They're probably unique, but the search space is so large you can't be sure that the specific section you have is the section you're checking for from the targe

They're probably unique, but the search space is so large you can't be sure that the specific section you have is the section you're checking for from the target. There's only the 4 base pairs in your DNA, so for any given length of base pairs 4^n combinations that are possible to exist. A complete human genome is 3.2 billion base pairs long. So yeah, it's definitely a length vs information density problem. Though those numbers may seem very very large, they get cut down to size very very quickly. Across all human's, there's very little variation in nearly all of our genome, something like 99.6% of those 3.2b genes are identical between all humans, which leaves 0.4% (around 12m) base pairs of DNA that make you you out of all other humans. We have identified (or at least think we have) some specific regions of those 12m pairs that control certain things, that's what the field of genetics has been up to with things like the Human Genome Project, so, plausibly, if they caught an environmental dna sample that was long enough to identify _which_ gene site they had, and they knew (or could at least guess) what value your genes would have at that site, yeah, they could probably tell whether it was you that was nearby, or at least someone related to you!