Practical-time decompositions against three kinds of S-boxes with different structures

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2025年5月28日

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Shiwei Chen,
Kaiyuan Wang,
Ensheng Chen

摘要

The study presents practical-time decompositions against Generalized Lai–Massey (GLM), Unbalanced-MISTY (U-M), and Unbalanced-Bridge (U-B) structures, which were designed to construct efficient S-boxes with smaller S-boxes. We propose one classification technique, which utilizes the relations among different sets to reduce the time complexity drastically in the decompositions of the S-boxes with U-M and U-B structures, respectively. Moreover, the equivalent structures of the three structures are obtained. For a 2n-bit S-box with the GLM structure, the time complexity of our decomposition algorithm is approximately $2^{n+2}$ $2^{n + 2}$ times S-box look-ups. For the 2n-bit S-box with U-M or U-B structure, the time complexity is $17 \cdot 2^{n-1}$ $17 \cdot 2^{n - 1}$ times S-box look-ups, and for a single fixed starting point, there are 24 equivalent structures obtained. All our results were verified by experiments.