# Arithmetic in Finite Fields Based on the Chudnovsky Multiplication Algorithm

### Abstract

Thanks to a new construction of the so-called Chudnovsky-Chudnovsky multiplication algorithm, we design efficient algorithms for both the exponentiation and the multiplication in finite fields. They are tailored to hardware implementation and they allow computations to be parallelized while maintaining a low number of bilinear multiplications. We give an example with the finite field $\mathbb{F}_{16}^{13}$.

Type
Publication
In Mathematics of Computation (Math. Comp.), AMS
Date