All of the fast algorithms that I have seen which factor integers work by searching for smooth numbers. Are there any fast algorithms for factoring integers that don't work by searching for smooth numbers? Is there any reason to believe that it is possible to construct fast algorithms for factoring integers that don't work by searching for smooth numbers?



Are there any fast algorithms for factoring integers that don't work by searching for smooth numbers?
This paper explains why smooth numbers play a key role in almost every modern integer factorization algorithm. Maybe it lists the exceptions, but I couldn't find them.


<http://www.math.dartmouth.edu/~carlp/PDF/paper104.pdf>‎


