New research suggests more than 1 billion data records were stolen from more than 1,500 individual data breaches last year. The latest findings from Gemalto, an enterprise security firm, represent a significant year-over-year increase in both corporate breaches and data theft.

PALO ALTO, Calif. — In late 2013, an A.T.M. in Kiev started dispensing cash at seemingly random times of day. No one had put in a card or touched a button. Cameras showed that the piles of money had been swept up by customers who appeared lucky to be there at the right moment.