@tfb
This means that adding noise drives up the cost of recovering the signal: driving up your opponents' costs is a rather good approach.
The problem is that people are really poor judges of what truly is "noise", and the costs for removing it keeps falling as technology advances. I also don't doubt that there are vulnerabilities in various obfuscation technologies that can make it very easy to turn their "noise" into a signal that can be easily subtracted.
In fact adding noise can do even better than that: if there is some pattern which occurs only once, the averaging will not recover it at all: it's simply hidden in the noise.
It could be quite the opposite. A unique signal in a sea of noise could act like a lighthouse. Consider this scenario: you're throwing around a lot of random data to hide your monitored-but-perfectly-legal regular activities. At some point your fabricated noise/signal soup hashes to an entry in a kiddie porn database. Your life is now about to get a lot more complicated. That's the thing about random data: as unlikely as it is to flip a coin and have it come up heads 1000 times in a row, it will happen if you flip enough coins. You can't "average" that away, or do any other operations to "hide" it without also reducing the randomness, and thus making your signal easier to pick out.
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