Cryptography is at the heart of Computer and Network Security solutions ubiquitously deployed over the Internet. This course will
introduce students to a cryptographic schemes built out of conjectured problems in lattice theory. These schemes have received
a lot of attention in recent years because of their conjectured resistance to quantum attacks and for their ability to achieve advanced homomorphic properties not enjoyed by classical schemes.
The course will introduce students to lattice theory, and its early application as a cryptanalysis tool (i.e. a tool to break other cryptographic schemes). We will then study conjectured hard problems in lattice theory, and their use in the construction of cryptographic schemes. We will then cover some of the most advanced cryptographic constructions and survey open problems and research directions in the field.
List of Topics
Introduction to Lattices, Conjectured Hard Problems on Lattices
The LLL algorithm and its application to cryptanalysis
Early construction of Cryptographic Schemes based on Lattice Problems
Learning with Errors and Short Integer Solution Problems and their relationship to lattice problems.
Basic Cryptographic Constructions: Collision-Resistant Hashing and Encryption
Lattices with Trapdoors and applications.
Learning with Rounding and construction of pseudo-random functions.
Fully Homomorphic Encryption
Attribute Based Encryption
Open Problems and Research Direction
Regular homework and final exam.