Faster Integer Multiplication Using Preprocessing

TL;DR

This paper introduces a new number theoretic transform that accelerates integer multiplication beyond traditional FFT-based methods by leveraging preprocessing, aiming for near-linear time complexity.

Contribution

It presents a novel NTT and a multiplication algorithm that significantly improves speed using preprocessing, approaching O(n) time complexity.

Findings

Faster integer multiplication algorithm using NTT

Achieves upper bounds of n log n / (log log n / log log log n)

Explores potential for O(n) time multiplication with preprocessing

Abstract

A New Number Theoretic Transform(NTT), which is a form of FFT, is introduced, that is faster than FFTs. Also, a multiplication algorithm is introduced that uses this to perform integer multiplication faster than O(n log n). It uses preprocessing to achieve an upper bounds of (n log n/(log log n/ log log log n). Also, we explore the possibility of O(n) time multiplication via NTTs that require only O(n) operations, using preprocessing.