Auditing Privacy in Multi-Tenant RAG under Account Collusion

Multi-tenant retrieval-augmented generation (RAG) services advertise per-account differential privacy as the operative leakage boundary: each account's queries are guaranteed to satisfy $(\varepsilon_{\text{acc}}, \delta_{\text{acc}})$-DP with respect to the index. We identify same-index multi-account collusion as a privacy-boundary failure: for $k$ same-tenant accounts coordinating against the tenant's index -- the operative regime -- known DP composition theory implies joint leakage degrades unconditionally at rate $\Theta(\sqrt{k} \cdot \varepsilon_{\text{acc}})$ for Gaussian-noised retrieval. Cross-tenant and external collusion match the rate only under explicit access-control failure (M4); without M4 these regimes have zero leakage by design and reduce to an architectural audit, not a DP audit. We exhibit an attack realizing the rate and derive a RAG-specific MIA prediction we test empirically. To make this per-account/joint gap auditable, we design the first audit protocol that operates against unmodified RAG deployments and issues a quantitative $(\textsf{PASS}, \varepsilon_{\text{audit}})$ verdict for the retrieval-score channel -- the noise-then-select step the per-account DP guarantee actually covers -- without index disclosure, pipeline redesign, or model-weight exposure. Generation-channel privacy (LLM output conditioned on selected documents) is a separate audit predicate that should compose with ours; we explicitly scope it out. The protocol composes generic cryptographic primitives (Merkle ledgers, ZK function-application proofs, Gaussian noise attestations) with six RAG-specific primitives (embedder commitment, index-content vector commitment, per-account query ledger, noise-then-select attestation, cross-tenant containment proof, coalition-size estimator) and supports both closed-form audit bounds and R\'enyi-DP moments-accountant tracking.