Toy curve · 112-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

record territory (the 112-bit prime-curve record needed about 215 PlayStation 3s in 2009)

{
  "id": "ed-112",
  "kind": "toy-ed25519-dlp",
  "curve": "-x^2 + y^2 = 1 + d*x^2*y^2 (mod p), the Ed25519 shape (a = -1)",
  "p": "47066689585820223404282335338626213",
  "d": "5720984381515354022216565020914263",
  "order": "47066689585820223622321404839832952",
  "l": "5883336198227527952790175604979119",
  "cofactor": 8,
  "G": [
    "16208016195390084939919686310335990",
    "15527937615586453215723426565037888"
  ],
  "Q": [
    "6488449092829812827247679392092861",
    "20175512810110202696634904881551912"
  ],
  "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"
  }
}