The "breakthrough" happened in the summer of 2012, and resulted in "a dramatic improvement of the data from video teleconferencing and the ability to decrypt this traffic". Within three weeks, the number of decrypted communications shot from 12 to 458.
Unfortunately, Der Spiegel didn't go into the details about what type of encryption was used, but the documents show that the Chinese have also been working on breaking into UN communications.
Needless to say, both countries were doing something that's in contravention with the Convention on the Privileges and Immunities of the United Nations (i.e. illegal).
Still, the existence of similar efforts by the US have been unveiled in 2010 when WikiLeaks leaked a confidential cable from the US State Department asking US diplomats to gather information on top UN officials, and ultimately nothing came of it.
The documents also confirmed again that the NSA has been spying on EU officials before and after the EU embassy was moved to new premises in New York late last year, and that they had repeatedly gained access to the computer network of the EU embassy in Washington via VPN. Every time they would be "kicked out", they would manage to return.
Among the documents is also evidence that the US has established and maintains a so-called "Special Collection Service" program that enables it to collect information from over 80 embassies and consulates around the world, often without the host country knowing anything about it.
These latest revelations only build up on those disclosed in early July, when it was made public that the US has been spying on EU officials both in America and Europe.
Finally, The Wall Street Journal has reported that NSA agents have occasionally been misusing the surveillance capabilities of the agency in order to spy on their love interests. According to the source, it didn't happen often (once every year), and the offenders were ultimately disciplined for it.
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