Nowadays, due to the advancement in networks, it has become easy to share multimedia information such as images, voice, and videos in real‐time. In the process of multimedia storage and transmission, it is crucial to ensure the security and privacy of multimedia data. The attendant issue is how to encrypt images or videos safely and efficiently. Here, a provable security model of image encryption is presented. Then, a new public image encryption scheme based on one‐way trapdoor permutation, with security in the presence of honest adversaries, is proposed. Furthermore, random reusable technology is adopted to improve efficiency and shorten ciphertext. Finally, the simulation results show the validity of the encryption scheme.