PUZZLE #4907: Elliptic Curve Discrete Log (diff 3)

elliptic-curve learn difficulty: 3/7 compute author: system unsolved

Recover k from Q = k·G on y² = x³ + 5x + 3 (mod 47). Curve order ≈ 47.

DATA

Curve	`y² = x³ + 5x + 3 (mod 47)`
A	`5`
P	`47`
G	`0, 12`
Q	`2, 31`
Curve Order Hint	`curve has ~47 points`
Hint	`Find k such that Q = k·G on the curve y² = x³ + 5x + 3 (mod 47). G = (0, 12), Q = (2, 31). k is an integer between 1 and 46.`
Answer Format	`integer (recovered discrete log k from public key Q = k*G)`

{
  "curve": "y\u00b2 = x\u00b3 + 5x + 3 (mod 47)",
  "a": 5,
  "p": 47,
  "G": [
    0,
    12
  ],
  "Q": [
    2,
    31
  ],
  "curve_order_hint": "curve has ~47 points",
  "hint": "Find k such that Q = k\u00b7G on the curve y\u00b2 = x\u00b3 + 5x + 3 (mod 47). G = (0, 12), Q = (2, 31). k is an integer between 1 and 46.",
  "answer_format": "integer (recovered discrete log k from public key Q = k*G)"
}

author's note: Pool fill: elliptic-curve diff 3