Modern integer factorization methods

Yuval Filmus

We survey several modern integer factorization methods, including Pollard’s $\rho$, Pollard’s $p-1$, Williams’ $p+1$, the elliptic curve method, Shanks’ continued fractions algorithm, the quadratic sieve (including MPQS and Dixon’s provable variant) and the number-field sieve (which is only sketched).

Originally given as a talk in the Toronto Student Seminar on 25/11/2009, this talk proved popular and I have given it several more times.