Amid growing concern about child safety on the computer, New Jersey lawmakers are considering a measure to prohibit released sex offenders from using the Internet and to impose new rules for online dating sites.

“We’re living in some very scary times,” said state Senate President Richard J. Codey, who is spearheading New Jersey’s effort. “No matter how much you trust your kids, no matter how much you think you know what they’re doing, there are some sick people out there who will stop at nothing to prey on them.”