Guardian Essential poll results published on Tuesday found just over half of respondents supported tighter restrictions on the amount of information companies could collect on consumers.
An overwhelming majority of the 1050 respondents also said they were worried about scammers stealing their identity to set up bank accounts, despite only 21 per cent saying they were directly affected by the Optus breach.
The survey comes after Optus's parent company advised it had engaged lawyers in case it was subject to any class action over the hack, which involved the personal details of more than 10 million customers being compromised.
In a statement to the Singapore stock exchange on Monday, Optus owner Singtel said it had not received any legal notice of a class action but any such move would be "vigorously defended".
The company also said it wanted to clarify media reports about potential fines or other costs relating to the incident.
"Singtel considers these reports speculative at this juncture and advises that they should not be relied upon," it said.
Optus on Monday revealed more than two million customers had their identification documents exposed in the data breach.
The telecommunications giant has launched an independent review conducted by consultancy firm Deloitte of the circumstances surrounding the data hack.
Embattled Optus chief executive Kelly Bayer Rosmarin recommended the review, saying the company was committed to rebuilding trust with customers.
Several government ministers have criticised the company's response to the incident and its failure to promptly advise customers or the government what personal details had been compromised.
Attorney-General Mark Dreyfus has said he will review Australia's privacy laws and tighter protections could be brought in by the end of the year.
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