We propose and numerically demonstrate a novel secure key distribution (SKD) scheme by using dynamically synchronized semiconductor lasers (SLs) subject to common dual injections from two mutually coupled SLs. The performance of hybrid chaos synchronization, complexity of chaotic signals, chaos-based key distribution, and the privacy of SKD scheme are systematically discussed. It is shown that high-quality hybrid chaos synchronization of zero lag and lead lag can be both achieved between two local lasers under different injection delay conditions, whereas low cross correlations are observed among the driving lasers and the local lasers. By randomly perturbing the injection delays with four independent random sequences, the outputs of local SLs can be dynamically synchronized. Extracting the outputs in the synchronization time slots of zero lag and lead lag, synchronous entropy sources are obtained and used to generate keys with high consistency at local ends of Alice and Bob, which are robust to the parameter mismatches of local lasers to some extent. Moreover, large BER is calculated in two types of typical illegal attacks, which demonstrates the security of the proposed scheme. This work proposed a high-level secure key distribution solution to one-time pad communication.