Mathematician with links to public-key cryptography wins PM prize

A mathematician specialising in symmetry which is central to public-key cryptography and enables encryption solutions like Cryptoloc Technology has won a prestigious award.  

Emeritus Professor Cheryl Praeger of the University of Western Australia has won the 2019 Australian Prime Minister’s Prize for Science for her contributions to pure mathematics. Professor Praeger specialises in the mathematics of symmetry.

“I feel very excited at this recognition of the research achievements of me and my colleagues and students in the mathematics of symmetry,” Professor Praeger says. 

“I was very lucky that early in my career an immensely powerful mega-theorem was born, identifying all the mathematical atoms or building blocks of symmetry – the so-called finite simple groups. 

“I was one of the first to exploit this watershed result to build new fundamental theory and new methods to study groups and symmetrical structures like networks and designs.” 

New algorithms Professor Praeger developed were built into the computer systems GAP and MAGMA and used by scientists and mathematicians world-wide.  

Professor Praeger’s career may have taken a different course if she had listened to the advice of her career advisor in high school, who told her girls don’t study mathematics. 

 By the time I was finishing high school I knew I wanted to continue my studies in mathematics, but the career adviser suggested becoming a nurse instead,” she says.  

“I could not imagine giving someone an injection, so for me being a nurse wasn’t something I could imagine doing.”  

Stubbornly dissatisfied with this advice, Professor Praeger became even more determined to study mathematics.  

How mathematics of symmetry is used in public-key cryptography 

Cryptoloc Chief Data scientist Melissa Crossman explains how the mathematics of symmetry, for which Professor Praeger is renowned world-wide, is used in publickey cryptography.  

A cryptographic key is a long word that looks like random letters and numbers. It encrypts confidential data using a complex mathematical equation that is only solvable with the appropriate cryptographic key. 

 When the person encrypting and sending the data and the person receiving and decrypting the data have the exact same key, it is called a symmetric key. Because both parties have access to the key, this process is referred to as symmetric key cryptography. 

 Symmetric key cryptography is useful for exchanging private information between known parties. However, it presents a security weakness. The symmetric key must be transported between parties and is at risk of interception in what is known as a middle-man attack. A third party can intercept a copy of the symmetric key when it is first shared and can decrypt any of the confidential data shared.  

 Public key cryptography was created to solve this vulnerability by creating a unique key for each user while also offering the benefits of being able to identify individual users. Both the sender and receiver have their private key that they keep secret. A one-way mathematical equation is then used to create a public key for each user.  

 The public keys by themselves cannot be used to decrypt the information and can, therefore, be easily shared without creating a vulnerability. The sender of the information then encrypts the data using a combination of their private key and the intended recipients public key. Then through the power of mathematics and how the recipient’s public key is used in the encryption, only their private key can decrypt the data, ensuring security. 

 When different keys are used to encrypt and decrypt that same data the keys are said to be asymmetric. Whenever you access a secure website, such as sites that start with https, part of how your browser communicates with that site uses a symmetric key and the other part uses asymmetric keys.  

 How Cryptoloc Technology uses mathematics of symmetry 

 Secure data cloud storage and sharing systems such as products by Cryptoloc Technology use several types of encryption keys and mechanisms including symmetric, asymmetric and private-public cryptography.  

 “Mathematics underpins every part of our digital technology, and in particular secure communication of our private data depends on novel protocols founded on the mathematics of symmetry, like those used by Cryptoloc,” Professor Praeger says. 

 “I am excited to think that my research in group theory may lead to future breakthroughs and innovations in cybersecurity and encryption solutions like these.”   

 The importance of women in STEM 

 Professor Praeger says she was fortunate to have female role models working in STEM, while her mother was also very encouraging.  

 “It was my mother’s dream that one of her children would have a university education,” she says.  

 Ms Crossman says it was her mother who also encouraged her into the STEM fields.  

 “I was lucky enough to have female role models working in STEM, with my mother also having a degree in science and mathematics,” she says. 

 “She contributed to the early development of the computer science and programming fields.  

 Both women share the same love of mathematics for its foundation in all problem solving.  

 Professor Praeger says she’d like to see more young people and girls being encouraged to study in the STEM fields.  

 “Australia needs more young people with strong STEM skills to face future technological challenges in society,” she says.  

“In particular we need more girls to choose STEM, as we cannot possibly do our best if we ignore half of our talent.”  

Cryptoloc congratulates Professor Praeger and will continue to be a strong proponent of girls and women working in the STEM fields. 

“Professor Praeger is an admirable role model and she’s certainly proven her high school career advisor wrong through her ground-breaking achievements in mathematics,” Ms Crossman says.