Split a secret into N shares where any K shares can reconstruct it. Uses polynomial interpolation over a finite field.
This tool splits a secret into N shares and rebuilds it from any K of them, where K (the threshold) is at most N. It encodes the secret as the constant term of a random polynomial of degree K-1 over a finite field, then gives each share one point on that curve; interpolating any K points recovers the polynomial, and its constant term is the secret. The surprise is that K-1 shares reveal nothing at all, not even a partial guess, because every possible secret remains equally plausible. The common mistake is treating shares as fragments that leak bits, or assuming all N shares are required.
A concrete input and expected output from the current implementation.
Input
Secret: 1234, N (shares): 5, K (threshold): 3, prime: 1613
Expected output
1: 1494 2: 329 3: 965 4: 176 5: 1188
Each share is one point on the polynomial f(x) = 1234 + 166x + 94x^2 evaluated modulo the prime 1613, whose constant term is the secret. The coefficients 166 and 94 are drawn at random, so a real run will differ; the arithmetic shown is fixed, and any three of the five points, for example (1, 1494), (2, 329), (3, 965), reconstruct 1234 by Lagrange interpolation.
Enter the secret, the number of shares N, and the threshold K. The scheme needs a finite field, so all arithmetic happens modulo a large prime. The tool builds a polynomial of degree K-1 whose constant term is the secret; the other K-1 coefficients are chosen at random. Evaluating it at N distinct x-coordinates (typically 1 through N) yields the N shares, each an (x, y) pair.
Enter any K of the N shares. A polynomial of degree K-1 is uniquely determined by K points, so the tool fits the unique curve through them via Lagrange interpolation, reads the constant term, and converts it back to the original text or number. Which K shares you choose makes no difference: any combination of K points determines the same polynomial, so the secret comes out identical.
No. Shamir sharing is information-theoretically secure: with K-1 shares, every candidate secret is exactly as plausible as every other, so no amount of computation or guessing changes anything. Your only options are obtaining the missing share or, if you still have the original secret, re-sharing it and distributing a fresh set.
No. Each run picks fresh random coefficients, so the same secret produces a completely different share set, and you cannot mix shares from two runs. If a share is lost before you need the secret, re-share and redistribute rather than guessing. The tool runs entirely in your browser, so the secret and its shares never leave your machine.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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