Binary code similarity analysis (BCSA) is a crucial research area in many fields such as cybersecurity. Specifically, function-level diffing tools are the most widely used in BCSA: they perform (similar) function matching one by one for evaluating the similarity between binary programs (binaries). However, such methods need a high time complexity, making it unscalable in large-scale scenarios (e.g., 1/n-to-n searching). Towards effective and efficient program-level BCSA, we propose KEENHash, a novel hashing approach that hashes binaries into program-level representations through large language model (LLM)-generated function embeddings. KEENHash condenses a binary into one compact and fixed-length program embedding using K-Means and Feature Hashing, allowing us to do effective and efficient large-scale program-level BCSA, surpassing the previous state-of-the-art methods. The experimental results show that KEENHash is 215 times faster than the state-of-the-art function matching tool while maintaining effectiveness. Furthermore, in a large-scale scenario with 5.3 billion similarity evaluations, KEENHash takes only 395.83 seconds while the tool will cost 56 days. We also evaluate KEENHash on the program clone search of large-scale BCSA across extensive datasets in 202,305 binaries. Compared with 4 state-of-the-art methods, KEENHash outperforms all of them by at least 23.16%, and displays remarkable superiority over them in the large-scale BCSA security scenario of malware detection.