We define $(varepsilon,delta)$-secure quantum computations

between two parties that can play dishonestly to maximise

advantage $delta$, however keeping small the probability

$varepsilon$ that the computation fails in evaluating correct value.

We present a simple quantum protocol for computing

one-out-of-two oblivious transfer that is

$(O(sqrt{varepsilon}),varepsilon)$-secure.

Using the protocol as a black box we construct a scheme for

cheat sensitive quantum bit commitment which guarantee that

a mistrustful party has a nonzero probability of detecting a

cheating.