A cannot be the answer since the phrase nevertheless implies that something is being done regardless of some condition. However, the context is that the Navajos were able to decode much quicker than computers. Thus, A essentially says that "Even though the Navajos were able to decode quicker than computers, the officials were convinced of their ability to decode" which doesn't make sense.
C is incorrect for the same reason as A - the word "still" implies that it was done regardless of some condition.
B is incorrect since nothing is being compared between the idea that the Navajos could decode quickly and that the officials were convinced of their skills.
Therefore, we are left with D.