An Algebraic Approach to Multilinear Maps for Cryptography (18w5118)

Arriving in Banff, Alberta Sunday, May 6 and departing Friday May 11, 2018

Organizers

Ted Chinburg (University of Pennsylvania)

(University of California, Irvine)

Dan Boneh (Stanford University)

Objectives

One of the main goals of this workshop is to bring cryptographers, number theorists and arithmetic geometers together to discuss problems of central importance to the future of electronic communication. Theoretical advances in arithmetic geometry over the last 15 years have opened the possibility of a revolution in the many parts of cryptography pertaining to multilinear maps. The rationale for this workshop is that by bringing together researchers from the more theoretical aspects of arithmetic geometry with cryptographers who are directly familiar with what is needed for a major advance, we will lay the ground for important new developments in both subjects.

The infrastructure of modern society depends on secure and efficient cryptography. Cryptographic methods in turn depend on increasingly sophisticated techniques in number theory and arithmetic geometry. Beginning with the RSA algorithm in the 1970's, there have been a succession of revolutions in cryptography driven by mathematical ideas. At the same time, cryptographers have observed that the existence of particular algebraic objects that have not yet been constructed would have powerful cryptographic applications.

The focus of the workshop will be on cryptographic multilinear maps. Over the last few years these maps have found numerous applications in cryptography enabling cryptographic systems that could not be previously constructed. One application of such maps is to allow many parties to generate a shared secret key. Other applications include "obfuscating" computer programs, to give a version that is functionally equivalent to the original program, and that is indistinguishable from a black-box implementation of the original program. Another application is certain advanced encryption schemes such as functional encryption and optimal broadcast encryption.

Finding groups that support an n-way multilinear map for large n, while ensuring that the required cryptographic problem is hard, is a central open problem in cryptography, and will be one of the primary topics for this workshop.

The workshop will include minicourses on cryptographic applications of multilinear maps, and on the arithmetic geometry of curves and surfaces. These minicourses will provide participants with the background needed to follow more advanced research talks later in the workshop. They will also be starting points for conversations among participants who will come to the workshop with very different backgrounds and areas of expertise. We expect this meeting to lead to new research directions in each of cryptography, arithmetic geometry and number theory.