一种生成具有相同代数性质的密钥相关S盒的新方法
A Novel Method to Generate Key-Dependent S-Boxes with Identical Algebraic Properties
AI总结：
本文提出一种基于对称群作用生成密钥相关动态克隆S盒的算法方案，保持双射、非线性、SAC和BIC等代数性质不变，并扩展了现有方法以同时作用于行列，显著增加克隆副本数量。
摘要：
S盒在任何密码系统中起着在密文和密钥之间产生混淆的关键作用，并且是许多分组密码中唯一的非线性组件。与静态S盒相比，动态S盒提高了系统的熵，从而对线性和差分攻击具有更好的抵抗力。文献[2]表明，虽然在密码系统中引入动态S盒足够安全，但它们不能保持非线性的不变性。本工作提供了一种算法方案，用于生成密钥相关的动态 $n\ imesimes n$ 克隆S盒，其具有与初始种子S盒相同的代数性质，即双射、非线性、严格雪崩准则（SAC）、输出比特独立准则（BIC）。该方法基于对称群 $S_n$ 和子群 $S_{2^n}$ 分别作用于S盒布尔函数（$GF(2^n)\ o GF(2)$）的列和行。证明了生成的克隆副本的双射、非线性、SAC和BIC的不变性。作为示例，提供了 $n=8$ 和 $n=4$ 的实例，并比较了克隆S盒与初始种子S盒的代数性质。所提出的方法是[3,4,5,6]的扩展，后者仅涉及 $S_8$ 对S盒布尔函数（$GF(2^8)\ o GF(2)$）列的群作用。对于 $n=4$，我们使用了由Carlisle Adams和Stafford Tavares[7]构造的初始 $4\ imesimes 4$ S盒来生成 $(4!)^2$ 个克隆副本。对于 $n=8$，可以看出[3,4,5,6]通过排列列可以构建的克隆副本数量为 $8!$。对于每种列排列，所提出的方法能够通过排列行生成 $8!$ 个克隆副本。
英文摘要：
The s-box plays the vital role of creating confusion between the ciphertext and secret key in any cryptosystem, and is the only nonlinear component in many block ciphers. Dynamic s-boxes, as compared to static, improve entropy of the system, hence leading to better resistance against linear and differential attacks. It was shown in [2] that while incorporating dynamic s-boxes in cryptosystems is sufficiently secure, they do not keep non-linearity invariant. This work provides an algorithmic scheme to generate key-dependent dynamic $n\times n$ clone s-boxes having the same algebraic properties namely bijection, nonlinearity, the strict avalanche criterion (SAC), the output bits independence criterion (BIC) as of the initial seed s-box. The method is based on group action of symmetric group $S_n$ and a subgroup $S_{2^n}$ respectively on columns and rows of Boolean functions ($GF(2^n)\to GF(2)$) of s-box. Invariance of the bijection, nonlinearity, SAC, and BIC for the generated clone copies is proved. As illustration, examples are provided for $n=8$ and $n=4$ along with comparison of the algebraic properties of the clone and initial seed s-box. The proposed method is an extension of [3,4,5,6] which involved group action of $S_8$ only on columns of Boolean functions ($GF(2^8)\to GF(2)$ ) of s-box. For $n=4$, we have used an initial $4\times 4$ s-box constructed by Carlisle Adams and Stafford Tavares [7] to generated $(4!)^2$ clone copies. For $n=8$, it can be seen [3,4,5,6] that the number of clone copies that can be constructed by permuting the columns is $8!$. For each column permutation, the proposed method enables to generate $8!$ clone copies by permuting the rows.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
