“…To rule out such algorithms, we typically rely on a fine-grained complexity-theoretic hypothesissuch as the Strong Exponential Time Hypothesis (SETH, see Section 2.3) or the Exponential Time Hypothesis (ETH). To that end, Bennett, Golovnev, and Stephens-Davidowitz recently showed quantitative hardness results for the Closest Vector Problem in p norms (CVP p ) [BGS17], which is a close relative of SVP p that is known to be at least as hard (so that this was a necessary first step towards proving similar results for SVP p ). In particular, assuming SETH, [BGS17] showed that there is no 2 (1−ε)n -time algorithm for CVP p or SVP ∞ for any ε > 0 and "almost all" 1 ≤ p ≤ ∞ (not including p = 2).…”