The FBI warned computer users that it would not contact victims online, and said any e-mails suggesting this should be viewed with caution "because they could be part of a malicious phishing scheme attempting to exploit this issue.
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Authorities announced this week three arrests in separate schemes to infect computers to allow them to be remotely controlled by malicious software, usually sent by spam e-mail.
FBI special agent Richard Kolko said "the vast majority" of the million computers were in the United States but added that "it's a global problem" and the US authorities have worked with partners from as many as 60 countries in the investigations.
"The majority of victims are not even aware that their computer has been compromised or their personal information exploited," said FBI assistant director for the cyber division James Finch in a statement.
"An attacker gains control by infecting the computer with a virus or other malicious code and the computer continues to operate normally