  Pollard's Rho is a method for solving the integer factorization problem. The
strategy searches for a suitable pair of elements belonging to a sequence of
natural numbers that given suitable conditions yields a nontrivial factor. In
translating the algorithm to a quantum model of computation, we found its
running time reduces to polynomial-time using a certain set of functions for
generating the sequence. We also arrived at a new result that characterizes the
availability of nontrivial factors in the sequence. The result has led us to
the realization that Pollard's Rho is a generalization of Shor's algorithm, a
fact easily seen in the light of the new result.
