Shafali Agarwal
Plano, Texas 75025, USA
Abstract
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.
Keywords
Burning ship fractal, Knuth shuffle method, Image encryption, Hilbert transformation, dynamic diffusion
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