Slashdot on brute force password cracking
Do you have even a basic understanding of maths? There are 2^2048 possible 2048-bit keys. If you split it between 2 computers, each has to do 2^2047. If you split it between 256 (2^8) then each has to do 2^2040. Split it between 1024 (2^10)? Each is still doing 2^2038. Maybe you've got over four billion computers. In that case, you only need to do around 2^2006 on each one.
In case you still have no concept of how big this number is, there are estimated to be around 10^80 atoms in the universe, which is around 2^266. That means that each of your four billion computers is having try 2^1740 keys for every atom in the universe.
To put it another way: Let's assume each of your four billion computers is a few orders of magnitude faster than anything I know of and can try four billion keys a second, giving you a total of around 2^64 keys tried per second. This means you can do around 2^76 per day. At this rate (and don't forget that we are assuming that you have almost as many computers that are orders of magnitude faster than anything real as there are people in the world) it will take you 2^1972 days to do an exhaustive search (although on average it will only take you 2^1971 days to find the key). For those following at home, that's around 2^1962 years. For reference, the universe is approximately 13.7 billion years old, which is a shade under 2^34 years.
In summary, if every atom in the universe was a computer that ran orders of magnitude faster than anything we can build today, and it ran for the life of the universe to date, you would not be able to crack a single 2048-bit message. If, however, you have a quantum computer, then you might be able to. - TheRaven64
In case you still have no concept of how big this number is, there are estimated to be around 10^80 atoms in the universe, which is around 2^266. That means that each of your four billion computers is having try 2^1740 keys for every atom in the universe.
To put it another way: Let's assume each of your four billion computers is a few orders of magnitude faster than anything I know of and can try four billion keys a second, giving you a total of around 2^64 keys tried per second. This means you can do around 2^76 per day. At this rate (and don't forget that we are assuming that you have almost as many computers that are orders of magnitude faster than anything real as there are people in the world) it will take you 2^1972 days to do an exhaustive search (although on average it will only take you 2^1971 days to find the key). For those following at home, that's around 2^1962 years. For reference, the universe is approximately 13.7 billion years old, which is a shade under 2^34 years.
In summary, if every atom in the universe was a computer that ran orders of magnitude faster than anything we can build today, and it ran for the life of the universe to date, you would not be able to crack a single 2048-bit message. If, however, you have a quantum computer, then you might be able to. - TheRaven64