A Proposal of a New Chaotic Map for Application in the Image Encryption Domain

F. Abu-Amara, Jawad Ahmad
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Abstract

Several chaos-based image encryption schemes have been proposed in the last decade. Each encryption scheme has pros and cons regarding its speed, complexity, and security. This paper proposes a new chaotic map called Power-Chaotic Map (PCM). Characteristics of the proposed PCM, such as chaotic behaviour, randomness, sensitivity, and s-unimodality, are investigated. As an application of the proposed chaotic map, an image encryption scheme is proposed to encrypt greyscale and text images. The proposed three-phase image encryption scheme performs a series of substitution and permutation operations. The Pixel-Level phase utilises the PCM’s generated keystreams to perform the substitution operation of image pixels. The Row-Level phase permutates, via a proposed pseudorandom number generator, pixel locations of each row and then shuffles row locations. Finally, the Column-Level phase performs a substitution operation on pixels of each column. Performance of the proposed PCM-based image encryption scheme is investigated through histogram analysis, statistical correlation analysis, key sensitivity, encryption performance of text images, and permutation and substitution properties. Experimental results indicate that the PCM has a wider range of chaotic behaviour than well-known one-dimensional maps, meets the s-unimodality property, has high sensitivity, and generates keystreams with random-like behaviour. Furthermore, results indicate that the PCM-based image encryption scheme provides high encryption security for text images, high key sensitivity, immunity against brute-force attacks, strong statistical correlation results, strong encryption performance, and low computational complexity.
一种新的混沌映射在图像加密领域中的应用
在过去的十年中,已经提出了几种基于混沌的图像加密方案。每种加密方案在速度、复杂性和安全性方面都有优缺点。本文提出了一种新的混沌映射,称为功率混沌映射(PCM)。研究了所提出的PCM的混沌行为、随机性、灵敏度和s-单峰性等特性。作为混沌映射的应用,提出了一种灰度图像和文本图像的加密方案。提出的三相图像加密方案执行一系列替换和排列操作。像素级阶段利用PCM生成的密钥流来执行图像像素的替换操作。行级相位通过提议的伪随机数生成器排列每行的像素位置,然后洗牌行位置。最后,column - level阶段对每个列的像素执行替换操作。通过直方图分析、统计相关性分析、密钥敏感性、文本图像的加密性能以及排列和替换特性来研究所提出的基于pcm的图像加密方案的性能。实验结果表明,与已知的一维映射相比,PCM具有更大的混沌行为范围,满足s-单峰特性,具有较高的灵敏度,并生成具有类似随机行为的密钥流。结果表明,基于pcm的图像加密方案对文本图像具有高加密安全性、高密钥敏感性、抗暴力破解、统计相关性强、加密性能强、计算复杂度低等优点。
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