Multiplication of polynomials over the binary field

TL;DR

This paper presents a fast algorithm for multiplying polynomials over the binary field using additive Fourier Transform, achieving a bit complexity of O(n(log n)(log log n)^2).

Contribution

It introduces a novel multiplication algorithm over the binary field with improved complexity using additive Fourier Transform techniques.

Findings

Achieves a bit complexity of O(n(log n)(log log n)^2)

Provides a new approach to polynomial multiplication over binary fields

Enhances efficiency of polynomial operations in binary field applications

Abstract

Additive Fourier Transform is sdudied. A fast multiplication algorithm for polynomials over the binary field is given. The bit complexity of the algorithm is $O(n(log n)(\log\log n)^2)$.