This paper explores the ability of a generative AI image model to generate remarkably realistic and creative images using billions of images from the internet as training data. However, copyright infringement issues have arisen in this process, and this paper presents an efficient method for determining whether a specific image or set of images was used to train the model. This method operates without explicit knowledge of the model's structure or weights (black-box membership inference), and is expected to play a crucial role in auditing existing models and developing fair generative AI models.