The commissioner of Alaska’s Department of Revenue was called into a special meeting last month to discuss a problem: The Permanent Fund Dividend Division was under cyberattack.

In a short period of time, more than 800,000 attempts were made to get into the division’s systems, which are in charge of paying the annual dividend to Alaskans. The division shut down its computers, the department’s firewalls held, and “no Alaskans’ data was accessed,” said Anna MacKinnon, director of the division.

“Our system repelled, as it should, the assault on our system,” she said last Friday...