TGHE: Template-based Graph Homomorphic Encryption for Privacy-Preserving GNN Inference in Edge-Cloud Systems

Fully homomorphic encryption (FHE) allows a server to run a language model directly on encrypted user prompts, but current approaches remain prohibitively slow. Ciphertexts natively support only addition, multiplication, and rotation, and multiplications may be composed only to a bounded depth before a costly bootstrapping operation is needed to continue. Every nonlinearity must therefore be approximated by an iterative method, and each iteration uses multiplications. A higher iteration count buys precision but exhausts the available depth faster and triggers more bootstraps, which dominate latency. Existing approaches fix the iteration counts uniformly across the model rather than tailoring them to each site's error tolerance. We introduce Homomorphic Encryption-Aware Training (HEAT), a fine-tuning method that makes the per-nonlinearity iteration counts learnable, enabling them and the model weights to co-adapt during training. HEAT optimizes iterations with respect to the task objective, allowing the model to adapt to approximation errors encountered during inference without architectural changes or retraining from scratch. On encrypted GPT-2 decoding, HEAT reduces iterations by $3.1\times$, bootstraps by $1.6\times$, and end-to-end latency by $1.4\times$, while improving decode agreement over the calibrated baseline.

Fully Homomorphic Encryption (FHE) enables privacy-preserving machine learning but incurs extreme computational and memory overhead. These costs come not only from expensive low-level primitives, including Number Theoretic Transform (NTT), rotation, and key-switching, but also from inefficient ciphertext packing at the application level. Existing packing strategies typically preserve either neighboring data elements or feature grouping, but not both, leading to wasted ciphertext slots, excessive rotations, and inflated ciphertext counts. We propose FEnc2, a unified and principled fragment-based encoding framework for CKKS-based private convolutional neural network inference. FEnc2 optimizes slot utilization, rotation complexity, and ciphertext density through two components: 1)Conv-aware Encoding, which analytically selects an optimal fragment size to decouple spatial dependencies and jointly minimize inner-outer rotations across layers, and 2)Arch-aware Ct Compression, which restores ciphertext density after feature- or channel-reduction layers. Together, these transformations reshape encrypted workload structure and reduce homomorphic operations by one to two orders of magnitude. With full memory capacity utilized, i.e., at maximum batch size, FEnc2 achieves end-to-end latency speedups over the state-of-the-art Orion of up to 228.83x on GPU and 226.06x on CPU for LeNet on MNIST, and up to 4.55x on GPU and 9.43x on CPU for MobileNet on ImageNet. FEnc2 is hardware-agnostic yet architecturally transformative: by optimizing encrypted tensor layout before execution, it reduces ciphertext count and workload pressure on hardware, complementing primitive-level optimizations such as NTT and keyswitch accelerators. These results show that application-level data layout is a first-order architectural design dimension for encrypted inference and an important enabler for next-generation FHE systems.

Fully homomorphic encryption (FHE) enables inference on private data without revealing it to the server, but evaluating an entire input under FHE is expensive. We study \emph{selective homomorphic inference}, where only a sensitive region of interest (ROI) is encrypted, and computations independent of that region are performed in plaintext. Selective evaluation produces the same output as full FHE on the same model, without retraining. Its efficiency depends on how quickly encrypted dependencies spread through the network. For small encrypted ROIs, locality-preserving architectures can achieve order-of-magnitude homomorphic-evaluation speedups, whereas architectures with early global mixing provide essentially no speedup. These results identify locality as the key architectural property governing the benefit of selective homomorphic inference.