A secure and reliable image encryption scheme is presented, which depends on a novel chaotic log-map, deep convolution neural network (CNN) model, and bit reversion operation for the manipulation process. CNN is utilized to generate a public key to be based on the image in order to enhance the key sensitivity of the scheme. Initial values and control parameters are then obtained from the key to be used in the chaotic log-map, and thus a chaotic sequence is produced for the encrypting operations. The scheme then encrypts the images by scrambling and manipulating the pixels of images through four operations: permutation, DNA encoding, diffusion, and bit reversion. The encryption scheme is precisely examined for the well-known images in terms of various cryptanalyses such as key-space, key sensitivity, information entropy, histogram, correlation, differential attack, noisy attack, and cropping attack. To corroborate the image encryption scheme, the visual and numerical results are even compared with available scores of the state of the art. Therefore, the proposed log-map-based image encryption scheme is successfully verified and validated by superior absolute and comparative results. As future work, the proposed log-map can be extended to combinational multi-dimensional with existing efficient chaotic maps.