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Simultaneous bandwidth (BW) enhancement and time-delay signature (TDS) suppression of chaotic lasing over a wide range of parameters by mutually coupled semiconductor lasers (MCSLs) with random optical injection are proposed and numerically investigated. The infl uences of system parameters on TDS suppression (characterized by autocorrelation function (ACF) and permutation entropy (PE) around characteristic time) and chaos BW are investigated. The results show that, with the increasing bias current, the ranges of parameters (detuning and injection strength) for the larger BW (>20 GHz) are broadened considerably, while the parameter range for optimized TDS (20 GHz) and perfect TDS suppression. In addition, the system can generate two-channel high-speed truly physical random number sequences at 200 Gbits/s for each channel.