Re: Variations on Shamir secret sharing



philip wrote:
Let's say you have six shares (let's call them A, B, C, D, E and F),
where a minimum of three shares are required to reconstitute the
secret. Is there a way to further divide the shares, such that for each
share, there are ten possibilities for that share? For example, ten As,
ten Bs, etc. Each is interchangeable with the other shares in it's own
letter, but you couldn't reconstitute the secret from multiple shares
within a letter.

Do the 10 shares of B have to be distinct? If not, the answer is yes. If so, why so?


My second question is if it's possible to require one of the shares.
Using the above example, let's say you need A, but any two other shares
would work.

Sure. Instead of sharing the original secret, S, itself, make up an A at random and share S^A among B-F.


--Mike Amling
.



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