Malicious software attacks are having an increasingly significant economic impact. Commercial malware detection software can be costly, and tools that attribute malware to the specific software vulnerabilities it exploits are largely lacking. Understanding the connection between malware and the vulnerabilities it targets is crucial for analyzing past threats and proactively defending against current ones. In this study, we propose an approach that leverages large language models (LLMs) to detect binary malware, specifically within JAR files, and uses LLM capabilities combined with retrieval-augmented generation (RAG) to identify Common Vulnerabilities and Exposures (CVEs) that malware may exploit. We developed a proof-of-concept tool, MalCVE, that integrates binary code decompilation, deobfuscation, LLM-based code summarization, semantic similarity search, and LLM-based CVE classification. We evaluated MalCVE using a benchmark dataset of 3,839 JAR executables. MalCVE achieved a mean malware-detection accuracy of 97%, at a fraction of the cost of commercial solutions. In particular, the results demonstrate that LLM-based code summarization enables highly accurate and explainable malware identification. MalCVE is also the first tool to associate CVEs with binary malware, achieving a recall@10 of 65%, which is comparable to studies that perform similar analyses on source code.