arXiv:2609.15039v3 Announce Type: replace Abstract: User prompts provided to large language models (LLMs) may contain private information. One way to protect them is to execute the LLM inside a trusted execution environment (TEE). However, this results in slow inference times as current TEEs are significantly slower than GPUs for LLM inference. To circumvent this, Tram\`er and Boneh (2019) proposed Slalom which splits neural network inference between a TEE and an untrusted GPU. They encrypt inputs to computations outsourced to the GPU. In this paper, we extend this split-inference architecture to LLM inference and instead protect intermediate inputs using differential privacy (DP). We first demonstrate that masking intermediate representations is necessary by showing an 80% accuracy on a prompt-reconstruction attack from these representations. Our main contribution is a global sensitivity analysis of key functions in LLM inference, which bounds the required scale of DP noise. Unlike encryption, DP avoids quantization, allowing the LLM to remain in the floating-point domain. We also derive an upper bound on the floating-point error from masking and subsequent noise cancellation as a function of the privacy parameter epsilon, keeping the same quality of the LLM response. We implement our architecture using the Intel TDX TEE and two LLMs: Llama-3.2-3B and Qwen3-4B. Our split execution is nearly twice as fast as fully TDX-based inference. Moreover, it is at most 43% faster than Slalom while achieving higher accuracy. Finally, we demonstrate that prompt reconstruction, even with knowledge of the DP mechanism, cannot recover more information than is contained in an unrelated prompt.