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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 bearXiv:0801.1416v3 fatcat:7vvehkcxmnferjdimsqdz2s2gi