  The continuous-variable quantum key distribution with entanglement in the
middle, a semi-device-independent protocol, places the source at the untrusted
third party between Alice and Bob, and thus has the advantage of high levels of
security with the purpose of eliminating the assumptions about the source
device. However, previous works considered the collective-attack analysis,
which inevitably assumes that the states of the source has an identical and
independently distributed (i.i.d) structure, and limits the application of the
protocol. To solve this problem, we modify the original protocol by exploiting
an energy test to monitor the potential high energy attacks an adversary may
use. Our analysis removes the assumptions of the light source and the modified
protocol can therefore be called source-device-independent protocol. Moreover,
we analyze the security of the continuous-variable source-device-independent
quantum key distribution protocol with a homodyne-homodyne structure against
general coherent attacks by adapting a state-independent entropic uncertainty
relation. The simulation results indicate that, in the universal composable
security framework, the protocol can still achieve high key rates against
coherent attacks under the condition of achievable block lengths.
