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An increasing demand of secure data transmission over internet leads to the challenge of implementing a consistent cryptosystem. In 2004, USA navy published the patent which highlights the importance of fractal as an encryption/decryption key in a cryptosystem [1]. Fractal possess butterfly effect i.e. sensitivity to initial condition, due to which small change in input produces a major change in output. This paper summarizes the various recent image encryption techniques in which fractal key is used to encrypt/decrypt followed by substitution, scrambling and diffusion techniques to provide strong cryptosystem. The algorithms covered both private key encryption as well as public key encryption technique in the paper. The analysed algorithms include a set of fractal function such as Mandelbrot set, Julia set, Hilbert curve, 3D fractal, multi-fractal, IFS and chaotic function to generate a complex key used in the encryption process. Corresponding performance of each algorithm is analysed by PSNR test, key space, sensitivity analysis and correlation coefficient value between the adjacent pixels of both images (Original image and encrypted image) which shows significant improvement in performance over the traditional encryption methods.

This paper proposes a fractal-based image encryption algorithm which follows permutation-substitution structure to maintain confusion and diffusion properties. The scheme consists of three phases: key generation process; pixel permutation using the Knuth shuffle method; and the dynamic diffusion of scrambled image. A burning ship fractal function is employed to generate a secret key sequence which is further scanned using the Hilbert transformation method to increase the randomness. The chaotic behavior of the fractal strengthens the key sensitivity towards its initial condition. In the permutation phase, the Knuth shuffle method is applied to a noisy plain image to change the index value of each pixel. To substitute the pixel values, a dynamic diffusion is suggested in which each scrambled pixel change its value by using the current key pixel and the previously ciphered image pixel. To enhance the security of the cryptosystem, the secret key is also modified at each encryption step by performing algebraic transformations. The visual and numerical analysis demonstrates that the proposed scheme is reliable to secure transmission of gray as well as color images.