A NOVEL S-BOX DESIGN VIA A 2D CHAOTIC MAP

Introduction: Substitution boxes (S-boxes) provide the main nonlinearity in modern symmetric ciphers, and their quality directly impacts resistance to linear and differential cryptanalysis. Chaos-based S-box generation is attractive due to sensitivity to initial conditions and strong mixing, but many existing designs suffer from narrow chaotic regions, limited reproducibility, or inconsistent security metrics. This work presents a novel two-dimensional (2D) chaotic map and a practical framework to construct robust bijective 8×8 S-boxes.

Methods: We introduce a discrete-time 2D chaotic map that combines trigonometric functions, an exponential term, and fractional-part folding to promote strong stretching–folding dynamics. S-box construction follows a two-stage procedure. First, a first-hit quantization strategy converts the chaotic orbit into a duplicate-free 256-element permutation, guaranteeing bijectiveness. Second, a deterministic swap-based hill-climb refines the seed S-box by selecting improving swaps under a score that prioritizes maximizing the minimum component nonlinearity while also reducing differential and linear indicators.

Results: The resulting 8×8 bijective S-box achieves strong cryptographic performance: all eight Boolean components reach nonlinearity 112, the average strict avalanche criterion (SAC) is 0.506836, the maximum differential uniformity is 4 (DP = 0.015625), and the maximum linear probability (bias) is 0.0625. Bit-independence is also strong, with BIC–NL = 112 and an average off-diagonal BIC–SAC of 0.500140.

Conclusions: The proposed 2D-map-driven, two-stage approach is simple, reproducible, and produces a competitive bijective 8×8 S-box with strong resistance to differential and linear attacks. This abstract reports original, unpublished work suitable for conference presentation.