How NSA can decrypt ciphers with 1024 bit keys? (May 24, 2015)
Here is the complete story.
The story is: Most of today's secure network data transfers (e.g. when you enter your credit card number in a website), is done based on protocols which are using Diffie-Hellman algorithm. This algorithm's implementation uses some fixed numbers as its input parameters.
NSA (supposedly) has pre-calculated different computation results for the single most common used parameter and using this set of pre-calculated data (plus several hundred CPU cores), it can decrypt text which is encrypted using 1024 bit keys.
If you use 2048 bit keys they will not be able to do this but currently most of client and server applications are pre-configured to use this type of key.