Asymptotically fast factorization of integers

The paper describes a "probabilistic algorithm" for finding a factor of any large composite integer n (the required input is the integer n together with an auxiliary sequence of random numbers). It is proved that the expected number of operations which will be required is O(exp{ 83Qn n In In n)l/2)) for some constant f > 0. Asymptotically, this algorithm is much faster than any previously analyzed algorithm for factoring integers; earlier algorithms have all required O(na) operations where a > 1/5.