Iconic US actress Mae West once commented that the curve was mightier than the sword, a view that holds particular relevance in the world of internet security. Mathematical calculations based on elliptic curves are delivering the next generation of cryptography systems to protect information.
Irish mathematicians are deeply involved in research in this area, known as Elliptic Curve Cryptography (ECC). ECC is providing second-generation public key cryptographic algorithms, which are designed to ensure that information transfer is fast and secure, explains Prof Gary McGuire from the school of mathematics, University College Dublin.
Speed is one of the key considerations and the new ECC-based methods are faster than the long-established RSA encryption systems.
"When you purchase something on the internet using your credit card, the card number needs to be encrypted. In the future, as computers become faster, the requirements of cryptography will also need to increase and Elliptic Curve Cryptography will take over from RSA in many applications," McGuire predicts.
RSA, named by the last initials of the three researchers who developed it in 1977, is a form of public key cryptography. It is based on mathematic problems that can only be solved when you have certain information, or keys, revealing how they were created. RSA cryptography has been the industry standard for many years.
Prof McGuire's group at UCD has been working on ECC for the past two years. ECC is an encryption procedure using calculations based on the arithmetic of elliptic curves. The use of the algebraic structure of these curves to encrypt information aims to provide greater security and more efficient performance when transferring information, he explains.
Prof McGuire's team came together under the umbrella of the Claude Shannon Institute for Discrete Mathematics, Coding and Cryptography. It includes mathematicians, computer scientists and engineers from UCD, Dublin City University, NUI Maynooth and University College Cork.
The mathematicians develop new theories for the curves, attempting to make them more efficient. The computer scientists and engineers then put the theory into practice, preparing the software and hardware needed to test the curves.
An example device would be a smart card. "You need a curve that would suit a small device with low power and low memory, where private personal information must be encrypted," says McGuire. "The mathematician can devise a great curve, but the engineer [ might] decide that it uses too much energy and may therefore be 'too hot' to use practically," he explains.
ECC is already being used for a number of applications, for example, the e-mails sent to and from Blackberry devices are encrypted using ECC. There is also a lot of interest in ECC technology in the US, says McGuire. The National Security Agency has spent €25 million on some of the licensing rights for ECC.
McGuire has been involved in organising an upcoming conference, where experts from all over the world will discuss the latest developments in ECC. The Claude Shannon Institute is hosting the conference, the 11th workshop on Elliptic Curve Cryptography 2007. It takes place at UCD from September 5th to 7th.
Joseph H Silverman (Brown University, US), a professor of mathematics, will give a public lecture on the eve of the conference. His lecture, The Ubiquity of Elliptic Curves is free and will take place at 7.30pm on September 4th at Lecture Theatre C004 Health Sciences, UCD. Booking not required.
For information about the public lecture and the Elliptic Curve Cryptography conference, see www.shannoninstitute.ie