{
  "slug": "algebraic-signature",
  "term": "Algebraic signature",
  "aliases": [
    "linear algebraic signature"
  ],
  "definition": "An algebraic signature is a compact finite-field fingerprint that preserves specified linear relations between data and parity.",
  "note": "For compatible field arithmetic and linear encoding, a parity fingerprint can be calculated from the data fingerprints. This lets a verifier compare compact responses instead of transferring the corresponding payloads. The primitive is not a cryptographic signature. [schwarz-miller]\n\nThe basic protocol's consistency check does not establish authenticity when sites cooperate to fabricate responses. The paper treats collusion separately using secret-dependent coding and blinding; that protection is not supplied by the fingerprint alone. [schwarz-miller]\n\nThe linked fixed GF(16) example maps four symbols to two. Every signature has 256 input blocks; the difference [2,3,1,0] preserves the signature. Its exhaustive counts illustrate collisions, not observed device errors or a replication of the paper's implementation. [hesela-example]\n\nThe block length is part of the detection contract. In the same GF(16) construction, powers of the evaluation point 2 repeat after 15 positions. At length 16, equal nonzero changes at positions 0 and 15 preserve both signature symbols; all one- and two-symbol changes are detected for lengths up to 15. The supplement derives and enumerates this boundary. Retaining separate, ordered page signatures detects its example; XORing them together does not. These are properties of the stated model, not physical error probabilities. [hesela-example]",
  "status": "research",
  "advantages": [],
  "limitations": [
    {
      "text": "Collision risk depends on the input-change model, field, signature construction and covered positions, not just the fingerprint width.",
      "citationIds": [
        "hesela-example"
      ]
    }
  ],
  "related": [
    "cold-archive",
    "checksum",
    "hash-collision",
    "erasure-coding",
    "data-scrubbing"
  ],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "citations": [
    {
      "id": "schwarz-miller",
      "title": "Schwarz and Miller, Store, Forget, and Check, ICDCS 2006, sections 3.1 and 4.2-4.3",
      "url": "https://www.ssrc.us/media/pubs/e368d255b625c27c9f49fe91ef025be645882ede.pdf",
      "accessed": "2026-10-23"
    },
    {
      "id": "hesela-example",
      "title": "Hesela: finite-field signature derivation, code and exhaustive tests",
      "url": "https://hesela.dev/research/algebraic-signature/README.md",
      "accessed": "2026-10-23"
    }
  ],
  "updated": "2026-10-23",
  "provenance": [
    "Historical research primitive with an educational finite-field calculation; no current product security guarantee or hardware experiment."
  ]
}