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Problem statement: In the last decade, dynamical systems were utilized to develop&#13; cryptosystems, which ushered the era of continuous value cryptography that transformed the practical region&#13; from finite field to real numbers. Approach: Taking the security threats and privacy issues into&#13; consideration, fractals functions were incorporated into public-key cryptosystem due to their complicated&#13; mathematical structure and deterministic nature that meet the cryptographic requirements. In this study we&#13; propose a new public key cryptosystem based on Iterated Function Systems (IFS). Results: In the proposed&#13; protocol, the attractor of the IFS is used to obtain public key from private one, which is then used with the&#13; attractor again to encrypt and decrypt the messages. By exchanging the generated public keys using one of&#13; the well known key exchange protocols, both parties can calculate a unique shared key. This is used as a&#13; number of iteration to generate the fractal attractor and mask the Hutchinson operator, so that, the known&#13; attacks will not work anymore. Conclusion: The algorithm is implemented and compared to the classical&#13; one, to verify its efficiency and security. We conclude that public key systems based on IFS transformation&#13; perform more efficiently than RSA cryptosystems in terms of key size and key space

Efficiency Analysis for Public Key Systems Based on Fractal Functions