Cryptography from Lattices

Cryptography inherently relies on mathematical problems that are
conjectured to be infeasible, e.g., factoring large integers.
However, most of the commonly used problems result in cryptosystems
that are too inefficient or inflexible for use in many environments.
Moreover, all of the commonly used problems behind today's public-key
cryptography can in principle be broken by quantum computers.

This talk will survey my efforts over the past decade to develop a new
mathematical foundation for cryptography, using geometric objects
called *lattices*. Compared to conventional cryptosystems,
lattice-based schemes offer a host of advantages: they are simple and
highly parallel, they can be proved secure under mild "worst-case"
intractability assumptions, and to date they remain unbroken by
quantum algorithms. However, due to the entirely different
mathematics of lattices, realizing even basic cryptographic notions,
and making them practical, has been a major challenge. The talk will
show that surprisingly, lattice-based cryptography can be
exceptionally flexible, robust, and efficient.
Chris Peikert is an Associate Professor in the School of Computer
Science at Georgia Tech. His research interests include cryptography,
computational complexity, and algorithms, especially in relation to
lattices, error-correcting codes, and number theory. He is the
recipient of a Sloan Fellowship, an NSF CAREER Award, a Google Faculty
Award, and multiple Best Paper and teaching awards.