PARIS (AP) — Russian television anchor Pavel Lobkov was in the studio getting ready for his show when jarring news flashed across his phone: Some of his most intimate messages had just been published to the web.

Days earlier, the veteran journalist had come out live on air as HIV-positive, a taboo-breaking revelation that drew responses from hundreds of Russians fighting their own lonely struggles with the virus. Now he'd been hacked.

"These were very personal messages," Lobkov said in a recent interview, describing a frantic call to his lawyer in an abortive effort to stop the spread of nearl...