Cryptography and cryptographic protocols have become a key element of information systems, protecting data and communications to ensure confidentiality, integrity and authenticity of data. While most symmetric key systems have relatively modest mathematical requirements, asymmetric or public key systems, as well as cryptographic protocols, have become increasingly mathematically sophisticated. Such systems rely for their security on the difficulty of specific mathematical problems such as integer factorization and the modular discrete logarithm problem. No rigorous mathematical proof of security has ever been given for any of these systems. The difficulty of these problems is usually established anecdotally through frequent and unsuccessful attempts by specialists to provide computationally efficient solutions to them. Indeed, several problems thought to be very difficult have recently been shown to be less intractable than previously believed. Furthermore, the possibility of quantum computing becoming practical would change this picture dramatically. If realized, most of the problems on which the security of public key cryptosystems rely drop from exponential complexity to polynomial, rendering currently deployed cryptographic systems useless. While the likelihood of this occurring in the short term is remote, this is an exciting area of research which may well lead to revolutionary advances in computation and secure information communication. This special meeting will attempt to make progress on these and other related problems.
The program will take place at the Fields Institute, which will mount an intensive program on Cryptography during the period June - December 2006. This program will engage and stimulate interaction between the cryptographic and mathematical communities. NSF funding will enable young U.S. researchers to participate in this program, and in doing so it will expose young researchers to a wide range of problems at the interface between mathematics and cryptographic applications. It will increase the degree of collaboration between cryptographers and theoreticians in attacking the important problems at the boundaries between the fields, and will impact on both cryptographic theory and practice.
