“Statistically, I was never going to end up any other way."

Craig Costello’s words feel both manifestly logical, yet undoubtedly poetic, given his lifelong love for mathematics and a career path that’s taken him to the front lines of cryptography.

From humble beginnings “chasing carrots” in Peter Gotley’s classroom at All Saints (we’ll get to the meaning of that later…) to the hallowed headquarters of Microsoft as its Principal Researcher, 2004 School Captain and Fulbright Scholarship recipient Craig Costello is now counted among the world’s top computational number theorists.

Craig describes himself as an ‘in-house academic’ for Microsoft, with a day-to-day workload that involves researching, creating, and testing cryptographic solutions in the field of quantum computing.

After graduating from All Saints, Craig knew a career in mathematics was going to be his calling.

“In my view, there's two avenues you can go down,” he explains. “You can go down the statistics, data analysis and calculus path, which I do still love, but to me it’s just nowhere near as beautiful as the path I chose which is pure number theory and algebra.”

Although this humble writer may never quite comprehend the numeric 'beauty' of which Craig speaks, we can certainly admire the fervour with which he is working to revolutionise his field - perhaps just as Shakespeare revolutionised the arts. 

In his 2019 TEDx Talk, Craig illuminated both the opportunities and threats that the emergence of quantum computers will bring to the world. 

These computers will be used to cure diseases, create large-scale environmental change, improve economies and much more in the very near future. 

But, in the wrong hands, they will also be able to hack even the toughest cybersecurity systems on the planet in milliseconds if a solution isn't discovered. 

"Cryptographers are the first line of defence in this war that has been going on for centuries; a war between code-makers and code-breakers; a war on information," said Craig during the TEDx Talk. 

"We code-makers thought we'd won this war for good with public key cryptography, but we were wrong, because quantum computers are going to change the game completely." 

As Microsoft's Principal Researcher, Craig is on a mission to create a mathematical code that no amount of quantum processing power can break. 

He has worked across multiple fields including elliptic and hyperelliptic curve cryptography, pairing-based cryptography, isogenies and zero knowledge proofs.

Reflecting on the toughest part of the job, Craig says that cryptographers can often spend years trying to solve a single problem. 

"I think the biggest career defining moment for me, scientifically speaking, was spending more than half of my career on one problem that turned out to be fruitless," he reflects. 

Craig refers to the seven years he spent working with a team using isogenies to try and achieve post-quantum protection. 

"The United States government set up this competition in 2016 and put the call out to cryptographers around the world to create the next generation of security, which all companies in America, including Facebook, Microsoft, Apple, Google and Amazon, would have to adopt," he says. 

"There was about 20 of us backing a scheme which made it to the final four, but less than a month after it had advanced, I got an email from two Belgian mathematicians one Friday afternoon. It read something like, 'Hi, I've got some bad news. We can now completely break this code quite easily'. To be honest, I'm still recovering!" 

But Craig certainly doesn't call this kind of experience a failure. In fact, to him it's quite the opposite.

"It forces you to look in new areas and find a love for new things," he says.

"Even though it was devastating at the time, it taught me how much I care about my work having an impact in the real world, and it taught me that I don't care most about accolades or the success of having a scheme chosen (for example) - I care most about the process of doing the work."

Having resurrected his interest in elliptic curves and armed with an unbreakable attitude, Craig is looking forward to climbing the next mathematical mountain.

Craig remembers his time at All Saints fondly and thanks Mr Gatley for teaching him how to maintain resilience and passion above all else. 

"He wasn't necessarily the math teacher for the masses, but he was the math teacher for someone like me," says Craig.

"He knew how to stoke the fire, dangling these impossible challenges like carrots in front of you. No matter how much you tried to go home and spend the night working on problems that would impress him the next day, the moment you accomplished them, he would have an even bigger carrot waiting for you."

"Because of him, and chasing those carrots, I was never going to be anything else." 

You can view Craig's TEDx Talk, The promise and peril of our quantum future, on YouTube.