  We propose a coin-flip protocol which yields a string of strong, random coins
and is fully simulatable against poly-sized quantum adversaries on both sides.
It can be implemented with quantum-computational security without any set-up
assumptions, since our construction only assumes mixed commitment schemes which
we show how to construct in the given setting. We then show that the
interactive generation of random coins at the beginning or during outer
protocols allows for quantum-secure realizations of classical schemes, again
without any set-up assumptions. As example applications we discuss quantum
zero-knowledge proofs of knowledge and quantum-secure two-party function
evaluation. Both applications assume only fully simulatable coin-flipping and
mixed commitments. Since our framework allows to construct fully simulatable
coin-flipping from mixed commitments, this in particular shows that mixed
commitments are complete for quantum-secure two-party function evaluation. This
seems to be the first completeness result for quantum-secure two-party function
evaluation from a generic assumption.
