It is proposed that a slave semiconductor laser (SL) with dual-path injection (DPI) can be driven by a master SL with double optical feedback (DOF) to conceal the time delay signature from both intensity and phase chaos. With the usage of auto-correlation function (ACF) and mutual information (MI) function, the time delay signature concealment effects under different schemes are compared and analyzed. The research results indicate that, as for the same type of lasers with the same parameter ranges, the time delay signature can be better concealed with the DOF-DPI scheme than the other schemes. In addition, as for the scheme with chaotic light injection, the concealing effect of the phase time delay characteristic is better than that of the intensity time delay characteristic; on the same concealment level of time delay characteristic peaks, the DOF-DPI scheme has a wider parameter range than the other schemes.