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
.

Relevant Pages

  • Re: Joint encryption?
    ... simply discards mail, so I don't have to deal with all the broken ... You don't need the "...used to gain access to the rest of the ... This is called "secret splitting", and there are a number of schemes by ... How the shares are stored is up to those charged with protecting them; ...
    (Bugtraq)
  • Re: Joint encryption?
    ... > simply discards mail, so I don't have to deal with all the broken ... >>the key can be used to gain access to ... > reconstruct the secret, but any M-1 of which can discover nothing about ... > How the shares are stored is up to those charged with protecting them; ...
    (Bugtraq)
  • Re: Secret sharing algorithm with chosen keys
    ... compute from these keys a shared secret that any T of the N persons ... But I'd like to be able to reconstruct the shared secret even ... For example, you might combine T shares thusly (forgive me, ... you don't need the tokens. ...
    (sci.crypt)
  • Re: Newbies questions about secret sharing schemes
    ... What's the simplest way to convert the secret S into an integer number ... reinterpret that as a series of GF field elements, ... tweak certain some of their shares; when you reconstruct the shared secret, ... reconstructed to something other than the actual value, but the characters ...
    (sci.crypt)
  • Re: Efficient Exponentiation of a Shared Secret
    ... shared among a number of parties. ... Shamir's scheme this is the case). ... Is there a scheme in which the secret s can be expressed as a product ... using any k out of n shares the secret x can be reconstructed, ...
    (sci.crypt)