A new image encryption algorithm based on optimized Lorenz chaotic system

Abstract

Summary In this article, an improved Lorenz system was constructed, in the first stage, a nonlinear term in general Lorenz system was replaced by the sum of term of exponential function and term of the square of single variable, then the dynamic characteristics of the improved Lorenz system were analyzed through the analysis on the phase diagrams and its Lyapunov exponents, and it is proved that the new system has good chaotic characteristics. In the second stage, to improve the security and anti‐attack ability of image encryption algorithm, a new image encryption algorithm was proposed based on this improved Lorenz chaotic system, which was used to generate two groups of key sequences which were used in scrambling encryption and alternative encryption. In the scrambling encryption stage, the gray values of image pixels were sorted in ascending order, and combining with the sequence of scrambled encryption key, the pixel position scrambling was realized. In the phase of the pixel value replacement encryption stage, the gray values of the pixels were changed by the method of cipher text feedback. In the third stage, the quantitative analysis of the effect of encryption was carried out by using histogram, information entropy, correlation coefficient of adjacent pixels. The experimental results show that the improved Lorenz formula is a nonlinear chaotic system, the encrypted algorithm based on this chaotic system can effectively resist chosen plaintext attack, in the encrypted image, the grey value shave random‐like distribution behavior and the adjacent pixels have zero correlation. The algorithm has a 299 bit key space and it is very sensitive to the key.

Image encryption scheme based on improved four-dimensional chaotic system and evolutionary operators

“…The sequences generated by the three-dimensional Lorenz chaotic system often exhibit weak broadband characteristics, limited randomness, and monotonicity in localized regions 28 . To address these shortcomings, researchers have endeavored to enhance the three-dimensional Lorenz chaotic system for application in image encryption 8 , 29 , 30 .…”

Image Encryption Using Lorenz Chaotic System

“…However, the proposed method gave fairly good results and the entropy was not competitive enough. In [16] proposed a chaotic system, which has been designed from three stages based on Lorenz equations, the equations have been modified and lost the character of linearity, where an exponent is added to the equation, the proposed method is good but very complex and consumes the system resources. This work aims to build an efficient and simple 3D image encryption system based on the chaotic Lorenz equations.…”

“…Moreover, the results confirm that the encryption algorithm is reliable as it achieved a strong difference between the original image and the encrypted image and did not preserve any of the features of the original image, which may thus facilitate the process of image detection through any kind of differential attacks. [11] 99.61 36.26 Method [15] 99.6 33.51 Method [16] 99.63 33.48…”

Hyperchaotic Image Encryption System Based on Deep Learning LSTM

“…Lorenz chaotic system is a three-dimensional nonlinear system of ordinary differential equations, which is composed of three coupled nonlinear differential equations with good chaotic properties and initial value sensitivity, and is often widely used as a classical pseudorandom generator in the field of image encryption [18]. The Lorenz system is defined as depicted in Eq.…”