Computationally bounded adversary
In information theory, the computationally bounded adversary problem is a different way of looking at the problem of sending data over a noisy channel. In previous models the best that could be done was ensuring correct decoding for up to d/2 errors, where d was the Hamming distance of the code. The problem with doing it this way is that it does not take into consideration the actual amount of computing power available to the adversary. Rather, it only concerns itself with how many bits of a given code word can change and still have the message decode properly. In the computationally bounded adversary model the channel – the adversary – is restricted to only being able to perform a reasonable amount of computation to decide which bits of the code word need to change. In other words, this model does not need to consider how many errors can possibly be handled, but only how many errors could possibly be introduced given a reasonable amount of computing power on the part of the adversary. Once the channel has been given this restriction it becomes possible to construct codes that are both faster to encode and decode compared to previous methods that can also handle a large number of errors.
At first glance, the worst-case model seems intuitively ideal. The guarantee that an algorithm will succeed no matter what is, of course, highly alluring. However, it demands too much. A real-life adversary cannot spend an indefinite amount of time examining a message in order to find the one error pattern which an algorithm would struggle with.
As a comparison, consider the Quicksort algorithm. In the worst-case scenario, Quicksort makes O(n2) comparisons; however, such an occurrence is rare. Quicksort almost invariably makes O(n log n) comparisons instead, and even outperforms other algorithms which can guarantee O(n log n) behavior. Let us suppose an adversary wishes to force the Quicksort algorithm to make O(n2) comparisons. Then he would have to search all of the n! permutations of the input string and test the algorithm on each until he found the one for which the algorithm runs significantly slower. But since this would take O(n!) time, it is clearly infeasible for an adversary to do this. Similarly, it is unreasonable to assume an adversary for an encoding and decoding system would be able to test every single error pattern in order to find the most effective one.
The stochastic noise model can be described as a kind of "dumb" noise model. That is to say that it does not have the adaptability to deal with "intelligent" threats. Even if the attacker is bounded it is still possible that they might be able to overcome the stochastic model with a bit of cleverness. The stochastic model has no real way to fight against this sort of attack and as such is unsuited to dealing with the kind of "intelligent" threats that would be preferable to have defenses against.
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