一类可逆移位不变函数的构造
A Construction of a Class of Invertible Shift-Invariant Functions
摘要: 在面向安全多方计算、全同态加密与零知识证明等的对称密码构件的设计中，人们需在大素数有限域上构造乘法复杂度低且可逆的非线性层。移位不变函数因其良好的非线性结构与实现优势而被广泛采用，Lai-Massey构造是其中具有代表性的一类。本文基于广义的Lai-Massey构造，提出了更一般的可逆移位不变函数的构造方法，为面向算术的非线性层设计提供了更丰富的可逆向量值函数。
Abstract: In the design of symmetric cryptographic components for secure multi-party computation, fully homomorphic encryption, and zero-knowledge proofs, one needs to construct nonlinear layers over large prime finite fields that are both invertible and of low multiplicative complexity. Shift invariant functions are widely adopted due to their favorable nonlinear structure and implementation advantages, with the Lai-Massey construction being a representative example. Building on generalized Lai-Massey constructions, this paper proposes a more general method for constructing invertible shift-invariant functions, providing a richer collection of invertible vector valued functions for arithmetization-oriented nonlinear layer design.
文章引用：丁肇鹏, 石景琦. 一类可逆移位不变函数的构造[J]. 理论数学, 2026, 16(2): 241-247. https://doi.org/10.12677/pm.2026.162054

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