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. 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.

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