Quantum algorithms and Learning With Errors- based Cryptography:

Post quantum cryptography is meant to replace today's standards like RSA and Elliptic Curve Cryptography (ECC), since these standards are threathened by quantum algorithms. The most researched post-quantum candidates are based on lattice problems, and in particular the Learning with Errors (LWE) problem. It is assumed that there exists no quantum algorithm that solves this problem efficiently. However, in a particular setting and under some strong hypothesis, it is very easy to solve LWE using a generalization of the Bernstein-Vazirani quantum algorithm. We will take a look at possible quantum cryptanalysis on LWE-based cryptographic applications.

Distance Labels and Tree Skeletons:

To answer distance queries on a fix known graph, it is interesting to do precalculation in order to reduce query time. A methode is to use Hub Labeling. Hub Labeling works well on road transport network. We will take a look at this methode and introduce the notion of Skeleton Dimension which give an insight on why it works well on road network.