# Fully Homomorphic Encryption

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arXiv Nov 10, 2026
Encrypted BERT-base inference drops the format conversions: MOAI amortizes 2.36 minutes per input, 52.8% faster than THOR
Fully homomorphic encryption lets a cloud evaluate a Transformer directly on ciphertext, but rotations and format conversions have kept it slow. MOAI chains column packing and diagonal packing into one fixed flow across all layers and evaluates Softmax and LayerNorm without rotations, needing only 9,648 homomorphic rotations across all matrix multiplications of BERT-base. On a single A100 GPU its end-to-end evaluation time is 52.8% lower than THOR, amortized to 2.36 minutes per input.
Fully homomorphic encryption lets a cloud evaluate a Transformer directly on ciphertext, but rotations and format conversions have kept it slow. MOAI chains column packing and diagonal packing into one fixed flow across all layers and evaluates Softmax and LayerNorm without rotations, needing only 9,648 homomorphic rotations across all matrix multiplications of BERT-base. On a single A100 GPU its end-to-end evaluation time is 52.8% lower than THOR, amortized to 2.36 minutes per input.
Linru Zhang（First author）
MOAI Secure Transformer Inference Fully Homomorphic Encryption Matrix Packing CKKS
arXiv Nov 3, 2026
Perseus folds the homomorphic inference stack into one public Python library, and its Llama-3-8B decode beats the fastest known implementation, Sylph
Homomorphic encryption can run a model directly on ciphertext, but the latency introduced by bootstrapping, the costly operation that refreshes a ciphertext's available multiplication depth, keeps encrypted large models impractical, and existing optimizations sit in different, sometimes closed-source frameworks that are difficult and time-consuming to integrate. Perseus is a public Python library spanning the cryptographic backend, data packing and bootstrap placement, with in-kernel key regeneration, complex-Cachemir packing and bootstrap planning driven by coefficient magnitude and packing periodicity on GPUs. On Llama-3-8B decoding its latency is lower than the fastest known implementation, Sylph, which runs on roughly the same hardware but on the closed-source HEaaN.
Homomorphic encryption can run a model directly on ciphertext, but the latency introduced by bootstrapping, the costly operation that refreshes a ciphertext's available multiplication depth, keeps encrypted large models impractical, and existing optimizations sit in different, sometimes closed-source frameworks that are difficult and time-consuming to integrate. Perseus is a public Python library spanning the cryptographic backend, data packing and bootstrap placement, with in-kernel key regeneration, complex-Cachemir packing and bootstrap planning driven by coefficient magnitude and packing periodicity on GPUs. On Llama-3-8B decoding its latency is lower than the fastest known implementation, Sylph, which runs on roughly the same hardware but on the closed-source HEaaN.
A. Zirilli（First author）
Perseus Fully Homomorphic Encryption CKKS Encrypted LLM Inference
arXiv Oct 2, 2026
HAO applies zero-mean centering to temporal-difference targets, achieving 0% boundary breaches across all seeds in FHE reinforcement learning
The work introduces the Homomorphic Advantage Operator (HAO), which applies the zero-mean centering projection from advantage-based value estimation directly to temporal-difference targets to annihilate the uniform state-value baseline that drives Bellman drift; across a three-tier evaluation (tabular MDP, encrypted CartPole with real CKKS operations, and a 20-node logistics routing benchmark), HAO strictly bounds network pre-activations within the safe polynomial approximation domain with 0% boundary breaches across all random seeds, whereas regularization alone breached the bound on 3 of 5 seeds and the unstabilized baseline did so in 83.8% of episodes, and HAO improves optimal policy accuracy by 18.0 percentage points in tabular domains.
The work introduces the Homomorphic Advantage Operator (HAO), which applies the zero-mean centering projection from advantage-based value estimation directly to temporal-difference targets to annihilate the uniform state-value baseline that drives Bellman drift; across a three-tier evaluation (tabular MDP, encrypted CartPole with real CKKS operations, and a 20-node logistics routing benchmark), HAO strictly bounds network pre-activations within the safe polynomial approximation domain with 0% boundary breaches across all random seeds, whereas regularization alone breached the bound on 3 of 5 seeds and the unstabilized baseline did so in 83.8% of episodes, and HAO improves optimal policy accuracy by 18.0 percentage points in tabular domains.
University of Eloued
Mohamed Nadhir Abid（First author）
Homomorphic Advantage Operator Fully Homomorphic Encryption Reinforcement Learning Bellman drift

You’re all caught up

Encrypted BERT-base inference drops the format conversions: MOAI amortizes 2.36 minutes per input, 52.8% faster than THOR

Perseus folds the homomorphic inference stack into one public Python library, and its Llama-3-8B decode beats the fastest known implementation, Sylph

HAO applies zero-mean centering to temporal-difference targets, achieving 0% boundary breaches across all seeds in FHE reinforcement learning