Memory adds no cost to lattice sieving for computers in 3 or more spatial dimensions
Bibliographic record
Abstract
The security of lattice-based crytography (LWE, NTRU, and FHE) depends on the hardness of the shortest-vector problem (SVP). Sieving algorithms give the lowest asymptotic runtime to solve SVP, but depend on exponential memory. Memory access costs much more in reality than in the RAM model, so we consider a computational model where processors, memory, and meters of wire are in constant proportions to each other. While this adds substantial costs to route data during lattice sieving, we modify existing algorithms to amortize these costs and find that, asymptotically, a classical computer can achieve the previous RAM model cost of 2 0.2925 d + o ( d ) to sieve a d -dimensional lattice for a computer existing in 3 or more spatial dimensions, and can reach 2 0.3113 d + o ( d ) in 2 spatial dimensions, where “spatial dimensions” are the dimensions of the physical geometry in which the computer exists. Since this result implies an increased cost in 2 spatial dimensions, we make several assumptions about the constant terms of memory access and lattice attacks so that we can give bit security estimates for Kyber and Dilithium. These estimates support but do not increase the security categories claimed in the Kyber and Dilithium specifications, at least with respect to known attacks.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.009 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.022 | 0.006 |
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".