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Mathematical research

Submitted by sgarcia on Mon, 2010-04-05 15:32.

April 6, 2010

Developing mathematics for more secure on-line communication

Keeping information secure requires sophisticated
mathematics. Funding for two new Collaborative Research Groups (CRGs) at
the University of Calgary focus on the mathematics needed for such studies
and will develop new theories that will advance science and society in
ways not understood yet.

In early March, The Alberta Ministry of
Advanced Education and Technology awarded $1.2 million in support of the
Pacific Institute for the Mathematical Sciences (PIMS) program. The
University of Calgary received $600,000 in funding over three years from
PIMS. As well, PIMS is providing and additional $400,000 in support for
these two CRGs.

Today, the Department of Mathematics and
Statistics, is launching two new CRGs: Mathematics of Quantum Information,
and L-Functions and Number Theory. It is hosting public lectures this
afternoon with world-renowned mathematicians: Eyal Goren of McGill
University and Gilles Brassard of Université de Montréal.

Barry
Sanders, who will be directing the Mathematics of Quantum Information
group, says these CRGs at the University of Calgary will address the
mathematics deficit that holds back progress in information security.

"There are unsolved mathematical problems that, if solved, could
show how to create and trust new means for secure communication," says
Sanders who is also a physics professor and director of the U of C's
Institute for Quantum Information Science.

"The societal problem
is that, from e-commerce to the battlefield, we rely on encryption to
communicate secretly through public channels, but our belief in security
relies on assumptions about the hardness of breaking the codes. In other
words, our trust is not proven but rather "believed". Much effort goes
into proving security under certain conditions or breaking security in
other conditions."

Some of the greatest mathematical problems
today are about whole numbers (1, 2, 3, 4 and so on), which is what number
theorists are interested in.

"Numbers form the alphabet of the
digital world. Although each individual character in this alphabet is
extremely simple, the subtle properties of the language they form are
directly responsible for the utility of number theory in the field of
digital communications: Every credit card transaction, every email sent,
relies on number theory to ensure it is transmitted securely," says
Matthew Greenberg, an assistant professor in the Department of Mathematics
who leading the L-Functions and Number Theory CRG.

Although the
University of Calgary has been previously involved in PIMS' CRGs, this is
the first time PIMS' CRGs have been directed by researchers at the
University of Calgary.

More information about today's launch: http://www.pims.math.ca/scientific-event/100406-pccl

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