Editor's note: Since this story was published, we have learned that multiple arrests have been made as part of the investigation. Read the most current news here: "FBI arrest 14 in Anonymous hacking investigation"

The FBI searched homes of alleged Anonymous members in New York and California this morning, CBS News has learned.

A law enforcement source confirmed for CBS News that FBI agents with search warrants conducted raids at four New York residences this morning in connection with an ongoing investigation into the hacking group.

No arrests were made, the source said, but agents seized computers and computer accessories under search warrants at four homes of suspected hackers in Brooklyn, in the Bronx, and in the Long Island cities of Baldwin and Merrick.

The source said additional FBI raids were conducted on locations in California this morning in connection with the investigation. A U.S. government official later told CBS News that there are more than a dozen raids happening across the United States in connection with the investigation. It is described as a major law enforcement operation, and the official said he wouldn't be surprised if a few arrests are made.

Fox News first reported news of three raids in New York this morning. The three people cited in the search warrants apparently were between their late teens and early 20s, Fox News reported.

Law enforcement has had some success targeting Anonymous members. Last year, an alleged 16-year-old member of the group was arrested in the Netherlands. In January, five people were arrested for allegedly having ties to Anonymous. Following those arrests, the FBI executed more than 40 search warrants to root out Anonymous members in the U.S.

Even so, determining who to target is difficult. Anonymous is a decentralized group, apparently without a clear hierarchy, making it difficult to investigate. And whether the people the FBI reportedly targeted today in its investigations are even members of the organization might not be so easy to figure out.

The battle continues

The FBI's reported search is the latest in an ongoing battle between law enforcement and hackers worldwide. Last month, the FBI worked with London police to investigate 19-year-old Ryan Cleary for allegedly engaging in hacking activities.

After Cleary was arrested, he was charged with five counts of hacking related to a series of distributed denial-of-service (DDoS) attacks against Britain's Serious Organized Crime Agency, the International Federation of the Phonographic Industry, and the British Phonographic Industry.

Cleary was subsequently freed on bail, but is not allowed to have access to the Internet or own any products that can help him to go online. Cleary also has a curfew and must remain at home from 7 p.m. to 9 a.m. every day.

Following his arrest, Cleary was linked to hacking group LulzSec, which went on a 50-day tear this spring, targeting PBS, Sony, and the CIA, among others. However, LulzSec denied that Cleary was involved with its organization, saying only that he hosted one of the organization's chat rooms on his IRC server.

Cleary's arrest was quickly followed by a reported investigation by the FBI in Ohio last month of a man who, reports claimed, was linked to LulzSec. Unconfirmed reports suggested at the time that the man may have given authorities information on Cleary.

In a posting last month, LulzSec named two people who gave up information on Cleary, including one man who lived in the same town in Ohio. LulzSec said that the man was "involved in the hacking of the game 'Dues Ex' and was/is involved in countless other cybercrimes."

Last month, LulzSec announced the end of its operations, saying that it would be joining Anonymous to engage in the latter's AntiSec campaign.

Since then, Anonymous has been especially active. Last week, military contractor Booz Allen Hamilton announced that it had been a victim of Anonymous after 90,000 military e-mail addresses were exposed on the Web. Anonymous also targeted Monsanto, saying that it wanted to detail the company's "corrupt, unethical, and downright evil business practices." It exposed documents containing over 2,500 names, addresses, and e-mail addresses apparently belonging to the company.

In addition, Anonymous announced last week that it would take aim at Exxon Mobile, ConocoPhillips, and Imperial Oil, among other oil companies.

Anonymous has also targeted government organizations, including Arizona's Department of Public Safety, by exposing documents containing e-mail addresses and passwords of the state's police officers. It also engaged in a public spat with the city of Orlando.

An FBI representative told CNET today that the agency is engaged in an "ongoing investigation." The representative would not comment on whether the reported searches were related to Anonymous.

Updated at 6:21 a.m. PT with the FBI's response. Updated at 8:59 a.m. and 10:35 a.m. with details from CBS News.