Abstract
An Efficient Image Generation Algorithm is proposed. It generates Message Authentication Image (MAI) by using Fractals and chaos theory. The fractal images are generated by using Iterated Function System (IFS) techniques. We implemented and generated the fractal images exploring the properties of chaos. Chaos is an unpredictable behavior arises in a dynamical system so that the future behavior is not in a predictable way. Chaos is based on the initial condition that is generated by Pseudo Random Number Generator (PRNG). The chaotic behavior of the system is also analyzed. We use these Fractal images as a digital signature. This technique can be employed in online transactions like Banking, Shopping. to avoid phishing and also we can watermark this fractal image and use it for government and private identification proofs.
Highlights
The paper is organized as follows-section 2 deals with literature survey on fractals, section 3 explains the techniques of Chaos, Deterministic System and Pseudo Random Number Generator (PRNG), Lucas series and difference equations, in section 4, Image generation algorithm is proposed, in section 5, Chaotic Stegosystem with some experimental results, tables and Chaotic chart analysis are given and in section 6 we bring out the conclusion and future work
The Fibonacci sequence with the Morkov chain is a chaos. This could be embedded in fractal, based on this idea, we introduced chaos in steganography. It explains the generation of Message Authentication Image (MAI) using chaos theory and Iterated Function System (IFS) technique
Based upon the initial condition it starts to draw the representation for the given binary data according to the rules framed in an Image generation algorithm
Summary
The geometric shapes of the fractals are very complex and it is infinitely detailed. The small sections of them are recursively defined and it is similar to large ones. The fractals have the elements of chaos and it is first imagined by Julia and Mandelbrot, but the essence is based in mathematics. It is originally from the normal triangle, choose any vertices from the triangle and start from the middle to draw the triangle, repeat this process infinitely for number of iterations. The paper is organized as follows-section 2 deals with literature survey on fractals, section 3 explains the techniques of Chaos, Deterministic System and Pseudo Random Number Generator (PRNG), Lucas series and difference equations, in section 4, Image generation algorithm is proposed, in section 5, Chaotic Stegosystem with some experimental results, tables and Chaotic chart analysis are given and in section 6 we bring out the conclusion and future work
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