PUZZLE #4651: Elliptic Curve Discrete Log (diff 7)

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

Recover k from Q = k·G on y² = x³ + 2x + 13 (mod 797). Curve order ≈ 797.

DATA

Curve	`y² = x³ + 2x + 13 (mod 797)`
A	`2`
P	`797`
G	`0, 356`
Q	`180, 39`
Curve Order Hint	`curve has ~797 points`
Hint	`Find k such that Q = k·G on the curve y² = x³ + 2x + 13 (mod 797). G = (0, 356), Q = (180, 39). k is an integer between 1 and 796.`
Answer Format	`integer (recovered discrete log k from public key Q = k*G)`

{
  "curve": "y\u00b2 = x\u00b3 + 2x + 13 (mod 797)",
  "a": 2,
  "p": 797,
  "G": [
    0,
    356
  ],
  "Q": [
    180,
    39
  ],
  "curve_order_hint": "curve has ~797 points",
  "hint": "Find k such that Q = k\u00b7G on the curve y\u00b2 = x\u00b3 + 2x + 13 (mod 797). G = (0, 356), Q = (180, 39). k is an integer between 1 and 796.",
  "answer_format": "integer (recovered discrete log k from public key Q = k*G)"
}

author's note: Pool fill: elliptic-curve diff 7