The encryption system used by banks, the military and others to keep information secure is again under attack, this time by a Young Scientist contestant. The student has developed a new way to crack the codes and now needs a more powerful computer to see how good his new system is.
There are always a number of startlingly difficult maths projects on show at the exhibition and two individual efforts by Abdusalam Abubakar and Ardit Kroni, both 16 and third-year classmates at Synge Street CBS, are prime examples.
Abdusalam, originally from Somalia, is leading a fresh attack on RSA - the world's most popular and widely used data encryption system. Ardit, who came to Ireland from Kosovo, is working in pure theoretical mathematics, studying a concept known as infinite product expansion.
RSA was developed in the 1970s and is the most secure method of its kind, explained Abdusalam. Yet it also represents a challenge that mathematicians find difficult to ignore. The student began studying partially successful mathematical attacks on RSA by Wiener, Hinek and Dujella and attempted to find similarities within them. "I decided to generalise the work to understand why it is done in this way.
"Dujella does Wiener in a better way but using a very complex method," he said. He decided to take the work done by both Wiener and by Hinek and extend it in a "pincer movement" against RSA, as Abdusalam described it.
He began developing a series of theorems that step-by-step generalised the other methods. By his ninth theorem he had improved on Dujella's work, both simplifying it and making it deliver results much faster.
He ran a spreadsheet calculation showing Dujella's computations taking about 59 seconds, while his ninth theorem achieved the same result in about 0.1 seconds. Now Abdusalam has developed a 10th theorem which has left behind the work done by the earlier contributors, he said. "Nobody has come this way - this is a totally new result." The problem is he has no idea how good his new formula for breaking RSA actually is. All his programming to test the theorems has been done in Visual Basic but this is far too slow for this level of number crunching. He now has to learn a faster computer language, C++, and then test his new theorem to gauge its power.
"I will be going for infinite decimal points in C++ to see how far I can go with this technique," he said. He suggested, however, that banks and others should begin looking for alternative encryption methods to secure information in the future.
Ardit's project is equally impressive but hasn't an apparent use outside of theoretical mathematics. His work on infinite products, insoluble values such as the square root of two, is "a subject not often taken up by mathematicians", Ardit acknowledges.
A Synge Street entrant in Young Scientist 2005, Gohar Abbasi, tackled infinite products for square roots and Ardit wanted to build on this work but for infinite products for cube, fourth and higher roots.
Drawing on work by other mathematicians he "set out on my project to solve Gohar's problems", Ardit said.
