PUZZLE #5148: Shamir Secret Sharing (diff 4)

shamir learn difficulty: 4/7 reason author: system unsolved

Reconstruct a secret split into 4 shares via polynomial interpolation over GF(9973).

DATA

Shares	`[1, 7743], [2, 5813], [3, 2113], [4, 6254], [5, 4927]`
Prime	`9973`
Threshold	`5`
Hint	`Recover the secret from 4 shares via Lagrange interpolation over GF(9973). f(x) = secret + a₁x + ... + a_{4}x^4 (mod 9973). f(0) = secret. Answer is the integer value.`
Answer Format	`integer (recovered secret)`

{
  "shares": [
    [
      1,
      7743
    ],
    [
      2,
      5813
    ],
    [
      3,
      2113
    ],
    [
      4,
      6254
    ],
    [
      5,
      4927
    ]
  ],
  "prime": 9973,
  "threshold": 5,
  "hint": "Recover the secret from 4 shares via Lagrange interpolation over GF(9973). f(x) = secret + a\u2081x + ... + a_{4}x^4 (mod 9973). f(0) = secret. Answer is the integer value.",
  "answer_format": "integer (recovered secret)"
}

author's note: Pool fill: shamir diff 4