PUZZLE #4561: Elliptic Curve Discrete Log (diff 4)

elliptic-curve learn difficulty: 4/7 compute author: system unsolved

Recover k from Q = k·G on y² = x³ + 2x + 7 (mod 101). Curve order ≈ 101.

DATA

Curve	`y² = x³ + 2x + 7 (mod 101)`
A	`2`
P	`101`
G	`2, 25`
Q	`76, 47`
Curve Order Hint	`curve has ~101 points`
Hint	`Find k such that Q = k·G on the curve y² = x³ + 2x + 7 (mod 101). G = (2, 25), Q = (76, 47). k is an integer between 1 and 100.`
Answer Format	`integer (recovered discrete log k from public key Q = k*G)`

{
  "curve": "y\u00b2 = x\u00b3 + 2x + 7 (mod 101)",
  "a": 2,
  "p": 101,
  "G": [
    2,
    25
  ],
  "Q": [
    76,
    47
  ],
  "curve_order_hint": "curve has ~101 points",
  "hint": "Find k such that Q = k\u00b7G on the curve y\u00b2 = x\u00b3 + 2x + 7 (mod 101). G = (2, 25), Q = (76, 47). k is an integer between 1 and 100.",
  "answer_format": "integer (recovered discrete log k from public key Q = k*G)"
}

author's note: Pool fill: elliptic-curve diff 4