Friday, February 03, 2012

l:l Secret Sharing

This is yet another type of a secret sharing scheme which I came across while reading this, for a project last semester.

In this scheme a secret s (a random number modulo prime p) is split into a set of l secret shares s1,s2, ... , sl such that: s1 + s2 + ... + sl = s

With such a set of secret shares the idea is to give different combinations of these l shares to n nodes such that k of them will have to collude to be able to reconstruct s. In other words, any k-1 nodes together will not have the required shares to reconstruct the main secret.

To generate the share sets for each node :

First, generate node l = nCk sets of size k such that each set is unique.
Then, create share sets for each node by including the ith share in that set if the node is not in the corresponding ith set defined above.

This is described with an example in section 4.1 here.

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