We define a family of efficiently computable invariants for (n,m)-functions under EA-equivalence, and observe that, unlike the known invariants such as the differential spectrum, algebraic degree, and extended Walsh spectrum, in the case of quadratic APN functions over \(\mathbb {F}_{2^n}\) with n even, these invariants take on many different values for functions belonging to distinct equivalence classes. We show how the values of these invariants can be used constructively to implement a test for EA-equivalence of functions from \(\mathbb {F}_{2}^{n}\) to \(\mathbb {F}_{2}^{m}\); to the best of our knowledge, this is the first algorithm for deciding EA-equivalence without resorting to testing the equivalence of associated linear codes.

我们在 EA 等价下为 ( n , m ) 函数定义了一系列可有效计算的不变量，并观察到，与已知的不变量（例如微分谱、代数次数和扩展沃尔什谱）不同，在二次 APN 函数的情况下过\（\ mathbb {F} _ {2 ^ N} \）与ñ甚至，这些不变量取许多不同的值对属于不同的等价类的功能。我们展示了如何建设性地使用这些不变量的值来实现对从\(\mathbb {F}_{2}^{n}\)到\(\mathbb {F}_{ 2}^{米}\); 据我们所知，这是第一个无需测试相关线性代码的等效性即可确定 EA 等效性的算法。