The minimum key length for the AES algorithm is 128 bit. Assume that a special-p

Question

The minimum key length for the AES algorithm is 128 bit. Assume that a
special-purpose hardware key-search machine can test one key in 10 ns on one processor.
The processors can be parallelized. Assume further that one such processor
costs $10, including overhead. (Note that both the processor speed and the prize are
rather optimistic assumptions.) We assume also that Moore’s Law holds, according
to which processor performance doubles every 18 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?

Explanation / Answer

number of keys to be tested(n) = 2128

time taken to test these keys by one processor (t1)= 2128*10ns =2128 *10-8 s

processors recquired to test these keys in a week = t1/ seconds in a week

                                                                                                      =2128*10-8/(7*24*60*60)

number of processors we can afford in $1 million today is = 105

Now suppose x units of 18 months are recquired to get the number of processors we need in $1 million, then

=> 2x *105 = 2128*10-8/ (7*24*60*60)

=> 2x =2128*10-13/(7*24*3600)

=> x = log2[(2128*10-13)/7*24*3600)]

=> x= 19.75

number of months required = 19.75*18 = 355 months =29.6 years.

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