A new hyperchaotic map and its application in an image encryption scheme

• We propose a new 2D map derived from the serpentine curve equations.
• We prove that the proposed map is hyper-chaotic.
• We propose a new algorithm for generating random permutations.
• We propose a new image encryption scheme.
• We performed a standard analysis of the performances of the proposed encryption scheme.

Recently, the hyperchaotic maps have been investigated in order to develop more secure encryption schemes. In this paper we propose a new hyperchaotic map derived from parametric equations of the serpentine curve. Its complex behavior was proven theoretically and numerically, using Lyapunov exponents, bifurcation diagram and correlation dimension of the attractor. The proposed map is then used in a new image encryption scheme with a classic bi-modular architecture: a diffusion stage, in which the pixels of the plain image are shuffled using a random permutation generated with a new algorithm, and a confusion stage, in which the pixels are modified with a XOR-scheme based on the proposed map. The results of its statistical analysis show that the proposed image encryption scheme provides an efficient and secure way for image encryption.