The Sch\"onhage-Strassen algorithm (SSA) is the de-facto standard for multiplication of large integers. For N-bit numbers it has a time bound of O(N⋅logN⋅loglogN). De, Kurur, Saha and Saptharishi (DKSS) presented an asymptotically faster algorithm with a better time bound of N⋅logN⋅2O(log∗N). In this diploma thesis, results of an implementation of DKSS multiplication are presented: run-time is about 30 times larger than SSA, while memory requirements are about 3.75 times higher than SSA. A possible crossover point is estimated to be out of reach even if we utilized the whole universe for computer memory.
@article{arxiv.1503.04955,
title = {Fast Multiplication of Large Integers: Implementation and Analysis of the DKSS Algorithm},
author = {Christoph Lüders},
journal= {arXiv preprint arXiv:1503.04955},
year = {2015}
}