Secret sharing

Before to write about the possible implementation of elliptic curves over fields of characteristic 2, I want to propose another option: do some implementation over multi-public-key cryptography. This is if you have a secret that can not be trusted in only one person you can divide your secret in parts and give only one to one person. But under one reconstruction of this secret, you need all the people present.

If the secret that I said before is divided using a (n, t)-threshold scheme then your secret is shared between n players, but it can be reconstructed with t survivants from an attacker conspirator (this becomes from the thriller films).

You can create schemas with all the combination that you imagination gives. If you have a group of 10 people with a two heads, and two subgroups of four; and what you want if to have present two people of each subgroups and one of the heads (at least) you should have an schema (3-3)-threshold for the main secret and this keys to the shared secret will be re-shared as a (2-1)-threshold for the heads, and 2 (4-2)-threshold for each subgroup.

In Barcelona there are people working in this things. I meet some of them in some congresses and they are really nice people. For a long time, the secret sharing schemas have had charm for me. Could be interesting to implement this over embedded systems...