These were the words that made a young Muslim woman burst into tears beside Lake Burley Griffin the day after the Christchurch terror attacks.

But while the world was crying tears of grief, these were rare tears of happiness.

The Arabic phrase translates to "peace be upon you". The person offering those words of comfort to the young woman was Hunter, a six-year-old Canberra boy at the Skyfire festival.

The little boy's father, Dr John Coyne, knows more about the impacts of terrorism than most.

A former Australian Federal Police officer specialising in counterterrorism and organised crime, Dr Coyne is now a security expert leading the Australian Strategic Policy Institute's programs on strategic policing and law enforcement, and border security.

Few are better placed to assess the threat posed by right-wing extremists, including white supremacists like the accused Christchurch killer, and how best to stamp them out.

It's why Dr Coyne taught Hunter the words that made the young Muslim woman's day at a time of great sorrow.

"It's simple acts like that, and it's not just after the attack that that needs to occur," Dr Coyne told the Sunday Canberra Times.

"We need to make efforts in our community to get rid of hate speech.

"I'm a security hawk, I'm not some Kumbaya-singing, left-wing hippie who's saying these things.

"I'm saying that if you want to stay in a safe and secure society, that's what you've got to do.

"You've got to drive those [anti-hate speech] narratives from little kids to adults."

The average person's exposure to far-right extremist views including white supremacy is greater than ever before, Dr Coyne believes.

He said public figures like the controversial former senator Fraser Anning had normalised language used by white supremacists when talking about immigration and minority groups, while social media had created a platform to spread these views to mainstream society.

Political philosopher and former race discrimination commissioner Tim Soutphommasane has warned of the troubling rise of nationalist populism in Australia in his latest book, On Hate.

"Make no mistake, race politics is back in Australia," Professor Soutphommasane told a recent event at the University of Sydney.

He pointed to former Attorney-General George Brandis' defence of people's rights to be bigots and calls from the likes of Pauline Hanson for a ban on Muslim immigration as examples of normalising racism and hatred.

"These ideas would've been dealt with swiftly and emphatically not that long ago, but now they're left to stew in our political debate and discourse."

Professor Soutphommasane called on politicians to provide strong leadership in this area, but said society at large also had to take some responsibility.

He said there was a tendency for people to think they should only care about racism because minority groups were vulnerable to experiencing it, when really, "racism diminishes us all as a society".

"When democracies collapse, let's remember, they don't collapse because something external comes and replaces it," he said.

"They collapse from within."

While white supremacy is enjoying increased exposure, the most vile ideas and discussions remain hidden away from the majority on the online messageboard 4chan.

Dr Coyne said this was also the domain of drug-dealers and people sharing child exploitation material, which should send a strong message about how inappropriate it was to be racist.

"If you want to be a white supremacist, you're hanging with people who hurt children," Dr Coyne said.

"That's the level of who you are, socially."

Dr Coyne said people should not be living in fear of white supremacists, saying there were only a handful of people like the accused Christchurch gunman in the world.

He said white supremacists also tended to be depicted in the media as being part of groups, but they had no shared dogma and often grouped together for short periods of time before breaking apart again.

Dr Coyne said unless Australians stood up and called out hateful behaviour and language where they saw it, they risked further normalising it and bringing together dislocated people with bad intentions.

Asked whether tools like social media increased the likelihood of more white supremacists turning to violence, Dr Coyne said even for those intent on committing violent acts, they were less likely than people elsewhere to be capable of inflicting large-scale damage.

Our gun laws were much tighter than those in New Zealand, making it impossible for anyone to legally obtain the type of assault weapons used in the Christchurch attacks.

"If you're a Muslim family in Canberra and you're worried about being targeted by someone while you're praying, I would say to you, 'Well, I can't say that's impossible, but I think it's unlikely'," Dr Coyne said.

"But is there a chance someone will make an inappropriate Islamic joke, say something socially insensitive or use some kind of hate language? It's probably likely that people will.

"We've always got to get the high-level threat problem up here [in terms of importance] and law enforcement has to be constantly reviewing the risk and the threat of the people wanting to do us harm.

"But we've all got a part to play, from the prime minister down to you and I, in that other narrative of what's acceptable and what the norm is in our society.

"I think [standing up to hate speech] is in all of us. It's a community response."

That message will be a key part of Dr Coyne's presentation on white supremacy in Australia before and after the Christchurch attacks.

He will deliver the free talk at the Canberra Museum and Gallery from 12.30pm on Tuesday, and stressed that it was an event for everyone, not just to inform and reassure members of the Muslim community who may still be on edge after the Christchurch attacks.

Dr Coyne said it was not enough for people to sit back and say, "I don't behave that way" when they encountered racism.

He said Australians tended to be laid back and would often laugh off some inappropriate comments as jokes, when instead they should call those comments out for what they were.

"We need to assert as a country, what our values are," Dr Coyne said.

"There's a lot of conversation in government around citizenship, around Australian values and Australian norms.

"We have to sit there and address hate messaging and say that those things are unacceptable.

"We need to probably be more alive to those sorts of issues because it's about normalising that sort of language."

Already, Dr Coyne's son has shown the way.

The words of a six-year-old might not be able to undo the hurt caused by attacks that claimed 51 lives in New Zealand, but gestures like Hunter's are where healing begins.

"Language is important," Dr Coyne said.

"In the minutes, hours, weeks, months and I think even years after Christchurch, there will be fears.

"It starts with our values - what's acceptable and what's not acceptable.

"I think it starts in the houses of Canberra, in families, in schools, in this office, in lunches, in public speeches.

"That's what's important. That's the only way you'll stamp [white supremacy] out."