Lattices have received considerable attention as a potential source of computational hardness to be used in cryptography, after a breakthrough result of Ajtai (STOC 1996) connecting the average-case and worst-case complexity of various lattice problems. The purpose of this paper is twofold. On the expository side, we present a rigorous ... more >>>

The generalized knapsack problem is the following: given $m$ random
elements $a_1,\ldots,a_m\in R$ for some ring $R$, and a target $t\in
R$, find elements $z_1,\ldots,z_m\in D$ such that $\sum{a_iz_i}=t$
where $D$ is some given subset of $R$. In (Micciancio, FOCS 2002),
it was proved that for appropriate choices of $R$ ... more >>>