Concomitant with advances in technology, the number of systems and devices that utilize image data has increased. Nowadays, image processing devices incorporated into systems, such as the Internet of things, drones, and closed-circuit television, can collect images of people and automatically share them with networks. Consequently, the threat of invasion of privacy by image leakage has increased exponentially. However, traditional image-security methods, such as privacy masking and image encryption, have several disadvantages, including storage space wastage associated with data padding, inability to decode, inability to recognize images without decoding, and exposure of private information after decryption. This article proposes a method for partially encrypting private information in images using FF1 and FF3-1. The proposed method encrypts private information without increasing the data size, solving the problem of wasted storage space. Furthermore, using the proposed method, specific sections of encrypted images can be decrypted and recognized before decryption of the entire information, which addresses the problems besetting traditional privacy masking and image encryption methods. The results of histogram analysis, correlation analysis, number of pixels change rate, unified average change intensity, information entropy analysis, and NIST SP 800-22 verify the security and overall efficacy of the proposed method.