In the official Clay problem description for P versus NP it's stated that $P \neq NP$ would follow from showing that every language in $E$ [the class of languages recognizable in exponential time with a deterministic Turing machine] can be computed by a Boolean circuit family $<B_n>$ such that for at least one $n$, $B_n$ has fewer gates than the maximum needed tocompute any Boolean function $f: \{0,1\}^n \longrightarrow \{0,1\}$. However, the only reference is that this is an intriguing observation by V. Kabanets. Could someone please point me to a published version of this implication with the proof?
Proof that circuit upper bounds for $E$ imply $P \neq NP$
cc.complexity theory;circuit complexity