## Conference on The Mathematics of Public-Key Cryptography

#### The following is a brief report on the conference *The Mathematics of
Public-Key Cryptography*, which was held at the Fields Institute from June
12 to June 17, 1999.

The lectures at this conference primarily dealt with implementation issues,
and also security issues which pertain to a certain facet of Information Security
commonly referred to as Public-Key Cryptography. The security provided by
these systems relies on the computational difficulty of certain mathematical
problems, such as integer factorization, and the computation of discrete logarithms
in finite abelian groups.

The talks given at this conference were at the highest scientific level,
and were extremely well attended by the participants, as commonly noticed
by many throughout the conference. Some of the more recent developments discussed
during these lectures included the recent factorization of the RSA 140-digit
challenge number, which represents a new milestone on this problem, a general
subexponential-time algorithm for the computation of discrete logarithms in
the jacobian of a hyperelliptic curve, and the infeasibility of the "Xedni-Calculus"
attack on the elliptic curve discrete logarithm problem.

These results represent the leading edge in research in computational number
theory as it applies to cryptography. Some notable discussions included the
recent possibility of a general parallel algorithm for solving large sparse
systems of linear equations. It is widely believed that this problem is the
main bottleneck in the ability to factor large numbers. Consequently, such
a development would have enormous impact on the security of the RSA cryptosystem,
which is currently being used in just about every computing facility in the
world having any sort of security requirement.

The conference was attended by many young mathematicians as participants,
many of which would not have been able to attend without the funding given
to them by the Fields Institute. These graduate students and postdoctoral
fellows were very much involved in the conference, attending all of the lectures,
and some of them giving lectures; such as Mark Bauer, Doug Kuhlman, Julia
Chen, Andreas Enge, Andreas Stein, and Edlyn Teske. As opposed to a conference
of "experts only", it was refreshing to see so many younger and enthusiastic
mathematicians involved. From a research point of view, it was crucial to
the subject area to bring these individuals into the fold.

Finally, the Fields Institute organized this conference in collaboration
with The Communications Security Establishment, Certicom Corporation, Entrust
Technologies, and RSA Data Security. Thus, it was a collective effort of Acadmia,
Government, and Industry, perhaps the first of its kind. This progressive
format shows clearly that the Fields Institute is a leading edge research
organization, and as the main organizer of this particular conference, was
a privilege to deal with this mathematical institute, and organize the conference.