Paper bounds leftover linear self-symmetries of inverse-based S-boxes
Original title: Linear Self-Symmetries of Inverse-Based S-boxes: Generic Rigidity and Applications
The leading decay depends on the smallest prime divisor of the extension degree, and the full AES S-box has none.
A cryptography paper studies how often nontrivial linear self-symmetries of finite-field inversion survive a random outer invertible linear layer. Matching upper and lower bounds fix the leading quadratic exponent, which is governed by the smallest prime divisor of the extension degree rather than dimension alone. The authors give a rigidity criterion, prove the full AES S-box has no nontrivial linear self-symmetry, and discuss ARIA and Vision.
- The analysis reduces the problem to semilinear conjugacy and centralizer estimates.
- The decay rate depends on the arithmetic of the field extension, not only its dimension.
- Applications named in the paper are AES, ARIA, and Vision.
From the original article
1 min read at arxiv.orgFinite-field inversion is a basic nonlinear building block in the design of S-boxes for symmetric cryptography. In inverse-based S-boxes, finite-field inversion is often combined with linear or affine layers that may preserve or destroy algebraic symmetries of the inverse function.
By Zheng Zhang · arxiv.org
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