  Two prominent methods for integer factorization are those based on general
integer sieve and elliptic curve. The general integer sieve method can be
specialized to quadratic integer sieve method. In this paper, a probability
analysis for the success of these methods is described, under some reasonable
conditions. The estimates presented are specialized for the elliptic curve
factorization. These methods are compared through heuristic estimates. It is
shown that the elliptic curve method is a probabilistic polynomial time
algorithm under the assumption of uniform probability distribution for the
arising group orders and clearly more likely to succeed, faster asymptotically.
