Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
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Section: New Results

Fast arithmetic for faster integer multiplication

Participants : Svyatoslav Covanov [contact] , Emmanuel Thomé.

The paper [20] describes an algorithm for the multiplication of two n-bit integers. It achieves the best asymptotic complexity bound O(nlogn·4log*n) under a hypothesis on the distribution of generalized Fermat primes of the form r2λ+1. This hypothesis states that there always exists a sufficiently small interval in which we can find such a prime. Experimental results give evidence in favor of this assumption. A journal submission is planned shortly.