3D-JST Cryptography Algorithm With Cascaded 2D-FrFT Encryption for Efficient and Secure HEVC Communication

“…The Jigsaw transform [34] is a non-linear transposition function that alternates the adjacent blocks of an image [35]. One of the Jigsaw transform features is the unitary conservation of the energy during the transformation process.…”