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A Novel Optimization Method for Constructing Cryptographically Strong Dynamic S-Boxes | IEEE Journals & Magazine | IEEE Xplore

A Novel Optimization Method for Constructing Cryptographically Strong Dynamic S-Boxes


The proposed novel dynamic S-box construction method strikes a balance between three design objectives: 1) the quality of generated S-box (e.g., nonlinearity), 2) the dyn...

Abstract:

The resistance of S-box-based cryptosystems to linear cryptanalysis is often determined by the nonlinearity (NL) and the linear approximation probability (LAP) of the und...Show More

Abstract:

The resistance of S-box-based cryptosystems to linear cryptanalysis is often determined by the nonlinearity (NL) and the linear approximation probability (LAP) of the underlying S-box. Constructing dynamic bijective S-boxes with high nonlinearity is a challenging problem. In this paper, we propose a novel S-box construction method based on the concept of constrained optimization. The proposed method uses a random-restart hill-climbing algorithm to construct randomized S-boxes and maximize the nonlinearity of each Boolean function under bijectivity constraints. The proposed algorithm dramatically reduced the S-box construction time. Compared to recent S-box construction methods, the proposed method strikes a better balance among the three design objectives of dynamic S-boxes, namely, cryptographic strength, dynamicity, and speed of construction. On the average, the proposed method constructs a new dynamic 8\times 8 S-box with NL=112 every 118 ms, whereas a NL=110 S-box can be generated in 5.3 ms, which makes it suitable for real time applications. The proposed method also constructs 8\times 8 S-boxes with NL=114, which is among the highest reported in literature. Moreover, we demonstrate the extensibility of the proposed constrained optimization formulation to improve other S-box design criteria. Namely, we propose an algorithm to optimize the LAP of an S-box while preserving its NL and bijectivity.
The proposed novel dynamic S-box construction method strikes a balance between three design objectives: 1) the quality of generated S-box (e.g., nonlinearity), 2) the dyn...
Published in: IEEE Access ( Volume: 8)
Page(s): 225004 - 225017
Date of Publication: 16 December 2020
Electronic ISSN: 2169-3536

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