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

Abstract : 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 $\mathbb F_{256}/\mathbb F_4$.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-02906403
Contributor : Alexis Bonnecaze <>
Submitted on : Friday, July 24, 2020 - 4:46:32 PM
Last modification on : Saturday, July 25, 2020 - 3:42:13 AM

### Identifiers

• HAL Id : hal-02906403, version 1
• ARXIV : 2007.08203

### Citation

Stéphane Ballet, Alexis Bonnecaze, Thanh-Hung Dang. Optimization of the scalar complexity of Chudnovsky$^2$ multiplication algorithms in finite fields. 2020. ⟨hal-02906403⟩

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