  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.
