In 1976, Diffie and Hellman introduced the revolutionary concept of public-key cryptography, also called asymmetric cryptography. Today, asymmetric cryptography is routinely used to secure the Internet. The most famous and most widely used asymmetric cryptosystem is RSA, invented by Rivest, Shamir and Adleman almost thirty years ago.
Unfortunately, there are very few alternatives known, and most of them are also based on number theory. In this course, we will present the main cryptanalysis techniques in asymmetric cryptography, in particular lattice basis reduction. We will explain why security notions for asymmetric cryptography have evolved.