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How secure are your credit cards?

Recent credit card breaches at Target and Neiman Marcus have put the topic of cybersecurity front and center once again.

Though the extent of the current attacks are still being investigated, consumers shouldn't think the worst is over. According to one expert, victims will likely be dealing for a long time with the fallout of having their information stolen.

"We should expect these people to be targeted for spam and phishing campaigns in the near future—perhaps ones masquerading as warnings from Target or other major retailers about the data breach," said Max Eddy, junior software analyst at PCmag.com.

In an interview with CNBC, Target Chairman and CEO Gregg Steinhafel said that the security technology used in the U.S. is outdated and that we should adopt EMV—Europay, MasterCard and Visa—technology.

(Read more: Dysfunctional credit cards)

"It's a well-established standard ... throughout the world," he said. "It's time for America to make that commitment to get to that standard."

In the meantime, Steinfhafel acknowledged, customers can't do much to protect themselves against this kind of breach.

People who suspect their data was stolen should watch credit card transactions closely and change their card PIN, if possible, according to Pete Pachal, technology editor at Mashable.

"They should also be extra wary of phishing attacks—which they should be wary of anyway," he said.

—By Christina Medici Scolaro