{
  "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"
  }
}