One of the government websites targeted in a cyber attack last month was bombarded with traffic from more than 50,000 internet addresses in the space of just three seconds.
Details of the scale of the attack have been revealed in emails seen by RTÉ News.
When services were restored, staff dealing with the problem warned that it was not possible to say the attacks were over.
The emails, released under Freedom of Information, say that the attacks were carried out on a "large scale" and that those behind them moved targets in order to continue disrupting services.
A Distributed Denial-of-Service or DDoS attack involves a massive amount of data requests being directed at a particular network in order to overwhelm it and disrupt access.
Last month, a wave of these attacks crashed the websites of government departments and agencies such as the Central Statistics Office, the Courts Service and the Health Service Executive.
Investigations into the attacks are continuing involving the cyber security team in the Department of Communications and the Garda computer crime investigation unit.