arXiv:2611.14061v1 Announce Type: new Abstract: Retrieval-Augmented Generation (RAG) systems increasingly rely on vector databases containing documents governed by different access-control policies. Recent search-preserving geometric approaches enforce such access control by structuring the embedding space so that transformed embeddings, which we call protected representations, remain retrievable without exposing information across policy boundaries. We provide a unified security analysis of this paradigm, covering policy isolation, representation confidentiality, query forgery resistance, and policy-membership hiding. We consider both a curious cloud service provider observing the protected representations stored in the vector database and a curious user holding aligned pairs of original embeddings and protected representations. Evaluating the available implementations of the works proposing these geometric transformation mechanisms across three encoders, we find that geometric transformations preserve retrieval utility and provide strong policy isolation, but do not provide the other security properties. A curious user can recover the original embeddings from a few hundred pairs and forge policy-compatible queries at a higher cost that grows with encoder dimension for secret per-policy transformations. Moreover, policy-dependent geometry can leak policy membership even when unauthorized retrieval is prevented. These results show that policy isolation, confidentiality, forgery resistance, and membership hiding are distinct security objectives.