Algorithms to factor integer numbers

There are several known algorithms that have subexponential estimated running time, to mention just a few:

• Continued fraction algorithm.
• Quadratic sieve algorithm.
• Class Group method.
• Elliptic curve algorithm.
• Number field sieve.
• Dixon's random squares algorithm.
• Valle's two-thirds algorithm.
• Seysen's class group algorithm.

References

A.K. Lenstra, H.W. Lenstra Jr. Algorithms in Number Theory. J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity Elsevier, pp. 673-715, 1990.