چکیده (انگلیسی):

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.