InstaHide's Sample Complexity When Mixing Two Private Images

Training neural networks usually require large numbers of sensitive training data, and how to protect the privacy of training data has thus become a critical topic in deep learning research. InstaHide is a state-of-the-art scheme to protect training data privacy with only minor effects on test accuracy, and its security has become a salient question. In this paper, we systematically study recent attacks on InstaHide and present a unified framework to understand and analyze these attacks. We find that existing attacks either do not have a provable guarantee or can only recover a single private image. On the current InstaHide challenge setup, where each InstaHide image is a mixture of two private images, we present a new algorithm to recover all the private images with a provable guarantee and optimal sample complexity. In addition, we also provide a computational hardness result on retrieving all InstaHide images. Our results demonstrate that InstaHide is not information-theoretically secure but computationally secure in the worst case, even when mixing two private images.