An exhaustive search of K is not conceivable. It would take too much time...
Let's assume the following hypothesis :
- every human (5 109)
- has the use of 106 processors (optimistic, but not realistic !)
- computing at 108 per second (app. today's speed)
They would produce together about 1,5 1033 encryptions per century
(5 * 109 humans * 106 processors/human * 108 encryptions/second.processor * 60 seconds/minute * 60 minutes/hour * 24 hours/day * 365.25 days/year * 100 years/century)
2127 (number of possibilities for K) is about 1,7 1039.
This means that, all together, we would need more than 1.000.000 centuries to compute all the possible values of K !