Four in five Europeans would want to be notified if their personal data had been lost, stolen or altered, according to a survey by the European Commission.
The survey of 27,000 households also found 43 percent remained offline, mainly due to privacy concerns.
Almost half of those surveyed were worried that personal data would be misused on social networking sites.
Unreliable speeds and the high cost of accessing the internet were also major reasons households avoided going online.
The EC hoped its promise of ubiquitous 30 Mbps broadband speeds and a coordinated fight against cyber-threats would encourage Europeans to take up a broadband subscription.
Its Digital Agenda plans to deliver 30 Mbps speeds to all Europeans by 2020 and 100 Mbps speeds to at least half by that date.
The commission also pointed to a telecoms reform package to be implemented in 2011, which would oblige telecommunications providers to alert national regulators or subscribers when a data breach occurred.
The breach provision would come as part of new requirements that force an ISP or carrier to retain customer data under the EU data retention directive.
Last month the EU also proposed a cyber-security package it hoped would counter botnets, spammers and, more broadly, attacks that compromised sensitive corporate and government information.