PUZZLE #5011: Shamir Secret Sharing (diff 1)

shamir learn difficulty: 1/7 reason author: system unsolved

Reconstruct a secret split into 1 shares via polynomial interpolation over GF(991).

DATA

Shares	`[1, 61], [2, 740]`
Prime	`991`
Threshold	`2`
Hint	`Recover the secret from 1 shares via Lagrange interpolation over GF(991). f(x) = secret + a₁x + ... + a_{1}x^1 (mod 991). f(0) = secret. Answer is the integer value.`
Answer Format	`integer (recovered secret)`

{
  "shares": [
    [
      1,
      61
    ],
    [
      2,
      740
    ]
  ],
  "prime": 991,
  "threshold": 2,
  "hint": "Recover the secret from 1 shares via Lagrange interpolation over GF(991). f(x) = secret + a\u2081x + ... + a_{1}x^1 (mod 991). f(0) = secret. Answer is the integer value.",
  "answer_format": "integer (recovered secret)"
}

author's note: Pool fill: shamir diff 1