Cryptographic Algorithm Using Newton-Raphson Method and General Bischi-Naimzadah Duopoly System

Abstract

Image encryption is an excellent method for the protection of image content. Most authors used the permutation-substitution model to encrypt/decrypt the image. Chaos-based image encryption methods are used in this model to shuffle the rows/columns and change the pixel values. In parallel, authors proposed permutation using non-chaotic methods and have displayed good results in comparison to chaos-based methods. In the current article, a new image encryption algorithm is designed using combination of Newton-Raphson’s method (non-chaotic) and general Bischi-Naimzadah duopoly system as a hyperchaotic two-dimensional map. The plain image is first shuffled by using Newton-Raphson’s method. Next, a secret matrix with the same size of the plain image is created using general Bischi-Naimzadah duopoly system. Finally, the XOR between the secret matrix and the shuffled image is calculated and then the cipher image is obtained. Several security experiments are executed to measure the efficiency of the proposed algorithm, such as key space analysis, correlation coefficients analysis, histogram analysis, entropy analysis, differential attacks analysis, key sensitivity analysis, robustness analysis, chosen plaintext attack analysis, computational analysis, and NIST statistical Tests. Compared to many recent algorithms, the proposed algorithm has good security efficiency.

A new hyperchaotic system with dynamical analysis and its application in image encryption based on STM32

“…Subsequently, numerical simulation methods such as MATLAB were employed to conduct in-depth analyses of the dynamic characteristics of hyperchaotic systems, including Lyapunov exponents' spectrum and bifurcation diagrams. Hyperchaotic systems hold vast potential for applications in fields like image encryption and communication security [58][59][60][61][62][63][64][65][66][67][68][69] , given their nonlinear characteristics and high security, thereby offering a promising avenue for research in information security and cryptography.…”

Entropy in Image Analysis III

“…Article [ 12 ] explains that, to encrypt/decrypt images, most researchers are using chaotic systems, whereas others prefer non-chaotic methods. In [ 12 ], a new encryption algorithm is proposed, which combines a non-chaotic Newton-Raphson’s method with a hyperchaotic two-dimensional map of a general Bischi-Naimzadah duopoly system.…”

“…Article [ 12 ] explains that, to encrypt/decrypt images, most researchers are using chaotic systems, whereas others prefer non-chaotic methods. In [ 12 ], a new encryption algorithm is proposed, which combines a non-chaotic Newton-Raphson’s method with a hyperchaotic two-dimensional map of a general Bischi-Naimzadah duopoly system. The multiple security experiments made for measuring the efficiency of the method (among which we find entropy analysis) show that the proposed algorithm possesses a good security efficiency.…”