On the Enlargement of Robust Region of Chaotic Tent Map for the Use in Key Based Substitution-Box (S-Box)

Abstract

Robust chaotic maps with wide robust region are favored in cryptography as it extends the key length. Chaotic tent map has robust chaos for control parameter μ = 2. Perturbation of control parameter values beyond control parameter 2, results in orbit diverging towards infinity and trajectories vanish. Thus, to avoid trajectories diverging to infinity and to keep trajectories chaotic beyond parameter value 2, a new technique is proposed that makes use of modulo and scaling operators. The parameter space of non-smooth maps is never considered for enlargement. Herein, modified tent map results in larger parameter space that in turn can be used to design key based S-box. The recently published chaotic key based S-box with chaotic map's parameter space does not achieve large key space. For modified tent map, the modulo operation keeps trajectories in domain (0, 1) while scaling allows for uniform distribution of points in domain (0, 1). These operations keep chaotic orbits globally stable and robust. In results, the robustness of chaotic tent map and modified chaotic tent map is compared using bifurcation diagram. The improved robust region of tent map justifies the effectiveness of proposed method that results to design key based S-box.