Differential uniformity of permutation polynomials has been studied intensively in recent years due to the differential cryptanalysis of S-boxes. The boomerang attack is a variant of differential cryptanalysis which combines two differentials for the upper part and the lower part of the block cipher. The boomerang uniformity measures the resistance of block ciphers to the boomerang attack. In this paper, by using the resultant elimination method, we study the boomerang uniformity of normalized permutation polynomials of the low degree over finite fields. As a result, we determine the boomerang uniformity of all normalized permutation polynomials of degree up to six over the finite field $${\mathbb {F}}_{q}$$ F q .

中文翻译：

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低次归一化置换多项式的回旋镖均匀性

由于 S 盒的差分密码分析，近年来对置换多项式的差分均匀性进行了深入研究。回旋镖攻击是差分密码分析的一种变体，它结合了分组密码上部和下部的两个差分。回旋镖一致性衡量分组密码对回旋镖攻击的抵抗力。在本文中，我们利用合成消除法研究了有限域上低次归一化置换多项式的回旋镖均匀性。因此，我们确定了有限域 $${\mathbb {F}}_{q}$$ F q 上所有阶数为 6 的归一化置换多项式的回旋镖均匀性。