Given an LLL-basis $B$ of dimension $n= hk$ we accelerate slide-reduction with blocksize $k$ to run under a reasonable assjmption in \
$\frac1{6} \, n^2 h \,\log_{1+\varepsilon} \, \alpha $ \
local SVP-computations in dimension $k$, where $\alpha \ge \frac 43$
measures the quality of the ... more >>>

A family of permutations in $S_n$ is $k$-wise independent if a uniform permutation chosen from the family maps any distinct $k$ elements to any distinct $k$ elements equally likely. Efficient constructions of $k$-wise independent permutations are known for $k=2$ and $k=3$, but are unknown for $k \ge 4$. In fact, ... more >>>

We consider a system of linear constraints over any finite Abelian group $G$ of the following form: $\ell_i(x_1,\ldots,x_n) \equiv \ell_{i,1}x_1+\cdots+\ell_{i,n}x_n \in A_i$ for $i=1,\ldots,t$ and each $A_i \subset G$, $\ell_{i,j}$ is an element of $G$ and $x_i$'s are Boolean variables. Our main result shows that the subset of the Boolean ... more >>>