The minimum key length for the AES algorithm is 128 bits. Assume that a special purpose hardware key-search machine can test one key in 10...

The minimum key length for the AES algorithm is 128 bits. Assume that a special purpose hardware key-search machine can test one key in 10 nanoseconds on one processor. The processors can be parallelized. Assume further that one such processor costs $10, including overhead. We assume that Moore’s law holds, according to which processor performance doubles every 18/Ö2 months.

How long do we have to wait until an AES key search machine can be built which breaks the algorithm on average in one week and which doesn’t cost more than $1 million?

Now instead of a wealthy individual, consider a government that is capable of building a massively parallel machine costing hundreds to billions of dollars. For instance, the Earth Simulator has a speed of 40 Teraflops (= 40 * 10^12 floating point operations per second). Assume a Rinjndael encryption may be realized in software running on this machine using 100 floating-point operations. Also assuming the supercomputer is updated every 18 months to double in speed, how long do we have to wait until the Earth Simulator will be capable to find a Rinjdael key in less than a week?