Lattices as a constructive and destructive cryptographic tool. The project is driven by the great number of potential applications of deep mathematical and algorithmic methods to different areas of modern cryptography. These areas provide a solid platform for more applied fields such as Computer and Information Security and E-commerce. It will lead to commercialisation and everyday-life improvements.
Elliptic curves: number theoretic and cryptographic aspects. Smart information use is of fundamental nature and has a great number of applications. First-generation security solutions are unable to support the modern requirements and new security infrastructures are emerging that must be carefully, but rapidly, defined. This urgently needs new mathematical tools, which is the main goal of this project.