Pseudorandom lattices for global optimization

On Pseudorandom Binary Lattices

Pseudorandom sequences and lattices

Pseudorandom Functions and Lattices

We give direct constructions of pseudorandom function (PRF) families based on conjectured hard lattice problems and learning problems. Our constructions are asymptotically efficient and highly parallelizable in a practical sense, i.e., they can be computed by simple, relatively small low-depth arithmetic or boolean circuits (e.g., in NC or even TC). In addition, they are the first low-depth PRF...

Constructions of Pseudorandom Binary Lattices

Three constructions for binary lattices with strong pseudorandom properties are given. These constructions are the two dimensional extensions and modifications of three of the most important one dimensional constructions. The upper estimates for the pseudorandom measures of the binary lattices constructed are based on the principle that character sums in two variables can be estimated by fixing...

A Large Family of Pseudorandom Binary Lattices

Recently P. Hubert, C. Mauduit and A. Sárközy introduced and studied the notion of pseudorandomness of binary lattices and gave a pseudorandom binary lattice. Later in other papers C. Mauduit and A. Sárközy constructed some large families of “good” binary lattices. In this paper a large family of pseudorandom binary lattices is presented by using the multiplicative inverse and the quadratic cha...