New Separations Results for External Information

We obtain new separation results for the two-party external information complexity of boolean functions. The external information complexity of a function \(f(x,y)\) is the minimum amount of information a two-party protocol computing \(f\) must reveal to an outside observer about the input. We obtain the following results: 1. We prove an exponential separation between external and internal information complexity, which is the best possible; previously no separation was known. 2. We prove a near-quadratic separation between amortized zero-error communication complexity and external information complexity for total functions, disproving a conjecture of \cite{Bravermansurvey}. 3. We prove a matching upper showing that our separation result is tight.