Optimization of the scalar complexity of Chudnovsky$^2$ multiplication algorithms in finite fields

Stéphane Ballet (1) , Alexis Bonnecaze (2) , Thanh-Hung Dang

1 IML - Institut de mathématiques de Luminy
2 I2M - Institut de Mathématiques de Marseille

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 $\mathbb F_{256}/\mathbb F_4$.

Domaines: Géométrie algébrique [math.AG]

Stéphane Ballet, Alexis Bonnecaze, Thanh-Hung Dang. Optimization of the scalar complexity of Chudnovsky$^2$ multiplication algorithms in finite fields. Cryptography and Communications–Discrete Structures, Boolean Functions, and Sequences, 2021, From Mathematics to Embedded Devices, 13 (4), pp.495-517. ⟨hal-02906403⟩