RSA 1024 Factored in xxx years.

>"invents the quantum computer"

We (as if you and I are involved - the collective human we) may be close to that.

I expect an quick method to factor primes may appear in the next 10-20 years and would not be surprised if we discover in that time frame agencies such as the NSA possess those methods. (Not that you need that to spy.  People are sloppy with their data.  Encrypt the communication then throw the decrypted message print out into the dumpster.)

Re: Brute force...while not factoring or defeating the algorithm itself, given a large enough group of message samples, there are methods to recover the data fairly quickly.  Probably another MIT experiment I read about.  I'll try to find a link.

As for the quantum computer... we're close to that for the last 20 years. I dont see that happening any time soon. If it should happen soon, then its not available to me, but maybe like you mentioned, the NSA.

Now we're speculating on whether or not hardware will be invented so it can break RSA-1024. And if that hardware will be available to us in the next thousand(s) of years. Thats not the point. If that ever happens then we need to increase the key-strength. Thats it.

Or... some genius finds a way to break a large number (2 to the power 1024) down to 2 primes easily. Mathematical guru's have been trying that for centuries, and they all failed. I have lots of respect for the guys at MIT, but they simply cant find this given a few samples. BTW, they dont need to find the RSA algorithm since, like any good encryption algorithm, it is well known:
http://en.wikipedia.org/wiki/RSA#A_working_example

Besides, if they do find a solution, they'd better run (ever saw the movie "sneakers"? :)

>>Now we're speculating on whether or not hardware will be invented so it can break RSA-1024.

It isn't mearly speculation. The assumption that RSA-1024 is strong is based on an *assumption* of the difficulty given the available hardware (and math).

It is necessary to consider the reality of progress in making an assumption of how long the method will be viable.  It is not reasonable to assume hardware and math reasearch will stop today, so saying RSA-1024 is good for a 1000 years is based on a false assumption.

Moore's law or not....progress happens.  Just considering the CPUs currently in the pipeline at AMD and Intel (therfore not mere speculation) we know we will soon have a significant boost in power thus reducing the time to factor RSA-1024.  Thats a 6-10 year pipeline.  

Sufficiently powerful computers to factor RSA-1024 exist.  

IBM BlueGene/L system, installed at DOE’s Lawrence Livermore National Laboratory has now achieved a record Linpack performance of 280.6 TFlop/s.

The 30 Opterons grid used for the RSA-640 challenge is kind of puny by comparison.

They are too expensive for some professor or a group of students to use to respond to the RSA challenge.  When it costs thousands of dollars a minute for time on those computers, the $200,000 prize won't get much attention.  That doesn't mean we should think it is going to hold up for a 1000 years.  The IMB PC is only 25 years old.

Maybe, maybe, but nowadays you still need a rather large grid to crack RSA-640. I wonder what kind of grid we need to crack RSA-1024... and if it fits on this planet if you want it done in time :)

The question is: when will it fit on this planet? and will it be within 1000 years?
Unfortunately we can keep going on and on, because we cant see the future of hardware. As for Moore's law, you might have noticed, it not true anymore. For the last 3 years anyway. Besides even if this law still exists in 1000 years, I still doubt the hardware would be fast and stable enough to calculate this. We need a mathematical breakthrough or quantum computer.

LOL.  3005?

"As for Moore's law, you might have noticed, it not true anymore. For the last 3 years anyway"

Moore's Law originally proposed a ten-fold increase every twelve months - this was revised to 18-24 a while ago which does still seem to fit but I guess there will be a shortfall as Intel changes from its P4 x086 technology (or AMD take over!).