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

Abdelrahman Karawia

doi:10.3390/e23010057

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.

Highlights

Algorithm Using Newton-RaphsonDigital images play a critical role in the world today
The key space of the IEGBNDS algorithm consists of the polynomial function with degree k and limits of [α, β] for the Newton-Raphson’s method, two initial values and eight parameters for General Bischi-Naimzadah Duopoly System (GBNDS)
GBNDS has been used to producing chaotic sequences to diffusion phase of image encryption algorithm

Summary

Introduction

Digital images play a critical role in the world today. Of the transmitted data via the Internet [1]. They often contain sensitive and valuable information which requires protection against unauthorised access in various applications such as military images, medical images and Satellite images. Researchers have been designing methods to protect digital images from piracy while they are transferred from one place to another such as encryption algorithms via chaos [2,3,4,5,6], DNA coding [7], and wavelets [8]. In Reference [10], the authors presented an efficient algorithm based on a class of Mordell elliptic curves to generate S-boxes.

Methods

Results

Conclusion