WASHINGTON—The administration of President Donald Trump is exploring ways to replace the Social Security number with a safer system based on modern technology in the wake of the Equifax Inc. EFX 2.45% hack, the White House cybersecurity czar said Tuesday.

Rob Joyce, the White House's cybersecurity coordinator, said one possibility is using cryptographic keys, or a combination of long random numbers, to unlock personal data. The merit of such numbers is that they could be revoked once they are found to be compromised, he said.

"I feel very strongly that the Social Security number has outlived its usefulness," Mr. Joyce said at a cybersecurity conference hosted by the Washington Post. "It's a flawed system. If you think about it, every time we use the Social Security number, we put it at risk." He described the current system as "untenable," noting that his own Social Security number has been compromised at least four times.

"We've got a modern digital age. We've got to find a way to use that modern cryptographic identifier to help us drive down that risk," Mr. Joyce said, adding he has asked various departments and federal agencies to submit ideas. He didn't provide a schedule for further policy steps.

'I feel very strongly that the Social Security number has outlived its usefulness.'

—Rob Joyce, the White House's cybersecurity coordinator

The White House official spoke Tuesday morning just as members of Congress grilled former Equifax Chief Executive Richard Smith at House panel hearing, asking questions about how the data breach occurred and how to address cybersecurity risks involving credit-rating firms. The hack exposed the personal data of 145.5 million Americans, including people's Social Security numbers and dates of birth—data that can't be changed even if it has been compromised.