  Quantum Key Distribution (QKD) in principle offers unconditional security
based on the laws of physics. Continuous variable (CV) quantum key distribution
has the potential for high-key-rate and low-cost implementations using standard
telecom components. Despite tremendous theoretical and experimental progress in
continuous-variable quantum key distribution, the security has not been
rigorously established for most current continuous-variable quantum key
distribution systems that have imperfections. Among the imperfections,
intensity fluctuation is a significant principal problem affecting security. In
this paper, we provide simple security proofs for continuous-variable quantum
key distribution systems with an intensity fluctuating sources. Specifically,
depending on device assumptions in the source, the imperfect systems are
divided into two cases for security proofs. Our proofs are simple to implement
without any hardware adjustment for the current continuous-variable quantum key
distribution system. Besides, we show some compensation schemes for the
decoding flaws for an outlook.
