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southerntofu OP wrote

Have you tried the demo i linked to? It's pretty intuitive.

Basically you have a secret "ACAB". Applying a special mathematical formula, you can divide it into X parts, such that Y (Y<X) parts are necessary to reconstruct ACAB.

For example, with X=4 and Y=3:

  • ACAB -> M + N + O + P
  • M + N (and other 2-part combinations) = NONSENSE
  • M + N + O = M + O + P = N + O + P = M + N + P = ACAB (all three-part combinations are valid to reconstruct the secret)

So the idea is to share a secret with some peers you do not trust 100%. Why? Either because they may turn evil, or because they may be compelled to act against you (think house search by the police).

So we divide the trust among those X peers, and mathematically enforce a threshold (Y) of necessary parts to reconstruct the secret. Two consequences:

  • if you divided the secret among X persons, you don't need all of those X persons to get back your secret if you need it, only Y persons (maybe some persons have moved, have died, have been imprisoned, or maybe they've lost the secret you gave them)
  • if a certain number of these persons have been compromised, your secret is safe (as long as this number remains below Y)

Is it more clear? Feel free to play around with the demo now and let me know if there's something you don't understand! :)

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