But most oppose government efforts to monitor their internet use.

The study, by technology company Unisys, found more than 80 per cent of Australians trust Medicare to guard private data such as biometrics (eye scans or fingerprints), while about 75 per cent trust the Taxation Office.

There was also very strong support – 87 per cent – for camera surveillance of public roads.

However, only about one in two people would willingly give biometric details to other government agencies.

The study also found that more than half of Australians opposed increasing government surveillance of their internet use.

Unisys conducted its survey before revelations this month that the United States' National Security Agency was collecting vast amounts of records of phone calls and internet use to monitor potential terrorism threats.

Those revelations shocked many Americans and have sparked a global debate about privacy rights in the age of terrorism.

The head of Unisys's security programs in the Asia-Pacific, John Kendall, told Fairfax Media on Wednesday that Australians were generally trusting of government.

"The only commercial organisation that ranks similarly is banks ...

"We've found previously that Australians are willing to give up a bit of their privacy if it's in return for something that benefits them directly," he said, giving the example of CCTV monitoring of roads.

But they were also "very worried about what might happen if there's a breach".

The survey found that, despite their faith in government, almost two-thirds of Australians were concerned about their welfare, tax or immigration details being stolen.

Mr Kendall warned governments to strengthen the security of mobile technologies in particular, which tended to be more vulnerable to hacking and viruses.

The company suggested government agencies set up a “corporate app store” to provide their staff with access to mobile apps that were safe to use.

The federal government tabled legislation last month that would force organisations to tell citizens when their private data had been accessed improperly.

Attorney-General Mark Dreyfus said last week the present, voluntary disclosure scheme was inadequate.

"Data breaches are underreported to the [Australian] Information Commissioner and we continue to find out about them only through media reports," he said.

Telstra began an investigation last month of reports that details of thousands of its customers – names, phone numbers, addresses and payment plans – had been published online.

Earlier this year, the ABC revealed that personal information about almost 50,000 of its website's users had also been published after its network was hacked.