{
  "type": "failure-mode",
  "name": "Unchecked curve point and subgroup membership",
  "slug": "unchecked-curve-point-and-subgroup-membership",
  "section": {
    "id": "audit",
    "number": "03",
    "title": "Auditing a ZK protocol",
    "url": "https://zkpick.com/audit/"
  },
  "url": "https://zkpick.com/audit/failure-modes/unchecked-curve-point-and-subgroup-membership/",
  "markdown": "https://zkpick.com/md/audit/failure-modes/unchecked-curve-point-and-subgroup-membership.md",
  "detail": "Proof elements are accepted without verifying that they lie on the curve and in the correct prime-order subgroup, enabling small-subgroup and invalid-curve attacks against the verifier.",
  "mitigation": "Validate every deserialised group element for curve membership and subgroup order before use, including in hand-written or gas-optimised verifiers where such checks are the first thing removed.",
  "relatedOptions": [
    {
      "name": "Verifier and integration review",
      "url": "https://zkpick.com/audit/verifier-review/"
    }
  ],
  "updated": "2026-09-12",
  "version": "1.3",
  "canonical": "https://zkpick.com/audit/failure-modes/unchecked-curve-point-and-subgroup-membership/",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "authors": [
    "MarketComp"
  ]
}