Based on vertical-cavity surface-emitting lasers (VCSELs) with optical injection and polarization-rotated optical feedback, we propose and numerically demonstrate a scheme for generating synchronized random bit sequences (SRBS) for two legal users at different locations. For the scheme, the chaotic signal generated by a driving VCSEL (D-VCSEL) subject to chaotic optical injection are utilized to simultaneously drive two VCSELs (A-VCSEL and B-VCSEL) with polarization-rotated feedback, then the chaotic outputs from A (B)-VCSEL are used as physical entropy sources to generate SRBS. The simulated results show that, the SRBS at a rate up to 400 Gbits/s can be achieved after adopting suitable post-processing method. The security of this scheme can be ensured by a high-quality synchronization between A-VCSEL and B-VCSEL while relatively low-quality synchronization between D-VCSEL and A (B)-VCSEL. Moreover, the BER and the randomness of generated SRBS are also discussed.