In this scheme a secret

**(a random number modulo prime p) is split into a set of**

*s***secret shares**

*l***such that:**

*s*_{1},s_{2}, ... , s_{l}

*s*_{1}+ s_{2}+ ... + s_{l}= sWith 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 =*sets of size

^{n}C_{k}*k*such that each set is unique.

Then, create share sets for each node by including the

*i*

^{th}share in that set if the node is

*not*in the corresponding

*i*

^{th}set defined above.

This is described with an example in section 4.1 here.

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