{"uid":"cap_6NOTYACdV0VSGnSXd-pr8","slug":"crypto-math-elliptic-curve-parameters-on-curve-point-validation-16145e9f","name":"Crypto Math – Elliptic Curve Parameters & On-Curve Point Validation","description":"secp256k1, P-256 and P-384 public parameters (p, n, G) from SEC 2, with an on-curve check of a public point.","url":"https://crypto-math.x402tookit.com/ec-params?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method"],"properties":{"type":{"type":"string","const":"http"},"method":{"enum":["GET"],"type":"string"},"queryParams":{"type":"object","required":["curve"],"properties":{"x":{"type":"string","description":"Point x coordinate, decimal or 0x hex (give with y)"},"y":{"type":"string","description":"Point y coordinate, decimal or 0x hex (give with x)"},"curve":{"type":"string","description":"secp256k1, secp256r1 (P-256) or secp384r1 (P-384)"},"publicKey":{"type":"string","description":"PUBLIC key hex: 04||X||Y uncompressed or 02/03||X compressed; not a private scalar"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"asOf":{"type":["null","string"]},"point":{"type":["null","object"],"properties":{"x":{"type":["null","string"]},"y":{"type":["null","string"]},"valid":{"type":["boolean","null"]},"yParity":{"type":["null","string"]},"isGenerator":{"type":["boolean","null"]},"compressedHex":{"type":["null","string"]},"uncompressedHex":{"type":["null","string"]}}},"params":{"type":["null","object"],"properties":{"a":{"type":["null","object"],"properties":{"hex":{"type":["null","string"]}}},"b":{"type":["null","object"],"properties":{"hex":{"type":["null","string"]}}},"p":{"type":["null","object"],"properties":{"hex":{"type":["null","string"]},"decimal":{"type":["null","string"]}}},"oid":{"type":["null","string"]},"name":{"type":["null","string"]},"order":{"type":["null","object"],"properties":{"hex":{"type":["null","string"]},"decimal":{"type":["null","string"]}}},"aliases":{"type":["array","null"],"items":{"type":"string"}},"cofactor":{"type":["null","number"]},"equation":{"type":["null","string"]},"commonUse":{"type":["null","string"]},"fieldBits":{"type":["null","number"]},"generator":{"type":["null","object"],"properties":{"x":{"type":["null","string"]},"y":{"type":["null","string"]}}},"securityStrengthBits":{"type":["null","number"]}}},"source":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"summary":{"type":["null","string"]},"verdict":{"type":["null","string"]},"degraded":{"type":["boolean","null"]},"disclaimer":{"type":["null","string"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","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":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_FWdSGSTVu_7fLmnYMAo1n","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Returns the SEC 2 public domain parameters (p, n, G, a, b) for secp256k1, P-256, or P-384, and optionally validates whether a given public point lies on the specified curve.","exampleAgentPrompt":"Can you look up the SEC 2 domain parameters for secp256k1 — specifically the field prime p, group order n, and generator point G — and also check whether this public key is a valid on-curve point: 04b0bd7e358e2d8f9d70e73e6b1c44b2b1dfe7d9c7a6c4f9e3b2a1d8e5f6c7b9a2?","exampleUseCases":[{"title":"Verify Ethereum public key validity","prompt":"I have an uncompressed secp256k1 public key starting with 04 — can you check whether it's actually a valid point on the curve? The key is 04a1b2c3d4e5f6a7b8c9d0e1f2a3b4c5d6e7f8a9b0c1d2e3f4a5b6c7d8e9f0a1b2c3d4e5f6a7b8c9d0e1f2a3b4c5d6e7f8a9b0c1d2e3f4a5b6c7d8e9f0a1b2."},{"title":"Implement P-256 ECDH from scratch","prompt":"I'm coding an ECDH implementation and need the full SEC 2 parameters for P-256 (secp256r1) — give me p, n, the generator point G in hex, the cofactor, and the curve equation."},{"title":"Check if raw x,y coordinates are on P-384","prompt":"I extracted x and y coordinates from a TLS certificate and want to confirm they form a valid point on the P-384 curve before using them — x is 12345678901234567890 and y is 98765432109876543210, curve is secp384r1."}],"resultDescription":"A JSON object containing: the full SEC 2 curve parameters (prime p, group order n, generator point G with x/y in hex and decimal, curve coefficients a and b, OID, aliases, field bit size, cofactor, curve equation string, common use description); and optionally a point sub-object with x, y coordinates, on-curve validity boolean, y-parity, isGenerator flag, and both compressed and uncompressed hex encodings.","failureModes":["Missing required 'curve' query parameter returns an error","Unrecognised curve name (not secp256k1, secp256r1, or secp384r1) returns an error","Malformed public key hex (odd length, non-hex characters) returns a parsing error","Providing x without y (or vice versa) may produce undefined point validation behaviour","Payment failure or missing x402 payment header returns 402 Payment Required"],"whenToPreferThis":"Choose this endpoint when you need authoritative SEC 2 elliptic curve domain parameters for secp256k1, P-256, or P-384, especially when you also want to validate a public point on-curve in the same call. It is a lightweight, deterministic lookup — ideal for cryptographic implementations, key validation pipelines, or educational tooling that needs both the parameters and point arithmetic without running a local crypto library.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-29T13:14:28.246Z","isFirstParty":false,"canonicalSlug":"crypto-math-elliptic-curve-parameters-on-curve-point-validation-16145e9f"}