WASHINGTON—Key advances in computing and software in recent years opened the door for the National Security Agency to analyze far larger volumes of phone, Internet and financial data to search for terrorist attacks, paving the way for the programs now generating controversy.

On Sunday, a self-described whistleblower who had worked for a major NSA contractor said the technical breadth of the surveillance program prompted him to disclose details about it in the hopes of sparking a debate over U.S. policies.

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