We propose a scheme of high-speed physical key distribution based on dispersion-shift-keying chaos synchronization in two semiconductor lasers without external feedback (response lasers), which are driven by a common external-cavity semiconductor laser (drive laser). In this scheme, the dispersion introduces a laser field beating-induced nonlinear transformation to the outputs of drive laser and renders the correlation elimination between the drive and response lasers improving the security of key distribution. Moreover, the commonly driven lasers without external feedback constitute an open-loop synchronization configuration and yield a short synchronization recovery time of a subnanosecond supporting the implementation of high-speed key distribution. With these two merits, we numerically demonstrate a 1.2 Gb/s secure key distribution with a bit error ratio below 3.8×10-3.