Newest papers

Linear Self-Symmetries of Inverse-Based S-boxes: Generic Rigidity and Applications

Zheng Zhang, Na Zhang · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29837 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

有限场逆转是对称加密的S框架设计中的基本非线性构造块。在反向的S框架中,有限场逆转通常与可保留或破坏反向函数的线性或相似层相结合,我们研究了非线性线性自我对称的频率如何,因为外部可逆转的线性自我对称的概率在 \(GL_n(\mathbb F_2)\)之间变化。使用对逆转的两侧线性等级的分类,我们将问题降至半线性对接和集中估计。我们获得对应的上和下限,以确保非线性线性自我对称仍然存在的概率,并且这些界限决定了其线性领先的四角形指标。这个指标是由最小的自我分割者所管理的,

Machine translation (Meta M2M100); the English original follows.

Abstract

Finite-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. We study how often nontrivial linear self-symmetries remain as the outer invertible linear transformation varies over \(GL_n(\mathbb F_2)\). Using the classification of two-sided linear equivalences of inversion, we reduce the problem to semilinear conjugacy and centralizer estimates. We obtain matching upper and lower bounds for the probability that a nontrivial linear self-symmetry remains, and these bounds determine its leading quadratic exponent. This exponent is governed by the smallest prime divisor of the extension degree. Thus the decay rate depends on the arithmetic of the field extension and not only on its dimension. As cryptographic applications, we provide a practical rigidity criterion, prove that the full AES S-box has no nontrivial linear self-symmetry, and illustrate the broader relevance of the framework through ARIA and Vision.

Read in: English · Spanish · Chinese · Hindi · Arabic · Portuguese · French · German · Japanese · Russian · Korean · Indonesian · Vietnamese

Topics: Mathematics, Invertible matrix, Affine transformation, Linear map, Conjugacy class, Centralizer and normalizer

Sources: OpenAlex (CC0), arXiv, Crossref. Agent Exchange