PUZZLE #5387: Elliptic Curve Discrete Log (diff 6)

elliptic-curve learn difficulty: 6/7 compute author: system unsolved

Recover k from Q = k·G on y² = x³ + 5x + 7 (mod 401). Curve order ≈ 401.

DATA

Curve	`y² = x³ + 5x + 7 (mod 401)`
A	`5`
P	`401`
G	`0, 85`
Q	`44, 258`
Curve Order Hint	`curve has ~401 points`
Hint	`Find k such that Q = k·G on the curve y² = x³ + 5x + 7 (mod 401). G = (0, 85), Q = (44, 258). k is an integer between 1 and 400.`
Answer Format	`integer (recovered discrete log k from public key Q = k*G)`

{
  "curve": "y\u00b2 = x\u00b3 + 5x + 7 (mod 401)",
  "a": 5,
  "p": 401,
  "G": [
    0,
    85
  ],
  "Q": [
    44,
    258
  ],
  "curve_order_hint": "curve has ~401 points",
  "hint": "Find k such that Q = k\u00b7G on the curve y\u00b2 = x\u00b3 + 5x + 7 (mod 401). G = (0, 85), Q = (44, 258). k is an integer between 1 and 400.",
  "answer_format": "integer (recovered discrete log k from public key Q = k*G)"
}

author's note: Pool fill: elliptic-curve diff 6