We put forth a new computational notion of entropy, which measures the
(in)feasibility of sampling high entropy strings that are consistent
with a given protocol. Specifically, we say that the i'th round of a
protocol (A, B) has _accessible entropy_ at most k, if no
polynomial-time strategy A^* can generate messages for A such that the
entropy of its message in the i'th round has entropy greater than k
when conditioned both on prior messages of the protocol and on prior
coin tosses of A^*. We say that the protocol has _inaccessible entropy_
if the total accessible entropy (summed over the rounds) is noticeably
smaller than the real entropy of A's messages, conditioned only on
prior messages (but not the coin tosses of A). As applications of
this notion, we

* Give a much simpler and more efficient construction of statistically
hiding commitment schemes from arbitrary one-way functions.

* Prove that constant-round statistically hiding commitments are
necessary for constructing constant-round zero-knowledge proof systems
for NP that remain secure under parallel composition (assuming the
existence of one-way functions).