Abstract

In our paper we study the effect of changing the commutative group operation used in Feistel and Lai-Massey symmetric structures into a quasigroup operation. We prove that if the quasigroup operation is isotopic with a group G,$\mathbb{G},$$\mathbb{G},$ the complexity of mounting a differential attack against our generalization of the Feistel structure is the same as attacking the unkeyed version of the general Feistel iteration based on G.$\mathbb{G}.$$\mathbb{G}.$ Also, when G$\mathbb{G}$$\mathbb{G}$ is non-commutative, we show that both versions of the Feistel structure are equivalent from a differential point of view. For the Lai-Massey structure, we introduce four non-commutative versions, we argue for the necessity of working over a group and we provide some necessary conditions for the differential equivalency of the four notions.

摘要

在我们的论文中，我们研究了将 Feistel 和 Lai-Massey 对称结构中使用的交换群运算更改为拟群运算的效果。我们证明如果拟群运算与群是同位素格,$\mathbb{G},$$\mathbb{G},$针对我们的 Feistel 结构的泛化进行差分攻击的复杂性与攻击基于的一般 Feistel 迭代的无密钥版本相同格。$\mathbb{G}。$$\mathbb{G}.$另外，当G$\mathbb{G}$$\mathbb{G}$是非交换的，我们证明从微分的角度来看，两个版本的 Feistel 结构是等价的。对于Lai-Massey结构，我们引入了四个非交换版本，我们论证了群上工作的必要性，并为这四个概念的微分等价提供了一些必要条件。