旋转对称布尔函数的线性结构和快速点

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-06-23 DOI:10.1007/s00200-022-00566-3

Lei Sun, Zexia Shi

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引用次数: 0

摘要

非零快点和线性结构的存在反映了布尔函数高阶导数的特性，这与许多密码差分攻击密切相关。旋转对称布尔函数（RSBFs）是对称函数的一个超类，在密码学中应用广泛。我们首先得到了具有 \(n-2\) 度的 n 变量 RSBFs 非零线性结构的一些存在性结果。此外，我们基于整数分割确定了具有度（n-3）和（n-4）的n变量RSBF的所有可能的快速点集。最后，我们研究了当 p 是奇素数时，p 变量和 2p 变量 RSBFs 的快速点的存在性。

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The linear structures and fast points of rotation symmetric Boolean functions

The existence of nonzero fast points and linear structures reflects the properties of Boolean function’s higher order derivatives, which is closely related to many cryptographic differential attacks. Rotation symmetric Boolean functions (RSBFs) is a super-class of symmetric functions, which are used widely in cryptography. We first obtain some existence results of nonzero linear structures of n-variable RSBFs with degree \(n-2\). Moreover, we determine all the possible sets of fast points of n-variable RSBFs with degrees \(n-3\) and \(n-4\) based on integer partition. Finally, we investigate the existence of fast points of p-variable and 2p-variable RSBFs when p is an odd prime.

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来源期刊

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.