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In any secret sharing scheme a secret s is divided into a set of shares to be distributed among a set of participants in such a way that just selected groups of participants can reconstruct teh secret. A typical application consists in dividing a cryptographic key in order that just in the concurrency of a privileged set of key holders can the whole key be used.

Any set of users that can open a secret is an access set. The access structure (AS) is the collection consisting of access sets. We will deal just with monotone structures: Any set containing an access set is also an access set. Let's call circuits the minimal access sets.

Guillermo Morales-Luna