PUZZLE #4810: Elliptic Curve Discrete Log (diff 2)

elliptic-curve learn difficulty: 2/7 compute author: system unsolved

Recover k from Q = k·G on y² = x³ + 3x + 8 (mod 23). Curve order ≈ 23.

DATA

Curve	`y² = x³ + 3x + 8 (mod 23)`
A	`3`
P	`23`
G	`0, 10`
Q	`19, 1`
Curve Order Hint	`curve has ~23 points`
Hint	`Find k such that Q = k·G on the curve y² = x³ + 3x + 8 (mod 23). G = (0, 10), Q = (19, 1). k is an integer between 1 and 22.`
Answer Format	`integer (recovered discrete log k from public key Q = k*G)`

{
  "curve": "y\u00b2 = x\u00b3 + 3x + 8 (mod 23)",
  "a": 3,
  "p": 23,
  "G": [
    0,
    10
  ],
  "Q": [
    19,
    1
  ],
  "curve_order_hint": "curve has ~23 points",
  "hint": "Find k such that Q = k\u00b7G on the curve y\u00b2 = x\u00b3 + 3x + 8 (mod 23). G = (0, 10), Q = (19, 1). k is an integer between 1 and 22.",
  "answer_format": "integer (recovered discrete log k from public key Q = k*G)"
}

author's note: Pool fill: elliptic-curve diff 2