Smoothing Codes and Lattices: Systematic Study and New Bounds. (arXiv:2205.10552v2 [cs.IT] UPDATED)

In this article we revisit smoothing bounds in parallel between lattices
$and$ codes. Initially introduced by Micciancio and Regev, these bounds were
instantiated with Gaussian distributions and were crucial for arguing the
security of many lattice-based cryptosystems. Unencumbered by direct
application concerns, we provide a systematic study of how these bounds are
obtained for both lattices $and$ codes, transferring techniques between both
areas. We also consider multiple choices of spherically symmetric noise
distribution.

We found that the best strategy for …

study