  The discrete-variable QKD protocols based on BB84 are known to be secure
against an eavesdropper, Eve, intercepting the flying qubits and performing any
quantum operation on them. However, these protocols may still be vulnerable to
side-channel attacks. We investigate the Trojan-Horse side-channel attack where
Eve sends her own state into Alice's apparatus and measures the reflected state
to estimate the key. We prove that the separable coherent state is optimal for
Eve amongst the class of multi-mode Gaussian attack states. We describe how
Alice may defend against this by adding thermal noise to the system and give an
analytic expression of the resulting secret key rate. We also provide a bound
on the secret key rate in the case where Eve may use any separable state, and
describe an active defense system based on optical modulators.
