One can also obtain a lower bound: there exists no algorithm which needs less than sous certaines restrictions naturelles on peut démontrer qu’il n’existe pas d’algorithme de multiplication des nombres à
chiffres avec le temps d’exécution inférieur à
bit-operations for the multiplication of two general
-bit numbers.
This is from the first page of the first chapter of Introduction to Modern Number Theory, by Yuri Manin and Alexi Panchishkin. And you can see this for yourself at Google Books.
