Tempora-Fusion: Time-Lock Puzzle with Efficient Verifiable Homomorphic Linear Combination

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.

Fully homomorphic encryption (FHE) provides strong cryptographic guarantees for private inference, but deploying transformer models under FHE remains prohibitively expensive. A key bottleneck is that non-linear operations such as softmax, normalization, and activation must be replaced with polynomial approximations compatible with the CKKS scheme, and the multiplicative depth consumed by these approximations dominates inference cost. Recent frameworks have advanced approximation techniques, yet all rely on manually configured approximation hyperparameters (e.g., number of iterations, polynomial degree), applied uniformly across all layers. While convenient, this uniform-configuration approach is overly rigid: different layers can tolerate different levels of approximation error without degrading predictive accuracy, and uniform configurations cannot exploit this variability to reduce latency. Allowing each layer to adopt its own configuration, however, causes the search space to explode with model depth, reaching roughly $10^{84}$ configurations for BERT/ViT (12 layers) and $10^{225}$ for LLaMA3 (32 layers), rendering manual exploration practically impossible. We present ATLAS, an automated framework that configures per-layer approximation settings by formulating the problem as a multi-objective optimization over latency and predictive accuracy. The resulting problem is inherently difficult: 1) competing objectives over a large decision space (120 or 320 variables for BERT/ViT or LLaMA3); 2) expensive evaluation, as each configuration takes 70-1,000 seconds even in cleartext; and 3) sparse optimization signals, as 35-50% of candidate configurations yield numerically invalid solutions. ATLAS addresses these challenges through a two-stage optimization strategy that progressively relaxes layer-wise constraints, combined with surrogate models to accelerate evaluation.

Outsourced Transformer inference exposes clients to model substitution and incomplete execution, while direct replay removes the computational benefit of delegation. We present GKR-HND, a registered-model protocol for verifying the polynomial backbone of Homomorphic--Nonhomomorphic Decomposition Transformers. The retained verifier checks the GKR transcript and registered-weight openings, but delegates expensive public evaluations to an assigned computation worker. Assuming an honest retained verifier and prover--worker non-collusion, the verifier accepts only when the worker's signed, request-bound response agrees with the proof claims. Experiments with pretrained HND models validate the proof path and the delegated public computation without dense-matrix replay.