Mr Heydon revealed his lack of computer knowledge in his ruling released on Tuesday which dismissed a union application for him to stand down over perceived bias.
"It should be noted that there is evidence that I have no computer and that all email correspondence is sent and received by my personal assistant," Mr Heydon wrote.
"Indeed it is notorious among the legal profession that I am incapable of sending or receiving emails. The consequence is that I read emails only after they have been printed out for me."
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Information released in Senate estimates hearings showed Mr Heydon was provided with an Apple iPhone 5 - which has a sophisticated mobile email and internet capability - as were senior and junior counsel.
Electronic Frontiers Australia executive officer Jon Lawrence told AAP anyone taking on a highly paid public role should at least have a basic level of digital literacy.
"You would have to wonder how inefficient these processes are and how much taxpayer money is being wasted," he said.
"It's no longer acceptable."
Mr Lawrence said local libraries provided courses in using the internet and the EFA would be happy to deliver basic training "to any high-ranking public officials that are in need of such remedial assistance".
The royal commission has also been provided tens of thousands of dollars in computer equipment.
