Security of software supply chains is necessary to ensure that software updates do not contain maliciously injected code or introduce vulnerabilities that may compromise the integrity of critical infrastructure. Verifying the integrity of software updates involves binary differential analysis (binary diffing) to highlight the changes between two binary versions by incorporating binary analysis and reverse engineering. Large language models (LLMs) have been applied to binary analysis to augment traditional tools by producing natural language summaries that cybersecurity experts can grasp for further analysis. Combining LLM-based binary code summarization with binary diffing can improve the LLM's focus on critical changes and enable complex tasks such as automated malware detection. To address this, we propose a novel framework for binary diff summarization using LLMs. We introduce a novel functional sensitivity score (FSS) that helps with automated triage of sensitive binary functions for downstream detection tasks. We create a software supply chain security benchmark by injecting 3 different malware into 6 open-source projects which generates 104 binary versions, 392 binary diffs, and 46,023 functions. On this, our framework achieves a precision of 0.98 and recall of 0.64 for malware detection, displaying high accuracy with low false positives. Across malicious and benign functions, we achieve FSS separation of 3.0 points, confirming that FSS categorization can classify sensitive functions. We conduct a case study on the real-world XZ utils supply chain attack; our framework correctly detects the injected backdoor functions with high FSS.