Story highlights Users in China are already getting alerts, one ex-journalist says

Google won't say how it knows governments are behind the hacking

Security chief says it doesn't want to give away anything that will help the hackers

The Internet giant warns users to strengthen passwords and upgrade software

Google has started warning users when it thinks they may be targets of government-sponsored hackers, the Internet giant announced.

Users whose accounts are compromised get a message at the top of their browser saying: "Warning: We believe state-sponsored attackers may be attempting to compromise your account or computer."

Users in China have already begun getting the message, said one former journalist who used to work in Beijing.

"I got this warning three times," said Mei, who asked to be identified only by her first name for security reasons.

Concerned that the warning itself was an attempt to hack her account, she posted a question in a closed Google group, asking if anyone else got the message.

"So far about 10 of us have received the same message, some in Chinese, some in English," she said. The group has about 200 members, she said.

"Some people are not even that surprised because they have suspicious followers on Twitter or Google," she said.

But Mei said she was startled to find out she was apparently a target because she is not a journalist anymore.

"I left this industry about three years ago, in 2009, and left Beijing. I was really surprised that I was still a target," she said.

Google did not accuse China of being behind the hacking, but the company has been at odds with Beijing in the past over Chinese attempts to control Internet use.

Google declined to say how it could tell that governments were behind the hacking attempts.

"We can't go into the details without giving away information that would be helpful to these bad actors," Eric Grosse, Google security engineering vice president, said Tuesday in a post on the company's website.

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"But our detailed analysis -- as well as victim reports -- strongly suggest the involvement of states or groups that are state-sponsored," he said.

Getting the warning does not mean a user's account has been hacked, the company said, but that Google believes the account has been a target of phishing, malware or other hacking tools.

Google advises users who get the message to strengthen passwords and update software. It also encourages users to be careful about where they enter their passwords.