EncryptFlow: Efficient and Lossless Image Encryption Network Based on Normalizing Flows

Compared to cryptographic image encryption schemes, neural networks (NN) based image encryption schemes exhibit a significantly larger key space and offer enhanced capabilities for parallel processing of image data. However, most existing NN-based image encryption schemes suffer from high time complexity in generating random keys, and their decryption processes often fail to fully recover the plaintext images without loss. In this paper, we first propose a normalizing flows based encryption network, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EncryptFlow</i>, designed to achieve efficient and lossless image encryption. Normalizing flows employ a special coupling structure to couple the partitioned data, thereby establishing interdependence among them. Specifically, we utilize coupling structures (e.g. additive coupling) that allows the image blocks to alternately encrypt each other during forward propagation. Additionally, we devise a key generation algorithm that produces sub-keys tailored for each layer of the encryption network. The proposed EncryptFlow network seamlessly integrates both encryption and decryption functionalities, leveraging the XOR operation as the encryption function within each layer. The experimental results and comparative analyses indicate that EncryptFlow can encrypt 256 × 256 grayscale images with an average time of merely 0.047<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i>, and similarly, it requires only 0.188<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> to encrypt color images of the same dimensions.