[
  {
    "id": "smart97-trace-one",
    "categoryId": "ecdlp-anomalous",
    "paperId": "smart97",
    "date": "1997-10-31",
    "datePrecision": "month",
    "time": {
      "coefficient": null,
      "expression": "Polynomial time in log p for trace-one curves"
    },
    "space": {
      "coefficient": null,
      "expression": "Not extracted from the source"
    },
    "tags": [
      "anomalous curves",
      "p-adic logarithm"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The HP technical report (October 1997), subsequently published in Journal of Cryptology (1999), gives the p-adic attack for #E(F_p)=p. Its stated linear algorithm is not translated into a bit-complexity exponent here. This exceptional-family attack does not solve general ECDLP.",
    "extra": {},
    "evidence": {
      "url": "https://cryptodeeptech.ru/doc/HPL-97-128.pdf",
      "locator": "HPL-97-128 abstract and construction",
      "sourceVersion": "HPL-97-128, October 1997; journal publication 1999"
    }
  }
]