It is well known that encryption algorithms developed based on Logistic map suffer from limited key space due to the narrow regions of system parameters which can be used, potential risk of security in the presence of numerous periodic windows within the key space, and weakness in known-plain-text attack due to the inherent correlation among the chaotic sequence used for encryption. To overcome these existing problems, this paper presents a secure image encryption algorithm based on a new highly nonlinear discrete dynamical system with ideal chaotic characteristics. Transcendental functions are introduced together with modulo operations which physically represent discontinuous time-varying nonlinearities, leading to extremely complex chaotic behavior that is highly sensitive to system parameters and initial conditions, both of which are considered as the key for the cryptosystem. Extensive numerical experiment results have revealed that the proposed image encryption algorithm offers advantages of unlimited key space and high-level security, since those problematic periodic windows are no longer present within the key space, and it is extremely robust against known-plain-text attack, since the chaotic sequence generated bears no correlation whatsoever due to the folding effect of modulo operation. The algorithm makes truly efficient yet highly secure image encryption based on chaotic systems a reality.
A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field
