Knowing interval of discrete log for elliptic curve Are there any special attacks I can apply if I know the upper bound for $n$ (meaning $0 \le n \le \text{Upper Bound}$) in the equation $Q = nP$, where $P$ is the base point and I'm trying to solve for $n$.
As mentioned in your answer to your other similar question, Pollard's $\lambda$ algorithm is still a good choice. If your search interval is $[a,b]$, then it may find the result in $O(\sqrt{b-a})$ time using very small storage.

That "may" in the previous paragraph illustrates the trade-off you must consider. Baby step, giant step requires more memory, but it is deterministic and thus guaranteed to finish in $O(\sqrt{b-a})$ time. Pollard's $\lambda$ can be parallelized which could speed up the run time (depending on your resources), but as it's probabilistic, the run time is not guaranteed at all.