Company and federal officials said they believed last week's theft of identity data on 3.3 million people with student loans was the largest-ever breach of such information and could affect as many as 5% of all federal student-loan borrowers.

Names, addresses, Social Security numbers and other personal data on borrowers were stolen from the St. Paul, Minn., headquarters of Educational Credit Management Corp., a nonprofit guarantor of federal student loans, during the weekend of March 20-21, according to the company.

ECMC...