All HSE systems are due back online later after the WannaCry virus.
It was confirmed yesterday that damage in Ireland was limited - with just one isolated incident involving a group funded by the HSE.
It comes as NUI Galway begins a new national research initiative in digital security today.
Dr Michael Madden said they are working with colleagues around Ireland.
“What we are trying to do is to draw together research that is already taking place across Ireland in universities around digital security.
“There are a lot of different dimensions to digital security, from protecting private individuals and their data to protecting societal infrastructure from disruption.”
However people are being warned to still be careful when opening emails from an unknown sender, with Dr Madden saying it may not be possible to be fully protected all the time.
“There's always trade-offs involved. If you want to connect to other people and have your computers exchange data across networks, there is going to be some level of risk involved.
“All we can do is balance risks versus benefits as widely as possible”