The move provided the agency with "a dramatic improvement of data from video teleconferences and the ability to decrypt this data traffic", the magazine quoted an NSA document as saying.
It said the NSA, which for months has been at the centre of revelations by intelligence leaker Edward Snowden, broke the encryption in the summer of 2012 and within nearly three weeks, had bumped up the number of decrypted communications from 12 to 458.
Der Spiegel also claims that the US agency kept tabs on the European Union after it moved into new offices in New York in September 2012. Among documents provided by Snowden were plans of the EU's premises, which the NSA codenamed "Apalachee".
Earlier reports in Der Spiegel and Britain's the Guardian newspaper had detailed alleged widespread covert surveillance by the NSA of EU offices, including diplomatic missions in Washington and at the United Nations in New York, as well as at the 28-member bloc's Brussels headquarters.
Revelations about PRISM and other programmes by the NSA to capture and store personal information gleaned from emails, phone calls and web searches have sparked outrage in Europe.
Snowden received temporary asylum in Russia on August 1 but is wanted by Washington on espionage charges linked to his media disclosures.