Re: How can that possibly work?
I assume the signal received is not in the GHZ range. It is a much more smoothed out blur of the encryption/decryption key.
However, just one or two hints in the direction of the key, reduces the search space many fold.
ED, if I had a million long line of gibberish as a key, but you picked up that the first half is a higher value than the second half, then you've reduced the search space from "completely random" to "at least similar to this".
With more data points, you can multisample too, so you can get down to smaller blocks of the key, and in the end (I assume) get like 100 small data points in the 4096bit key. Some saying "high" at this point, some saying "low" at others, possibly even "medium". Within this you search for the key, now within the computational power of your brute force server farm.