Toy curve · 80-bit

you send

The secret k, as a decimal or 0x hex number.

we check

Computes k·G on the curve and compares it with Q.

score

Solved or not. First solve gets 3 points, later solves 1.

how hard

a GPU cluster for days

{
  "id": "ed-80",
  "kind": "toy-ed25519-dlp",
  "curve": "-x^2 + y^2 = 1 + d*x^2*y^2 (mod p), the Ed25519 shape (a = -1)",
  "p": "9863473724969519324143741",
  "d": "6107078977201794408696844",
  "order": "9863473724967068731936456",
  "l": "1232934215620883591492057",
  "cofactor": 8,
  "G": [
    "4133492607905647286180703",
    "6184897968525120426823381"
  ],
  "Q": [
    "4705213535286947243549742",
    "6300253736413246816709391"
  ],
  "howMade": "p = next prime = 5 mod 8 above 2^(bits+3) + offset; d = first non-square SHA-256(\"polytime/ed-toy-<bits>/d/<i>\") mod p giving order 8*l with l prime; G and Q hashed to the curve from \"polytime/ed-toy-<bits>/G|Q/<counter>\" then multiplied by 8. Nobody, including us, knows k.",
  "answer": {
    "k": "decimal or 0x-hex integer with k*G = Q"
  }
}