  This paper elaborates on a sieving technique that has first been applied in
2018 for improving bounds on deterministic integer factorization. We will
generalize the sieve in order to obtain a polynomial-time reduction from
integer factorization to a specific instance of the multiple-choice subset-sum
problem. As an application, we will improve upon special purpose factorization
algorithms for integers composed of divisors with small difference. In
particular, we will refine the runtime complexity of Fermat's factorization
algorithm by a large subexponential factor. Our first procedure is
deterministic, rigorous, easy to implement and has negligible space complexity.
Our second procedure is heuristically faster than the first, but has
non-negligible space complexity.
