Fast Hermite interpolation and evaluation over finite fields of characteristic two

TL;DR

This paper introduces efficient algorithms for Hermite interpolation and evaluation over characteristic two finite fields, leveraging simple, multiplication-free reductions to standard problems, enhancing encoding and decoding of multiplicity codes.

Contribution

The paper proposes novel, low-complexity algorithms for Hermite interpolation and evaluation over characteristic two fields, simplifying implementation and improving performance.

Findings

Reduces Hermite problems to standard multipoint interpolation/evaluation

Algorithms are multiplication-free and easy to implement

Suitable for encoding/decoding in multiplicity codes

Abstract

This paper presents new fast algorithms for Hermite interpolation and evaluation over finite fields of characteristic two. The algorithms reduce the Hermite problems to instances of the standard multipoint interpolation and evaluation problems, which are then solved by existing fast algorithms. The reductions are simple to implement and free of multiplications, allowing low overall multiplicative complexities to be obtained. The algorithms are suitable for use in encoding and decoding algorithms for multiplicity codes.