We give upper bounds for the solving degree and the last fall degree of the polynomial system associated to the HFE (Hidden Field Equations) cryptosystem. Our bounds improve the known bounds for this type of systems. We also present new results on the connection between the solving degree and the last fall degree and prove that, in some cases, the solving degree is independent of coordinate changes.

中文翻译：

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为 HFE 系统计算 Gröbner 基的成本有更强的界限

我们给出了与 HFE（隐藏场方程）密码系统相关的多项式系统的求解度和上次下降度的上限。我们的边界改进了此类系统的已知边界。我们还提出了求解度与上次下降度之间关系的新结果，并证明在某些情况下，求解度与坐标变化无关。