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

Journal of Computer Science

Muhammad Asif Khan¹  Varun Jeoti¹ 

关键词: Substitution Box;    Nonlinear Dynamics;    Robust Chaos;    Tent Map;    Piecewise Non-Smooth Maps;   

DOI  :  10.3844/jcssp.2015.517.525

学科分类：计算机科学（综合）

来源: Science Publications

【 摘 要 】

Robustchaotic maps with wide robust region are favored in cryptography as it extendsthe key length. Chaotic tent map has robust chaos for control parameter µ = 2. Perturbation of control parametervalues beyond control parameter 2, results in orbit diverging towards infinityand trajectories vanish. Thus, to avoid trajectories diverging to infinity andto keep trajectories chaotic beyond parameter value 2, a new technique isproposed that makes use of modulo and scaling operators. The parameter space ofnon-smooth maps is never considered for enlargement. Herein, modified tent mapresults in larger parameter space that in turn can be used to design key basedS-box. The recently published chaotic key based S-box with chaotic map’sparameter space does not achieve large key space. For modified tent map, themodulo operation keeps trajectories in domain (0, 1) while scaling allows foruniform distribution of points in domain (0, 1). These operations keep chaoticorbits globally stable and robust. In results, the robustness of chaotic tentmap and modified chaotic tent map is compared using bifurcation diagram. Theimproved robust region of tent map justifies the effectiveness of proposedmethod that results to design key based S-box.

【 授权许可】

Unknown