New quantum attack on lattices (or Shor strikes again)? Lior Eldar and Peter W. Shor published a paper on arXiv.org in which they present a new quantum algorithm against a variant of BDD. They claim that their new algorithm can efficiently solve the following problem:


  Given a lattice $L$, a vector $v$, and numbers $b = {\lambda}_1(L)/n^{17}$, $a = {\lambda}_1(L)/n^{13}$ decide if $v$'s distance from $L$ is in the range $[a/2, a]$ or at most $b$, where ${\lambda}_1(L)$ is the length of $L$'s shortest non-zero vector


Moreover they state that 


  improving these parameters to $a = b = {\lambda}_1(L)/\sqrt{n}$ would invalidate one of the security assumptions of the Learning-with-Errors (LWE) cryptosystem against quantum attacks.


Now, while I assume the authors refer here to Regev's original proposal, nowadays, there exists a zoo of LWE-type assumptions, used in lattice-based crypto. These assumptions mainly differ in the choice of parameters / used distributions. 

My question is, does anyone have an idea how many of these or which class of LWE-type assumptions are broken by the proposed algorithm?
As mentioned in the comments, there is a serious flaw in the paper, and it has been withdrawn: see https://groups.google.com/forum/#!msg/cryptanalytic-algorithms/WNMuTfJuSRc/OtQMLRXgBwAJ and part (3) of http://www.scottaaronson.com/blog/?p=2996