Efficient dot product over word-size finite fields

TL;DR

This paper explores various implementation techniques to efficiently compute the dot product of vectors over word-size finite fields, focusing on practical performance improvements.

Contribution

It systematically compares multiple methods like floating point, discrete logs, tabulations, and Montgomery reduction for finite field dot product computation.

Findings

Certain techniques outperform others in specific scenarios

Tabulation and Montgomery reduction show promising efficiency

Practical guidelines for implementing finite field dot products

Abstract

We want to achieve efficiency for the exact computation of the dot product of two vectors over word-size finite fields. We therefore compare the practical behaviors of a wide range of implementation techniques using different representations. The techniques used include oating point representations, discrete logarithms, tabulations, Montgomery reduction, delayed modulus.