We give an O(N · log N ̇ 2O (log* N )algorithm for multiplying two N-bit integers that improves the O(N · log N · log log N) algorithm by Schönhage-Strassen |10|. Both these algorithms use modular arithmetic. Recently, Fürer |2| gave an O(N · log N ̇ 2O (log* 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 fron 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. Copyright 2008 ACM.