# Closest vector problem for orthogonal lattices

Let's say I have a reduced basis $\mathcal{B}$ for an orthogonal lattice in $\mathbb{R}^n$, then the Shortest Vector Problem is trivial (the shortest vector in the basis). According to my intuition, the Closest Vector Problem on this lattice should also be easy. Is this the case, or am I missing something fundamental? I couldn't find a source, but I wasn't exactly sure what to search for.

• en.wikipedia.org/wiki/Lattice_problem#Relationship_with_SVP Commented Nov 26, 2012 at 10:45
• @TenaliRaman That is the opposite direction. I know that in general I can't expect it to be true, but this is a specific lattice. Commented Nov 26, 2012 at 12:15
• I thought the second paragraph there was what you asked for (Though, there is a typo in that line which needs to be fixed)? Commented Nov 26, 2012 at 16:27
• @TenaliRaman The wording is confusing, but it seems to take a lattice basis, and uses CVP to compute the shortest vector in the lattice. This is not what I am after, since I already know how to find the shortest vector. Commented Nov 28, 2012 at 15:26
• ah yes you are right. Apologies, I was truly confused by the wording given there. Sorry about that. Commented Nov 28, 2012 at 15:34