For almost 35 years, Sch{\"o}nhage-Strassen's algorithm has been the fastest
algorithm known for multiplying integers, with a time complexity O(n ×
log n × log log n) for multiplying n-bit inputs. In 2007, F{\"u}rer
proved that there exists K > 1 and an algorithm performing this operation in
O(n × log n × K log n). Recent work by Harvey, van der Hoeven,
and Lecerf showed that this complexity estimate can be improved in order to get
K = 8, and conjecturally K = 4. Using an alternative algorithm, which relies on
arithmetic modulo generalized Fermat primes, we obtain conjecturally the same
result K = 4 via a careful complexity analysis in the deterministic multitape
Turing model