On the Scalar Complexity of Chudnovsky\(^2\) Multiplication Algorithm in Finite Fields

We propose a new construction for the multiplication algorithm of D.V. and G.V. Chudnovsky in order to improve scalar algebraic complexity. In particular, we improve the Baum-Shokrollahi construction for multiplication in \(\mathbb F_{256}/\mathbb F_4\) based on the elliptic Fermat curve \(x^3+y^3=1\).