## 3 The Methodology  
Figure 1 explains the architecture of our proposed BGM-GAN algorithm for ransomware detection. It consists of three main components: generator, discriminator, and loss functions. The generator learns artificial ransomware patterns based on feedback from the discriminator. It always tries to deceive the discriminator so as to identify the pre-encryption data as benign. Several components are needed for the generator to craft the artificial patterns, namely random inputs, generator network, discriminator network discriminator output, and generator loss. On the other hand, the discriminator is a classifier that distinguishes whether an instance of patterns is real or artificially created by the generator. The discriminator classification relies on training data coming from two different sources: real attack patterns and artificial patterns. The real patterns are used as positive instances whereas the artificial patterns are used as negative instances. The loss functions reflect the distance between the probability distributions of real and artificial patterns. In particular, there are two loss functions, one for the generator and the other for the discriminator. In this study, the Minmax function is used to control the upper limit of classification error by minimizing the maximum loss. This is suitable for the pre-encryption data that lack the sufficient attack patterns, where accurate estimation is challenging and classification error is inevitably high. In the following subsections, the design of the proposed algorithm, including the improved Minmax loss function will be elaborated. We start with a brief description of the GAN and CNN techniques.  
A. Generative Adversarial Networks:  
Generative Adversarial Networks (GANs) have emerged as a groundbreaking development in the field of machine learning, particularly in the realm of deep learning. Initially conceptualized by [PERSON] and his colleagues in 2014, GANs consist of two neural networks--a generator and a discriminator--that are trained simultaneously through a form of contest. While the generator strives to produce synthetic data that mimics a given data distribution, the discriminator aims to distinguish between genuine and synthetically generated data. This adversarial process leads to the continual refinement of both networks, enabling the generation of increasingly convincing synthetic data. The versatility of GANs has made them a subject of extensive research, with applications ranging from image and video generation to more complex tasks like data augmentation, anomaly detection, and even cybersecurity applications such as ransomware detection.  
B. Convolutional Neural Networks  
Convolutional Neural Networks (CNNs) have become a cornerstone in the field of machine learning, particularly for tasks related to image and video analysis. Introduced in the late 1980s and refined over subsequent decades, CNNs have demonstrated remarkable efficacy in the classification of visual data. Leveraging a specialized architecture that mimics the human visual cortex, CNNs are adept at automatically and adaptively learning spatial hierarchies of features from input images. Their ability to handle complex visual information has led to state-of-the-art results in a myriad of applications, from image and video recognition to medical image analysis. As a result, CNNs have become the go-to algorithm for problems involving such classifications.