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Research focuses on connection between mathematics and cyber security

Academic’s journey to second PhD inspired by his father

Mathematics has always been part of Dr Joseph Tonien’s life.

As a child, Dr Tonien learnt the basics from his father, who shared his love of numbers but was unable to continue his education past Year Five.

“My father grew up in a village on an island in Vietnam, so when he finished Year 5, there was no more school where he lived. He had to move to the city to finish his education,” Dr Tonien said.

“As he had packed his bag and was ready to get the boat to the mainland, his parents told him they wanted him to stay. He stayed. That was the end of his education. But he was very talented in mathematics, so when I was young, when he took me out to meet people or to have lunch, he would give me a maths riddle to solve.”

Today (Wednesday 18 July), Dr Tonien graduated with a Doctor of Philosophy in Mathematics, his second PhD.

A lecturer at the University of Wollongong’s School of Computing and Information Technology, Dr Tonien said it feels as if his father, who passed away nine years ago, has been with him on his journey to academic success.

“He was a real driving force in my love of mathematics. I have been trying to complete his history, because he didn’t get a chance to continue his education,” he said.

Dr Tonien’s love of mathematics as a child stemmed from his curiosity about numbers. But now, in the age of the internet, he is inspired by how mathematics can be applied to real-world problems.

To that end, his thesis has examined how number pattern in continued fractions can be used to strengthen cyber security.

“When we use secure pages, such as internet banking, there are huge numbers that allow our information to be transferred securely,” he said. “If hackers could work out the factorization of those numbers, then they would be able to read our confidential information. The numbers need to be so huge and the problem so hard that it can’t be solved by adversaries.

“My thesis shows that if numbers are not chosen carefully, the system can be compromised, so it is a warning for our banking system and for cyber security.”

Dr Tonien came to Australia from Vietnam more than 20 years ago to study at UOW. He completed a double degree, a Bachelor of Mathematics/Computer Science, and then a PhD in Computer Science.

Graduating with one PhD is an achievement, two is an incredible feat. But Dr Tonien credits that to the help of his two supervisors Associate Professor Peter Nickolas and Professor Martin Bunder.

He has five children, and said his ability to juggle study, work and family is due to the support of his wife, who also has a background in computer science.

Dr Tonien continues to be drawn to the study of mathematics because of the “beauty” of its patterns.

“I’m very curious. There is beauty and order in mathematics and it is amazing how our human brain can perceive this.