It’s an open secret: For years, hackers and feds have been strange bedfellows in the mission to defend military networks. Three-letter agencies set up recruiting booths with schwag at security conferences like Black Hat, and feds party it up with the computer nerds at the so-called “underground hacking conference” DefCon after enlisting intelligence help.

Darpa, with the help of former hacker Peiter “Mudge” Zatko, wants to find a way for the government make that alliance even easier. With an eye on hacker-minded researchers who operate on small budgets and in their free time, Darpa is awarding ...