We consider two-party quantum protocols starting with a transmission
of some random BB84 qubits followed by classical messages. We show a
general compiler improving the security of such protocols: if the
original protocol is secure against an almost honest adversary, then
the compiled protocol is secure against an arbitrary computationally
bounded (quantum) adversary. The compilation preserves the number of
qubits sent and the number of rounds up to a constant factor. The
compiler also preserves security in the bounded-quantum-storage model
(BQSM), so if the original protocol was BQSM-secure, the compiled
protocol can only be broken by an adversary who has large quantum
memory and large computing power. This is in contrast to known
BQSM-secure protocols, where security breaks down completely if the
adversary has larger quantum memory than expected. We show how our
technique can be applied to quantum identification and oblivious
transfer protocols.