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Leakage-resilient cryptography aims to design key exchange protocols to withstand leakage attacks. These protocols are examined using a leakage-resilient security model to determine whether they possess the claimed security properties. The security analysis focuses on how the leakage-resilient security model has evolved to meet increasing security requirements and cover a broader range of attacks. By studying and analyzing the presented security properties of these models, potential vulnerabilities in protocol design can be effectively addressed. This article delves into various leakage-resilient security models based on two models, CK and eCK, and provides examples of secure key exchange protocols defined within these models. Additionally, it explores the relationship between adversaries' capabilities in these models and different attack schemes in the real world. By offering insights into various leakage-resilient security models, leakage attacks, and the development of secure protocols, it contributes to advancing knowledge in this field.