Available evidence to date shows that introducing measures such as outlined in the Deputy's question may not have any material impact in terms of preventing illegal activity.
A proposal to register all customers of mobile phone services was considered previously by my Department. It was concluded at the time that such a proposal would be unlikely to solve the illegal and inappropriate use of mobile phones by persons determined to use the technology for illegal activity. There is also a risk that such measures could lead to the emergence in a black market for fraudulently registered or stolen SIM cards.
Furthermore, there are significant data protection issues associated with such a proposal. The routine collection and retention of an individual's personal information could be contrary to current Data Protection legislation.
For those reasons I am not currently considering any such legislative measures.