Section: New Results

Fast Integer Multiplication Using Generalized Fermat Primes

Participants : Svyatoslav Covanov, Emmanuel Thomé [contact] .

In [5] we described an algorithm for the multiplication of two $n$-bit integers. It achieves the best asymptotic complexity bound $O(nlogn·4^{{log}^{*}n})$ under a hypothesis on the distribution of generalized Fermat primes of the form $r^{2^{\lambda }}+1$. This hypothesis states that there always exists a sufficiently small interval in which we can find such a prime. Experimental results support this assumption. This article was submitted to Mathematics of Computation and was completely rewritten in late 2017-early 2018. It is now accepted for final publication.