标题： 八变量中数以百万计的非等价二次APN函数 显示英文标题

标题： Millions of inequivalent quadratic APN functions in eight variables

摘要： 目前已知的偶数维几乎完美非线性（APN）置换唯一例子是通过将CCZ等价应用于特定二次APN函数得到的。 受此结果的启发，最近有许多尝试构造新的二次APN函数。 目前，已知维度为8的32,892个二次APN函数，并有两个最近的猜想讨论了它们的可能总数。 第一个由Y. Yu和L. Perrin（Cryptogr. Commun. 14(6): 1359-1369, 2022）提出，认为这样的函数超过50,000个。 第二个由A. Polujan和A. Pott（Proc. 7th Int. Workshop on Boolean Functions and Their Applications, 2022）提出，认为它们的数量超过了非等价二次（8,4）-弯函数的数量，即92,515个。 我们计算构造了3,775,599个非等价的维度为8的二次APN函数，并估计总数约为600万。 显示英文摘要

摘要： The only known example of an almost perfect nonlinear (APN) permutation in even dimension was obtained by applying CCZ-equivalence to a specific quadratic APN function. Motivated by this result, there have been numerous recent attempts to construct new quadratic APN functions. Currently, 32,892 quadratic APN functions in dimension 8 are known and two recent conjectures address their possible total number. The first, proposed by Y. Yu and L. Perrin (Cryptogr. Commun. 14(6): 1359-1369, 2022), suggests that there are more than 50,000 such functions. The second, by A. Polujan and A. Pott (Proc. 7th Int. Workshop on Boolean Functions and Their Applications, 2022), argues that their number exceeds that of inequivalent quadratic (8,4)-bent functions, which is 92,515. We computationally construct 3,775,599 inequivalent quadratic APN functions in dimension 8 and estimate the total number to be about 6 million.