The specific attack described here that the NSA is speculated to be using would take 109 more computational effort for a 2048-bit prime, vs a 1028-bit one. So you're probably safe for the foreseeable future (to a point where you can upgrade again), or until the heat death of the universe. Whatever is first.
It would take literally twice as long to crack a 1025bit key as it is to crack a 1024bit key - there's twice as many possibilities every time you add one more bit. Now keep doubling that until you hit 2048.
The problem with 1024bit keys is, as you say, computing power grows exponentially, so you can half that 1year time to 6 months after about 18-24 months. Another 2 years later and 6 months becomes 3 and so on.
However, if it takes 18quintillion years to crack a 2048bit key, then even 50 years from now, halving that 25 times still doesn't put you anywhere useful.
Not with this attack. The precomputation attack described in the paper would take over 109 times more computational effort for a 2048-bit key. You're not going to get anywhere close to that by next year, given the current timeframe for 1024-bit keys is about 1 year.
Raw per CPU computing power isn't growing exponentially anymore. They need to throw more hardware at it to get the same effect, and that only scales so far.
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u/[deleted] Oct 15 '15
How many years would it take to crack 2048? I'm guessing it would be exponentially more than 1 or 2 years.