Elliptic Curve Cryptography (ECC) has emerged as a fundamental element of contemporary digital security, providing strong protection with shorter key sizes and reduced computational requirements compared to traditional public-key systems like Rivest-Shamir-Adleman algorithm (RSA). Nevertheless, recent progress in machine learning, especially deep learning (DL), has presented new possibilities and challenges for ECC. Deep learning can be utilized both to enhance cryptographic calculations and to simulate potential attacks, including side-channel and fault-based vulnerabilities. This paper offers an in-depth performance evaluation of deep learning-based methods applied to ECC, concentrating on their efficacy, computational efficiency, and effects on cryptographic robustness. By examining recent research and experimental results, author assess various DL frameworks, such as convolutional neural networks (CNNs), recurrent neural networks (RNNs), and autoencoders, in the context of ECC-related tasks.