Integer Factoring via Lattice Reduction?
I am not an expert in lattice problems, but I do know the exact-case problem, Shortest Vector Problem (SVP), is NP-hard. In this paper, Schnorr appears to reduce integer factorization to some form of the approximation version of Closest Vector Problem ($\gamma$-CVP), where CVP is a generalization of SVP. However, I do not believe there are known polynomial time algorithms for this.

Some known facts about $\gamma$-CVP:

Arora, et al (PDF), show that approximating the closest vector within any constant is NP-hard. 

Also, they show that, for $\epsilon > 0$, if you can approximate the closest vector within a factor of $2^{\log^{\frac{1}{2} - \epsilon}{n}}$ in polynomial time, then any problem in NP can be solved in quasi-polynomial time.

Dinur, et al (ACM Citation), later strengthened the inapproximability result to:

For $\epsilon > 0$, approximately finding the closest vector within a factor $n^{\frac{\epsilon}{\log\log{n}}}$ is NP-hard.

Although I'm unfamiliar with Schnorr's work, what we know of lattice problems would lead me to believe that this is not intended to lead to a polynomial-time algorithm directly. Rather, Schnorr spends some deal of time talking about actual implementations (e.g. running this program on such-and-such computer takes approximately so many weeks/months/years/eons).

P.S. As Suresh points out, it appears to be an effort to get "quick enough" or "quicker" run times for integer factorization, despite the complexity.

P.P.S. And if I can make a further conjecture: Given that Schnorr's paper pre-dates the work on hardness of approximating lattice problems, it's likely that there was some original hope that it might have led to a polynomial-time algorithm for integer factorization. In light of Arora et al and Dinur et al, however, it's clear that there's not a solution (or at least, a straightforward solution) along that route, however.