GIF: Locally Sound Geometric Information Flow Control for LLMs

We identify a security-fidelity tradeoff in defending LLMs against indirect prompt injection: defenses resist injected instructions largely by suppressing untrusted text, which corrupts tasks that must preserve it, such as translation and document editing. Attack-success metrics cannot see this, because a model that ignores an injection and one that faithfully processes it as data score identically. We introduce SecFid, a benchmark built so that executing an injection, processing it as data, and ignoring it produce distinguishable outputs. This makes fidelity measurable and exposes a frontier: across 1,168 examples and 48 configurations, no model or defense achieves both objectives. The highest-fidelity model reaches 96.5% fidelity at 47.8% security, while the most secure defenses invert this, at 99.3% security but only 71.0%-73.9% fidelity. Even defenses with identical security differ in how they earn it: some repair hijacks into faithful processing, others simply suppress benign content. A decision-theoretic analysis shows why no fixed choice can be right everywhere: the correct behavior is not a property of the defense but of the deployment, set by its relative cost of a hijack versus a dropped span. Security alone therefore measures only half of robustness, and reporting it without fidelity hides the price at which it was bought.

Prompt injection is the top security risk for LLM-integrated applications, yet every defense proposed so far has been broken. We prove this is not a coincidence: in shared-embedding architectures that lack enforced control-data separation, perfect prompt-injection prevention is mathematically impossible. We formalize prompted systems as Prompted Action Models whose outputs include control-authoritative actions: refusal decisions, tool authorization, policy routing, and memory writes. We define Semantic-Faithful Control (SFC), the property that such behavior depends only on the meaning of untrusted input, not on how it is encoded. We then prove SFC is unachievable within the shared pipeline, via three results: a provenance-recovery impossibility (shared representations make trusted and untrusted content statistically inseparable, bounded by total variation distance); control-path exposure (untrusted tokens enter control-relevant computation through the same attention value-aggregation that determines outputs); and a finite-coverage invariance gap (finite training cannot certify invariance over infinite semantic-equivalence classes). We ground each quantity in measurements on production tokenizers and models. The result is structural, not a gap in current defenses. It mirrors the code-data confusion in Von Neumann machines that gives rise to buffer overflows, a vulnerability class that took decades of layered defenses (DEP, Write-XOR-Execute, ASLR, stack canaries, and ultimately memory-safe languages) to contain, because no single mechanism sufficed. The implication is the same: prompt injection cannot be eliminated by better in-pipeline classification or alignment alone. It requires architectural separation of instruction and data channels. We identify the root cause and the class of solution it demands.

User prompts provided to large language models (LLMs) may contain sensitive or private information that can be misused by remotely deployed models, such as through inadvertent memorization during retraining. One way to protect user prompts is to execute the LLM inside a trusted execution environment (TEE), with the guarantee that the service provider has no access to computations performed within or information exchanged with the TEE. However, current TEEs are primarily CPU-based and significantly slower than GPUs optimized for LLM inference. To circumvent this, Tramer and Boneh (2019) proposed Slalom, which splits neural network inference between a TEE and an untrusted GPU and encrypts intermediate inputs sent to the GPU. We extend this split-inference architecture to LLM inference and instead protect intermediate inputs using differential privacy. We show that masking intermediate representations is necessary by showing that a prompt-reconstruction attack can recover prompts from these representations with nearly 80% accuracy. Our main contribution is a global sensitivity analysis of key LLM functions, which bounds the required scale of differentially private noise. Unlike encryption, differential privacy avoids quantization, allowing the LLM to remain in the floating-point domain. We also derive an upper bound on floating-point error from masking and noise cancellation in the TEE as a function of the privacy parameter epsilon. We implement our architecture using Intel TDX and evaluate it with two LLMs: Llama-3.2-3B and Qwen3-4B. Our split execution is nearly twice as fast as fully CPU-based inference inside TDX and 5-15 seconds faster than encryption-based Slalom while achieving higher accuracy. Finally, we demonstrate that prompt reconstruction, even with knowledge of the differential privacy mechanism, cannot recover more information than is contained in an unrelated prompt.