Our new DCS faculty member Vinod Vaikuntanathan will be teaching the
following grad course this Fall. It should be of interest to people
who want to learn about cryptography and/or the combinatorics of
lattices.

COURSE NUMBER: CSC 2414F (Fall 2011)
** NEW TIME: Tuesday 3-5 (room BA B025) **

COURSE TITLE: Topics in Applied Discrete Math: Lattices in Computer
Science

Course Description:

Integer lattices are powerful mathematical objects that have found
applications in many diverse facets of
computer science, most notably in the areas of cryptography and
combinatorial optimization. This course
gives an introduction to the theory of integer lattices -- their
algorithms and applications to
combinatorial optimization, their recent use in cryptography culminating
in the first construction of a
fully homomorphic encryption scheme, and the fascinating complexity
landscape associated with lattice problems.

This course will touch several related areas and applications:

• Algorithms and Combinatorial Optimization (1/4): The asymptotically
fastest Integer Programming algorithm
known to date is based on lattices. We will study lattice algorithms and
their applications to combinatorial
optimization.

• Cryptography (3/4): Lattices have proven themselves to be a
double-edged sword in cryptography.
While they
were first used to break cryptosystems, they have more recently been
instrumental in designing a wide range
of secure cryptographic primitives, including public key encryption,
digital signatures, encryption
resistant to key leakage attacks, identity based encryption, and most
notably, the first fully homomorphic
encryption scheme.

Prerequisites: We will assume knowledge of basic math (linear algebra
and probability) and introductory
level algorithms (analysis of algorithms, polynomial time and
NP-hardness). We will NOT assume any prior
knowledge of cryptography or advanced complexity theory.
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