Certainly! I think I misunderstood because it's unusual to drop a whole dimension like that (except maybe compared to a very naive approach). And, I've been around more than a couple of people who've made the 2^2n == 2(2^n) mistake before.
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A classic case of being able to bruteforce half as many bits, twice, is the 8 digit WPS pin. The way the protocol was setup, you could tell if the first half of the pin was correct even if the rest of the pin was wrong.
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All because there was structure to exploit.