Chaos-based gary image encryption using two coupled competition type maps

In this chapter, we present analytic study of nonlinear dynamics that exist in two coupled competition maps. The possible existence of various types of bifurcation in the model including flip bifurcation, pitchfork bifurcation and Neimark–Sacker bifurcation are explored. The presence of chaotic dynamics in behavior of the map has been detected for large domain of parameters. Then, numerical simulations are performed to prove theoretical analysis. Finally, a chaos-based encryption algorithm for gray images is presented as an application for the competition map. The proposed cryptography algorithm is based on the coupled competition map. The implementation of the algorithm is introduced and some aspects of security analysis such as NIST SP 800-22 statistical tests, sensitivity to mismatch in parameters, correlation coefficients for pixels, entropy analysis, and immunity to differential attacks are examined. Comparison with other related works are carried out. The numerical results given in this chapter elucidate that the introduced scheme has a large security keys space, high sensitivity to tiny variations in critical parameters and negligible small coefficients of correlation between adjacent pixels in cipher images.