论文标题
Chudnovsky标量复杂性的优化$^2 $乘法算法在有限字段中
Optimization of the scalar complexity of Chudnovsky$^2$ multiplication algorithms in finite fields
论文作者
论文摘要
我们为D.V.的原始乘法算法提出了几种构造。和G.V. Chudnovsky为了提高其标量复杂性。我们强调了一系列通用策略，这些通用策略是根据可参数的标准来构成标量复杂性的优化。例如，我们将此分析应用于类型的椭圆形Chudnovsky $^2 $乘法算法的小型扩展算法。作为一个案例研究，我们大大改善了Baum-Shokrollahi构造，以乘以$ \ Mathbb f_ {256}/\ Mathbb f_4 $。
We propose several constructions for the original multiplication algorithm of D.V. and G.V. Chudnovsky in order to improve its scalar complexity. We highlight the set of generic strategies who underlay the optimization of the scalar complexity, according to parameterizable criteria. As an example, we apply this analysis to the construction of type elliptic Chudnovsky$^2$ multiplication algorithms for small extensions. As a case study, we significantly improve the Baum-Shokrollahi construction for multiplication in $\mathbb F_{256}/\mathbb F_4$.
