Privacy protection data processing has been critical in recent years when pervasively equipped mobile devices could easily capture high-resolution personal images and videos that may disclose personal information. We propose a new controllable and reversible privacy protection system to address the concern in this work. The proposed scheme can automatically and stably anonymize and de-anonymize face images with one neural network and provide strong security protection with multi-factor identification solutions. Furthermore, users can include other attributes as identification factors, such as passwords and specific facial attributes. Our solution lies in a modified conditional-GAN-based training framework, the Multi-factor Modifier (MfM), to simultaneously accomplish the function of multi-factor facial anonymization and de-anonymization. It can successfully anonymize face images while generating realistic faces satisfying the conditions specified by the multi-factor features, such as gender, hair colors, and facial appearance. Furthermore, MfM can also de-anonymize de-identified faces to their corresponding original ones. One crucial part of our work is design of physically meaningful information-theory-based loss functions, which include mutual information between authentic and de-identification images and mutual information between original and re-identification images. Moreover, extensive experiments and analyses show that, with the correct multi-factor feature information, the MfM can effectively achieve nearly perfect reconstruction and generate high-fidelity and diverse anonymized faces to defend attacks from hackers better than other methods with compatible functionalities. Finally, we justify the advantages of this work through perceptual quality comparison experiments. Our experiments show that the resulting LPIPS (with a value of 0.35), FID (with a value of 28), and SSIM (with a value of 0.95) of MfM demonstrate significantly better de-identification effects than state-of-the-art works. Additionally, the MfM we designed can achieve re-identification, which improves real-world practicability.