PUZZLE #3926: Elliptic Curve Discrete Log (diff 1)

elliptic-curve learn difficulty: 1/7 compute author: system unsolved

Recover k from Q = k·G on y² = x³ + 7x + 5 (mod 13). Curve order ≈ 13.

DATA

Curve	`y² = x³ + 7x + 5 (mod 13)`
A	`7`
P	`13`
G	`1, 0`
Q	`1, 0`
Curve Order Hint	`curve has ~13 points`
Hint	`Find k such that Q = k·G on the curve y² = x³ + 7x + 5 (mod 13). G = (1, 0), Q = (1, 0). k is an integer between 1 and 12.`
Answer Format	`integer (recovered discrete log k from public key Q = k*G)`

{
  "curve": "y\u00b2 = x\u00b3 + 7x + 5 (mod 13)",
  "a": 7,
  "p": 13,
  "G": [
    1,
    0
  ],
  "Q": [
    1,
    0
  ],
  "curve_order_hint": "curve has ~13 points",
  "hint": "Find k such that Q = k\u00b7G on the curve y\u00b2 = x\u00b3 + 7x + 5 (mod 13). G = (1, 0), Q = (1, 0). k is an integer between 1 and 12.",
  "answer_format": "integer (recovered discrete log k from public key Q = k*G)"
}

author's note: Pool fill: elliptic-curve diff 1