In
a secret sharing scheme (SSS), a dealer generates secret
shares from the original secret and sends them to the
participants. Some of the participants together send their
shares to a combiner and the combiner will recover the
secret using some algorithm, while if receiving some other
shares the combiner may get no information about the secret.
A (t,n)-threshold SSS means that the secret can be reconstructed
if and only if at least t out of n participants together
send their shares.
We
propose a new model of SSS which generalizes the (t,n)-threshold:
Suppose the participants are divided into k groups P_1,P_2,.....,P_k.
In order to reconstruct the secret, group P_i needs to
contribute t_i shares, while totally t shares is needed.
We will show some good properties and results of this
scheme, both in the secure point-to-point channel settings
and the partial-broadcast settings.
This
model is useful. For example, imagine that a multiparty
organization needs to agree on a new proposal, or make
some decisions. A majority-voting can be easily applied,
but if there are some big parties controlling the result,
small ones may never benefit from it. So it's a good idea
to use a similar idea with our model so that every party
may have a least quota to protect their right.