WikiLeaks' founder, Julian Assange, has vehemently denied directing these attacks in any way. His lawyer told ABC News' Jim Sciutto, "Wikileaks is not in the business of revenge."
An Australian man who claims to be one of the organizers running the HiveMind told the Sydney Morning Herald it took only 800 computers to take down MasterCard, and 1,000 to take down Visa.
But some security experts say the effort is almost certainly aided by collections of tens of thousands of other computers, involuntarily and unknowingly participating in the campaign at the direction of a master computer.
"The truth is the actual attack is not coming from those few individuals," said Peter Schlampp, a cybersecurity expert with Solera Networks. "They're commanding an extremely broad network of ... computers being controlled by whatever the puppetmaster wants them to do."
These secret networks -- the botnets -- are common and are often amassed through viruses and worms without a computer user even knowing it.
"The infected computers can be told remotely to go do something: Send out spam, send out bad traffic. They can even be told to attack the Pentagon and steal data. They're robots," said Alan Paller, director of research at SANS Institute for Computer Security and Training.
Paller said there are millions of computers available to would-be cyberattackers via botnets, making it difficult for law enforcement agencies to root out the threat completely. But, he added, officials can often track down individuals behind the botnet controls.
Dutch National Police arrested a 16-year-old boy Wednesday in connection with the hack attacks, a spokesperson for the Dutch National Prosecutors Office told ABC News. The teen, he said, had confessed to involvement in the attacks on MasterCard's and Visa's websites.
But the botnets live on.
"Botnets wax and wane over time, but don't go away," said Schampp. "The only way to kill a botnet is for all the PCs to have updated antivirus and antimalware software, or to shut down the computers."
In the current battle, Paller said, resolution may more likely come through more cyberattacks -- from the other side.
"What will happen is that there are enough angry people on the side that doesn't like what Wikileaks did that are going to be vigilantes too. That's already started," he said. "They're attacking back."
ABC News' Zunaira Zaki and Jim Sciutto contributed to this story.