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  • $\begingroup$ I'm thinking that it has to do with being polynomially bounded which means many keys are not valid in the first place. Of course, an adversary is not going to choose invalid keys. So you need some other method to define security - the notion of a brute force attack doesn't hold anymore. Think of brute force as infinitely dumb, just iterating through every possible (bit) value. Even a dictionary attack is not brute force. $\endgroup$ Commented Jul 13, 2014 at 14:00