This encryption means ordinary citizens' messages cannot be intercepted by criminals or spies as they travel across the internet.

But some people worry that terrorists and criminals can communicate secretly this way.

"I think most people agree that there is a problem," said Prof Alan Woodward, a computer scientist at Surrey University.

"The trouble is trying to force companies to decrypt via legislation is the very reason end-to-end encryption was introduced - particularly by US-based firms post-Snowden - to give their global customer base confidence that no government could get them to do what the Australians now propose."

What does Australia want?

Mr Turnbull said encryption meant online messages were "effectively dark to the reach of the law", which he said was "not acceptable".

He said companies had to "assist the rule of law" and provide law enforcement with access to encrypted messages.

"For this to work, the companies will have to change their technical architecture or somehow weaken the encryption," said Prof Woodward. "Either is a bad idea."

Some politicians have called for apps to build a "back door" into their systems, to allow law enforcement access to unencrypted messages. But such a system could also be exploited by criminals, defeating the purpose of encryption.

Mr Turnbull said he was not seeking a "back door" and wanted communications handed over in "the usual way that applies in the offline world".

Prof Woodward said modern encryption methods had not been cracked.

But Mr Turnbull said Australian law would prevail over the laws of mathematics.

He told journalists: "The laws of mathematics are very commendable, but the only law that applies in Australia is the law of Australia."