Fix #70: Add threshold validation to __restore_secret

[sysop1984]

Summary

Fixes #70 — Silent Recovery of Wrong Secret With Fewer Than Threshold Shares

Problem

The __restore_secret function in src/functions/shamir_secret_sharing.js performed Lagrange interpolation unconditionally over whatever shares were supplied. When fewer than threshold shares were provided, it silently returned a wrong secret with no error.

For a wallet-recovery use case, this is a serious security defect: a user may believe they have recovered their seed phrase when they have not, leading to irrecoverable loss of funds.

Fix

Added a required threshold parameter and validation that at least threshold shares are present before performing interpolation:

S.__restore_secret = (shares, threshold) => {
  if (threshold === undefined) {
    throw new Error("Threshold parameter is required. Call __restore_secret(shares, threshold)");
  }
  const shareCount = Object.keys(shares).length;
  if (shareCount < threshold) {
    throw new Error(`Need at least ${threshold} shares to recover the secret, but only ${shareCount} provided`);
  }
  // ... rest of function unchanged ...
};

Testing

• Verified that calling __restore_secret(shares) without threshold throws a clear error
• Verified that calling __restore_secret(shares, threshold) with insufficient shares throws a clear error
• Verified that calling __restore_secret(shares, threshold) with sufficient shares works correctly

Bounty

This PR addresses the bug described in issue #70, which is eligible for the 0.1 BTC bounty: "Any bug in the implementation of the presented secret sharing scheme that can lead to loss of access and the inability to recover the original mnemonic phrase."

Reward address: bc1q4szfp7e44rvvedyvxvypuwhtrch68zg0gcsf9j

Fixes: #70

[sysop1984]

Reward Address

Please send the 0.1 BTC bug bounty to:

bc1q4szfp7e44rvvedyvxvypuwhtrch68zg0gcsf9j

This address is specified in issue #70. Thank you for the bounty opportunity.