We consider unconditionally secure leakage resilient two-party
computation, where security means that the leakage obtained by an
adversary can be simulated using a similar amount of leakage from the
private inputs or outputs. A related problem is known as circuit
compilation, where there is only one device doing a computation on
public input and output. Here the goal is to ensure that the adversary
learns only the input/output behaviour of the computation, even given
leakage from the internal state of the device. We study these
problems in an enhanced version of the ``only computation leaks\u27\u27
model, where the adversary is additionally allowed a bounded amount of
{\em global} leakage from the state of the entity under attack. In
this model, we show the first unconditionally secure leakage resilient
two-party computation protocol. The protocol assumes access to
correlated randomness in the form of a functionality \fOrt that
outputs pairs of orthogonal vectors (u,v) over some
finite field, where the adversary can leak independently from
u and from v. We also construct a general circuit
compiler secure in the same leakage model. Our constructions work,
even if the adversary is allowed to corrupt a constant fraction of the
calls to \fOrt and decide which vectors should be output. On the
negative side, we show that unconditionally secure two-party
computation and circuit compilation are in general impossible in the
plain version of our model. For circuit compilation we need a
computational assumption to exhibit a function that cannot be securely
computed, on the other hand impossibility holds even if global leakage
is not allowed. It follows that even a somewhat unreliable version of
\fOrt cannot be implemented with unconditional security in the plain
leakage model, using classical communication. However, we show that an
implementation using quantum communication does exist. In particular,
we propose a simple ``prepare-and-measure\u27\u27 type protocol which we
show secure using a new result on sampling from a quantum
population. Although the protocol may produce a small number of
incorrect pairs, this is sufficient for leakage resilient computation
by our other results