DEVELOPMENT OF ROBUST IMAGE CRYPTOGRAPHY SCHEMES USING CHAOTIC MATHEMATICAL MODELS

Abstract

With the exponential growth of multimedia data and increasing concerns over privacy and information security, image encryption has become a crucial area of research. Traditional encryption algorithms, though effective for textual data, are often ineffi- cient for images due to their large size, high redundancy, and strong pixel correlations. Despite their importance, these image encryption algorithms face several drawbacks. First, many image-specific methods suffer from key sensitivity issues. Second, some algorithms fail to provide resistance against classical attacks, thereby compromising security. Third, some methods fail in resisting the statistical attacks and differential attacks. Fourth, some methods cannot even reduce the correlation coefficient between the adjacent image pixels. To overcome these drawbacks, chaotic maps were used in the application of image encryption. Chaotic maps, with its inherent features of sensitivity to initial conditions, unpredictability, and ergodicity, are popular for designing secure and efficient image encryption algorithms. But a few chaotic maps available in literature suffer from limi- tations including narrow range of control parameter, non-uniform output distributions, low and negative Lyapunov exponents and insufficient randomness. This thesis introduces a novel set of discrete chaotic maps designed to overcome limitations in chaos-based image encryption algorithms, such as narrow chaotic range and non-uniform distribution. The proposed maps demonstrate a significantly broader chaotic range, a uniform output distribution, and higher Lyapunov exponents, culmi- nating in robust pseudo-random number generators. These generators form the core of a new image encryption algorithms that integrate novel confusion-diffusion architec- ture, specifically designed to minimize adjacent pixel correlation and maximize cipher image randomness. The effectiveness of the proposed approach is rigorously validated through a comparative security analysis against state-of-the-art algorithms. Compre- hensive tests including statistical, differential, and chosen-plaintext attacks, low corre- lation coefficient and information entropy closer to 8, confirms the algorithm’s superi- ority, while maintaining high computational efficiency. The collective contributions of this work establish a more secure, efficient, and reliable framework for digital image encryption.