On Chudnovsky-Based Arithmetic Algorithms in Finite Fields

TL;DR

This paper introduces new Chudnovsky-based algorithms for finite field arithmetic that are optimized for hardware, enabling efficient, parallelizable multiplication and exponentiation with fewer bilinear multiplications.

Contribution

It presents a novel construction of the Chudnovsky-Chudnovsky algorithm, improving finite field operations for hardware implementation and parallel processing.

Findings

Efficient algorithms for finite field multiplication and exponentiation

Reduced number of bilinear multiplications

Example implementation in ${f F}_{16^{13}}$

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 ${\mathbb F}_{16^{13}}$.