The Prime Minister's special adviser on cyber security has told the Senate the denial of service attacks on the census website were small and predictable and should not have brought it down on census night.

Malcolm Turnbull now has the report Alastair MacGibbon conducted on behalf of the Prime Minister to determine "which heads will roll and when" as a result of the debacle.

"They were indeed small attacks," Mr MacGibbon told a Senate committee on Tuesday. "The attacks were around three gigabits per second. To have some comparison, it's not uncommon now to see attacks of 100 gigabits per second, and some of the attacks against some of the internet infrastructure such as domain name servers are up to 1000 gigabits per second.

"There was a massive difference between the size of the attacks on the Bureau of Statistics' census website and the ones that are encountered routinely by corporations and governments."