We exhibit a hierarchy of polynomial time algorithms solving approximate variants
of the closest vector problem (CVP). Our first contribution is a heuristic
algorithm achieving the same distance tradeoff as
HSVPalgorithms, namely
for a random
lattice
of
rank
.
Compared to the so-called Kannan’s embedding technique, our algorithm
allows the use of precomputations and can be used for efficient batch
CVP
instances. This implies that some attacks on lattice-based signatures lead
to very cheap forgeries, after a precomputation. Our second contribution is
a proven reduction from approximating the closest vector with a factor
to the shortest vector problem (SVP) in dimension
.