An (n, n) multi-secret image sharing scheme shares n secret images among n shared images. In this type of schemes, n shared images can be used to recover all n secret images, but the loss of any shared image prevents the recovery of any secret image. Among existing image sharing techniques, Boolean-based secret schemes have good performance because they only require XOR calculation. This study presents a secure Boolean-based secret image sharing scheme that uses a random image generating function to generate a random image from secret images or shared images. The proposed function efficiently increases the sharing capacity on free of sharing the random image. The use of a bit shift subfunction in the random image generating function produces a random image to meet the random requirement. Experimental results show that the proposed scheme requires minimal CPU computation time to share or recover secret images. The time required to share n secret images is nearly the time as that required to recover n secret images. The bit shift subfunction takes more computation load than the XOR subfunction needs.