Differentially 4-uniform involutions on ${\mathbb{F}}_{2^{2k}}$ play important roles in the design of substitution boxes (S-boxes). Despite the active researches on differentially 4-uniform permutation, there is not so much research on differentially 4-uniform involutions, especially over the field ${\mathbb{F}}_{2^n}$ with $4|n$. In this paper, we introduce a new approach to construct differentially 4-uniform involutions by using Carlitz form. With this approach, we explicitly construct two new classes of differentially 4-uniform involutions over ${\mathbb{F}}_{2^n}$ with $4|n$. We also show that our constructions have high nonlinearity and optimal algebraic degree. With the help of computer, we show that our constructions are CCZ-inequivalent to the known differentially 4-uniform involutions over ${\mathbb{F}}_{2^8}$.

上的微分 4-一致对合 ${\mathbb{F}}_{2^{2克}}$在替代盒（S-box）的设计中发挥重要作用。尽管对微分 4-一致置换的研究很活跃，但对微分 4-一致对合的研究并不多，尤其是在该领域${\mathbb{F}}_{2^n}$ 和 $4|n$. 在本文中，我们介绍了一种使用 Carlitz 形式构造差分 4-均匀对合的新方法。使用这种方法，我们明确地构建了两个新类别的差分 4-均匀对合${\mathbb{F}}_{2^n}$ 和 $4|n$. 我们还表明，我们的构造具有高非线性和最优代数度。在计算机的帮助下，我们表明我们的构造是 CCZ 不等价于已知的差分 4-均匀对合${\mathbb{F}}_{2^8}$.