Abstract
Problem statement: In the last decade, dynamical systems were utilized to develop cryptosystems, which ushered the era of continuous value cryptography that transformed the practical region from finite field to real numbers. Approach: Taking the security threats and privacy issues into consideration, fractals functions were incorporated into public-key cryptosystem due to their complicated mathematical structure and deterministic nature that meet the cryptographic requirements. In this study we propose a new public key cryptosystem based on Iterated Function Systems (IFS). Results: In the proposed protocol, the attractor of the IFS is used to obtain public key from private one, which is then used with the attractor again to encrypt and decrypt the messages. By exchanging the generated public keys using one of the well known key exchange protocols, both parties can calculate a unique shared key. This is used as a number of iteration to generate the fractal attractor and mask the Hutchinson operator, so that, the known attacks will not work anymore. Conclusion: The algorithm is implemented and compared to the classical one, to verify its efficiency and security. We conclude that public key systems based on IFS transformation perform more efficiently than RSA cryptosystems in terms of key size and key space.
Highlights
The digital information revolution has brought about changes in our society and our lives
This study focuses more on the mathematical aspects of fractal functions and briefly exposes the reader to the latest application of fractal functions in cryptography, namely public key cryptosystems
A novel fractal protocol is proposed to be used in the public key systems
Summary
The digital information revolution has brought about changes in our society and our lives. New technology and new applications bring new threats and drives us to invent new protection mechanisms. With this rapid development in information technology, there is a growing demand for cryptographic techniques, which has spurred a great deal of intensive research activities in the study of cryptography (Menezes et al, 1997). Many properties of chaotic systems have their corresponding counterparts in traditional cryptosystems. They are characterized by sensitive dependence on initial conditions and similarity to random behavior, a part from geometrical and statistical complexity, that explain to why this application field qualifies for encryption purposes. Fractals are attractors of dynamical systems; the place where chaotic dynamics occur (Jacquin, 1992)
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