(Leveled) Fully Homomorphic Encryption without Bootstrapping
Bibliographic record
Abstract
We present a novel approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions. A central conceptual contribution in our work is a new way of constructing leveled, fully homomorphic encryption schemes (capable of evaluating arbitrary polynomial-size circuits of a-priori bounded depth), without Gentry’s bootstrapping procedure. Specifically, we offer a choice of FHE schemes based on the learning with error (LWE) or Ring LWE (RLWE) problems that have 2 λ security against known attacks. We construct the following. (1) A leveled FHE scheme that can evaluate depth- L arithmetic circuits (composed of fan-in 2 gates) using O ( λ . L 3) per-gate computation, quasilinear in the security parameter. Security is based on RLWE for an approximation factor exponential in L . This construction does not use the bootstrapping procedure. (2) A leveled FHE scheme that can evaluate depth- L arithmetic circuits (composed of fan-in 2 gates) using O ( λ 2) per-gate computation, which is independent of L . Security is based on RLWE for quasipolynomial factors. This construction uses bootstrapping as an optimization. We obtain similar results for LWE, but with worse performance. All previous (leveled) FHE schemes required a per-gate computation of Ω ( λ 3.5), and all of them relied on subexponential hardness assumptions. We introduce a number of further optimizations to our scheme based on the Ring LWE assumption. As an example, for circuits of large width (e.g., where a constant fraction of levels have width Ω ( λ )), we can reduce the per-gate computation of the bootstrapped version to O ( λ ), independent of L , by batching the bootstrapping operation. At the core of our construction is a new approach for managing the noise in lattice-based ciphertexts, significantly extending the techniques of Brakerski and Vaikuntanathan [2011b].
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".