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Lattice Basis Length Estimator
x402
Lattice Basis Length Estimator is a paid API for AI agents from quantum.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-09-14).
Estimates Gaussian-heuristic and reduced-basis vector lengths in log2 units from a lattice dimension, log2 determinant, and assumed root-Hermite factor — without executing actual lattice reduction.
Price / call$0.003
Success—
StatusUnknown
How this service works
Uses lattice dimension, log2 determinant and an assumed root-Hermite factor to estimate Gaussian-heuristic and reduced-basis vector lengths in log2 units. It does not execute lattice reduction, validate an LWE instance or provide a cryptographic security level.
Output
Returns the Gaussian-heuristic expected shortest vector length and the estimated reduced-basis vector length, both expressed in log2 units, computed analytically from the supplied dimension, log2 determinant, and root-Hermite factor — without performing actual lattice reduction.
Example use cases
LWE parameter feasibility check
“I'm designing an LWE-based scheme with dimension 1024 and a log2 determinant of 8192. Assuming a root-Hermite factor of 1.005, can you estimate the Gaussian-heuristic and reduced-basis vector lengths so I can see if the parameters look geometrically reasonable?”
Comparing Hermite factor impact
“Can you run the lattice basis length estimate for dimension 256 and log2 determinant 2048 using a root-Hermite factor of 1.01? I want to see what the estimated reduced vector length is in log2 units.”
NTRU lattice basis norm estimation
“For an NTRU lattice with dimension 677 and a log2 determinant of roughly 5000, what would the Gaussian heuristic and reduced basis vector lengths look like in log2 if I assume a root-Hermite factor of 1.0045?”
Technical details
Endpoint
POSThttps://quantum.halowerk.com/v1/lattice-checkWhen to prefer
Choose this endpoint when you need quick analytical estimates of lattice basis vector lengths from known parameters — ideal for parameter exploration, sanity-checking lattice designs, or comparing reduction quality proxies without the computational cost of running actual BKZ or LLL. Not suitable when you need a verified cryptographic security level, actual lattice reduction output, or LWE hardness estimates.
Side effects
- dimension below 2 or above 100000 causes validation error
- root_hermite_factor outside [1,2] range rejected
- log2_determinant outside [-1e9, 1e9] range rejected
- missing required fields (dimension, log2_determinant) returns 400
- payment failure (x402) if USDC balance is insufficient
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| dimension | integer | |
| log2_determinant | number | |
| target_norm_log2 | number | |
| root_hermite_factor | number |
Tags
x402
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