A new image encryption algorithm using random numbers generation of two matrices and bit-shift operators

• Published in: Soft computing (Berlin, Germany) Vol. 24; no. 5; pp. 3829 - 3848
• Main Authors: Es-Sabry, Mohammed, El Akkad, Nabil, Merras, Mostafa, Saaidi, Abderrahim, Satori, Khalid
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Color imagery; Computational Intelligence; Control; Correlation coefficients; Data encryption; Encryption; Engineering; Fourier transforms; Fractals; Graph theory; Mathematical analysis; Mathematical Logic and Foundations; Matrices (mathematics); Matrix algebra; Mechatronics; Methodologies and Application; Numbers; Operators (mathematics); Pixels; Random numbers; Robotics; Signal to noise ratio; Image encryption; Security; Bit-shifting operators; Random numbers generation
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-019-04151-8

In this work, we proposed a new approach to encrypt color images using two matrices with size of 16 × 16 whose integer values are between 0 and 255 generated randomly, and the bit-shift operators. These matrices are used to perform the first encryption phase. The first value of the first matrix is calculated from the pixels of each channel (red, green and blue) of the original image; the rest of the values are randomly generated; each value must be unique; the values of the second matrix are unique and generated randomly. The first encryption phase of the original image is done by digraph (two-digit sequence). We take the first digit in the first matrix, the second digit in the second matrix; then, we look in these matrices for the numbers that complete the rectangle. In the second encryption phase, we used a right circular shift of bits; the number of bits to shift is calculated according to a function which considers the values of the two matrices as well as their positions (row and column). Therefore, any change in the two keys (two matrices) will completely change the encrypted image. Our encryption system is resistant against brute force attacks, statistical attacks as well as differential attacks. The results are justified by applying several safety criteria, such as correlation coefficient, entropy and peak signal-to-noise ratio (PSNR). In addition, our method is very sensitive to the change made, either in the original image or in the two keys used for the encryption, which was justified by calculating the number of changing pixel rate (NPCR > 99.69) and the unified averaged changed intensity (UACI > 33.54).