{"uid":"cap_vTAUNoInOPcL2cl6pMSXK","slug":"lattice-basis-length-estimator-491caa08","name":"Lattice Basis Length Estimator","description":"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.","url":"https://quantum.halowerk.com/v1/lattice-check","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"dimension":{"type":"integer","maximum":100000,"minimum":2},"log2_determinant":{"type":"number","maximum":1000000000,"minimum":-1000000000},"target_norm_log2":{"type":"number","maximum":1000000000,"minimum":-1000000000},"root_hermite_factor":{"type":"number","maximum":2,"minimum":1}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_Kt4yXWaJJIJVDLcPlQUoP","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"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.","exampleAgentPrompt":"Can you estimate the Gaussian-heuristic and reduced-basis vector lengths in log2 for a lattice with dimension 512, log2 determinant 4096, and a root-Hermite factor of 1.0045?","exampleUseCases":[{"title":"LWE parameter feasibility check","prompt":"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?"},{"title":"Comparing Hermite factor impact","prompt":"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."},{"title":"NTRU lattice basis norm estimation","prompt":"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?"}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T00:41:42.805Z","isFirstParty":false}