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. 2018 Jul 12;20(7):525.
doi: 10.3390/e20070525.

A New Hyperchaotic System-Based Design for Efficient Bijective Substitution-Boxes

Eesa Al Solami  1 , Musheer Ahmad  2 , Christos Volos  3 , Mohammad Najam Doja  2 , Mirza Mohd Sufyan Beg  4
Affiliations

A New Hyperchaotic System-Based Design for Efficient Bijective Substitution-Boxes

Eesa Al Solami et al. Entropy (Basel). .

Abstract

In this paper, we present a novel method to construct cryptographically strong bijective substitution-boxes based on the complicated dynamics of a new hyperchaotic system. The new hyperchaotic system was found to have good characteristics when compared with other systems utilized for S-box construction. The performance assessment of the proposed S-box method was carried out based on criteria, such as high nonlinearity, a good avalanche effect, bit-independent criteria, and low differential uniformity. The proposed method was also analyzed for the batch-generation of 8 × 8 S-boxes. The analyses found that through a proposed purely chaos-based method, an 8 × 8 S-box with a maximum average high nonlinearity of 108.5, or S-boxes with differential uniformity as low as 8, can be retrieved. Moreover, small-sized S-boxes with high nonlinearity and low differential uniformity are also obtainable. A performance comparison of the anticipated method with recent S-box proposals proved its dominance and effectiveness for a strong bijective S-box construction.

Keywords: 5-D hyperchaotic system; batch-generation; bijective; small-sized S-boxes; substitution-box.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Phase portraits of the 5-D hyperchaotic system (2) (a) projection on the x-y plane; (b) projection on the x-u plane; (c) projection on the z-w plane; (d) 3-D view in x-y-z space; (e) 3-D view in x-z-u space; and (f) 3-D view in y-u-w space.
Figure 1
Figure 1
Phase portraits of the 5-D hyperchaotic system (2) (a) projection on the x-y plane; (b) projection on the x-u plane; (c) projection on the z-w plane; (d) 3-D view in x-y-z space; (e) 3-D view in x-z-u space; and (f) 3-D view in y-u-w space.
Figure 2
Figure 2
Performance of generation of 100,000 8 × 8 S-boxes for (a) average nonlinearity, (b) maximum differential uniformity, (c) SAC, (d) average BIC-nonlinearity, and (e) BIC-SAC.
Figure 2
Figure 2
Performance of generation of 100,000 8 × 8 S-boxes for (a) average nonlinearity, (b) maximum differential uniformity, (c) SAC, (d) average BIC-nonlinearity, and (e) BIC-SAC.
See this image and copyright information in PMC

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