University of Calgary

Mathematical research

April 6, 2010

Developing mathematics for more secure on-line communication

Barry Sanders
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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