Almost perfect nonlinear (APN) and almost bent (AB) functions are integral components of modern block ciphers and play a fundamental role in symmetric cryptography. In this paper, we describe a procedure for searching for quadratic APN functions with coefficients in ${\mathbb{F}}_2$ over the finite field ${\mathbb{F}}_{2^n}$ and apply this procedure to classify all such functions over ${\mathbb{F}}_{2^n}$ with $n\le 9$. We discover two new APN functions (which are also AB) over ${\mathbb{F}}_{2^9}$ that are CCZ-inequivalent to any known APN function over this field. We also verify that there are no quadratic APN functions with coefficients in ${\mathbb{F}}_2$ over ${\mathbb{F}}_{2^n}$ with $6\le n\le 8$ other than the currently known ones.

几乎完美的非线性（APN）和几乎弯曲（AB）函数是现代分组密码的组成部分，在对称密码学中起着基本作用。在本文中，我们描述了一种搜索系数为的二次APN函数的过程。${\mathbb{F}}_2$ 在有限域上 ${\mathbb{F}}_{2^{ñ}}$ 并应用此过程对所有此类功能进行分类 ${\mathbb{F}}_{2^{ñ}}$ 与 $ñ\le 9$。我们发现了两个新的APN功能（也都是AB）${\mathbb{F}}_{2^9}$CCZ等效于此字段上任何已知的APN函数。我们还验证了不存在系数为的二次APN函数${\mathbb{F}}_2$ 过度 ${\mathbb{F}}_{2^{ñ}}$ 与 $6\le ñ\le 8$ 除了目前已知的以外。