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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.16647 |
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| _version_ | 1866911690680958976 |
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| author | Brito, Luis |
| author_facet | Brito, Luis |
| contents | Fully homomorphic encryption (FHE) changes sequence-model design because rotations, encrypted products, ciphertext materialization, multiplicative depth, and bootstrapping pressure can dominate ordinary neural-network costs. This paper presents public-decay homomorphic state space models (HSSMs), recurrent/state-space blocks whose carried state is updated through ciphertext-plaintext public decay while ciphertext-ciphertext multiplication remains on a local write path. The design keeps a fixed encrypted state across the sequence. The evaluated workflow separates client-side tokenization, frozen fastText lookup, projection, clipping, encryption, decryption, and thresholding from server-side encrypted evaluation over bounded projected features. On full Rotten Tomatoes and SST-2 validation splits, the encrypted HSSM path exactly matches plaintext classifications and reaches 0.7505 and 0.7420 accuracy. Against HE-friendly polynomial attention on the same fastText workloads, HSSM matches or exceeds full-sequence task quality while running about 5x faster. Paired L40S operation-level rows show 1.34-1.62x lower latency than cached final-token polynomial attention, 30-258x lower latency than full-sequence polynomial attention, and lower logical encrypted-state footprint. A T = 16/32 comparator with encrypted public-linear input and Q/K/V projections shows projected HSSM succeeding under depth 8/ring 32768, while projected attention succeeds under depth 10/ring 65536. A matched T = 8 OpenFHE/FIDESlib trace finishes at final level 3 and noise-scale degree 2 on both backends. These results make public-decay carry a practical FHE co-design lever for encrypted sequence inference from bounded projected features. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16647 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Public-Decay Homomorphic State Space Models for Private Sequence Inference Brito, Luis Cryptography and Security Machine Learning E.3; I.2.6 Fully homomorphic encryption (FHE) changes sequence-model design because rotations, encrypted products, ciphertext materialization, multiplicative depth, and bootstrapping pressure can dominate ordinary neural-network costs. This paper presents public-decay homomorphic state space models (HSSMs), recurrent/state-space blocks whose carried state is updated through ciphertext-plaintext public decay while ciphertext-ciphertext multiplication remains on a local write path. The design keeps a fixed encrypted state across the sequence. The evaluated workflow separates client-side tokenization, frozen fastText lookup, projection, clipping, encryption, decryption, and thresholding from server-side encrypted evaluation over bounded projected features. On full Rotten Tomatoes and SST-2 validation splits, the encrypted HSSM path exactly matches plaintext classifications and reaches 0.7505 and 0.7420 accuracy. Against HE-friendly polynomial attention on the same fastText workloads, HSSM matches or exceeds full-sequence task quality while running about 5x faster. Paired L40S operation-level rows show 1.34-1.62x lower latency than cached final-token polynomial attention, 30-258x lower latency than full-sequence polynomial attention, and lower logical encrypted-state footprint. A T = 16/32 comparator with encrypted public-linear input and Q/K/V projections shows projected HSSM succeeding under depth 8/ring 32768, while projected attention succeeds under depth 10/ring 65536. A matched T = 8 OpenFHE/FIDESlib trace finishes at final level 3 and noise-scale degree 2 on both backends. These results make public-decay carry a practical FHE co-design lever for encrypted sequence inference from bounded projected features. |
| title | Public-Decay Homomorphic State Space Models for Private Sequence Inference |
| topic | Cryptography and Security Machine Learning E.3; I.2.6 |
| url | https://arxiv.org/abs/2605.16647 |