Hybrid Cryptosystem Based on Pseudo Chaos of Novel Fractional Order Map and Elliptic Curves

Abstract

Securing transmission of information between legitimate transmitter and receiver sides is a great challenge for mathematicians, computer scientists and engineers in recent years. This paper aims at achieving three goals. The first of them is to introduce a novel fractional order two dimensional (2D) map having very complex chaotic behavior and distinct large positive values of Lyapunov exponents over wide range of parameters, compared with other 2D maps in literature. Secondly, a new reliable secure encryption scheme combining the associated chaotic pseudo-orbits of the proposed map with the advantages of elliptic curves in public key cryptography is suggested, for first time, and applied to colored images. The hybrid scheme is capable to confirm reliable secret keys exchange in addition to highly obscure and hide transmitted information messages. Finally, a thorough mathematical analysis of security performance and evaluation of encryption scheme immunity against all possible attacks are carried out and proved its efficiency and robustness.

Keywords

• Chaos-based cryptography
• chaotic maps
• discrete fractional calculus
• elliptic curves
• pseudo-orbits