In a quiet neighborhood in Budapest, Hungary, sits an ordinary building that holds a dark secret. Behind the walls of this unassuming duplex is the headquarters of BAC Consulting, a company that is now linked to a deadly series of explosions in Lebanon and Syria. These explosions, caused by pagers, have killed at least 12 people, including children, and injured thousands more.

The pagers, which are small electronic devices typically used for sending messages, were part of what appears to...