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Fractal&rsquo, s spatially nonuniform phenomena and chaotic nature highlight the function utilization in fractal cryptographic applications. This paper proposes a new composite fractal function (CFF) that combines two different Mandelbrot set (MS) functions with one control parameter. The CFF simulation results demonstrate that the given map has high initial value sensitivity, complex structure, wider chaotic region, and more complicated dynamical behavior. By considering the chaotic properties of a fractal, an image encryption algorithm using a fractal-based pixel permutation and substitution is proposed. The process starts by scrambling the plain image pixel positions using the Henon map so that an intruder fails to obtain the original image even after deducing the standard confusion-diffusion process. The permutation phase uses a Z-scanned random fractal matrix to shuffle the scrambled image pixel. Further, two different fractal sequences of complex numbers are generated using the same function i.e. CFF. The complex sequences are thus modified to a double datatype matrix and used to diffuse the scrambled pixels in a row-wise and column-wise manner, separately. Security and performance analysis results confirm the reliability, high-security level, and robustness of the proposed algorithm against various attacks, including brute-force attack, known/chosen-plaintext attack, differential attack, and occlusion attack.

A chaos-based cryptosystem has been suggested and investigated since last decade because of its sensitivity to the initial condition, unpredictability and ergodicity properties. The paper introduces a new chaotic map which helps to enhance the security of image transmission by blending the superior fractal function with a new 2D-Sine Tent composite map (2D-STCM) to generate a key stream. A trajectory map of a proposed 2D-STCM show a wider chaotic range implies better unpredictability and ergodicity feature, suitable to design a cryptosystem. A fractal based image encryption increases the key space of the security key up-to hundreds of bits, thus secure the proposed cryptosystem from brute-force attack. The requirement of confusion and diffusion are fulfilled by applying chaotic circular pixel shuffling (CCPS) to change the pixel position repeatedly and the execution of an improved XOR operation i.e., complex XOR, designed to increase the encryption quality. The proposed cryptosystem has been analyzed using statistical analysis, key sensitivity, differential analysis and key space analysis. The experimental result proves that the new scheme has a high security level to protect the image transmission over the network.