Fast Integer Multiplication using Modular Arithmetic release_7vvehkcxmnferjdimsqdz2s2gi

by Anindya De, Piyush P Kurur, Chandan Saha, Ramprasad Saptharishi

Released as a article .

2008  

Abstract

We give an O(N· N· 2^O(^*N)) algorithm for multiplying two N-bit integers that improves the O(N· N· N) algorithm by Schönhage-Strassen. Both these algorithms use modular arithmetic. Recently, Fürer gave an O(N· N· 2^O(^*N)) algorithm which however uses arithmetic over complex numbers as opposed to modular arithmetic. In this paper, we use multivariate polynomial multiplication along with ideas from Fürer's algorithm to achieve this improvement in the modular setting. Our algorithm can also be viewed as a p-adic version of Fürer's algorithm. Thus, we show that the two seemingly different approaches to integer multiplication, modular and complex arithmetic, are similar.
In text/plain format

Archived Files and Locations

application/pdf  188.8 kB
file_sn2u6fglezcgle45t22kps7ig4
archive.org (archive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2008-09-19
Version   v3
Language   en ?
arXiv  0801.1416v3
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 991bee6f-cf16-4943-8f5c-7a1bcd197543
API URL: JSON