Re: How to refresh secret shares?

From: Henrick Hellström (henrick.hellstrm_at_telia.com)
Date: 05/04/03 

Date: Sun, 04 May 2003 21:12:39 GMT

David Wagner wrote:
> Sounds like you want proactive security / proactive cryptography.
> See the references I posted just a few weeks ago.
>
> (It sounds like one might be able to achieve your desired criterion by
> computing a random sharing of 0, i.e., r0 + ... + rn = 0, then asking
> everyone to replace their old zi by the new value zi + ri.)

How? I know you can do that with the sub shares sij that can be
reconstructed into the zi values, but how do you do that with the zi
values themselves?

A Shamir sharing of 0 will be based on a polynomial with a zero order
coefficient equal to zero. It will not necessarily be such that the sum
of all shares equals zero.

A trivial counter example: Use f(k) = 0 + k (mod 7) to share the secret
zero among three share holders. The shares will be f(1), f(2) and f(3),
and they will sum up to 6 (mod 7).

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