  We show that computational problem of testing the behaviour of quantum
circuits is hard for the class of problems known as QMA that can be verified
efficiently with a quantum computer. This result is a generalization of the
techniques previously used to prove the hardness of other problem on quantum
circuits. We use this result to show the QMA-hardness of a weak version of the
problem of detecting the insecurity of a symmetric-key quantum encryption
system, or alternately the problem of determining when a quantum channel is not
private. We also give a QMA protocol for the problem of detecting insecure
encryption to show that it is QMA-complete.
