Access Structure

Related Concepts

Perfectly Secure Message Transmission; Secure Multiparty Computation (SMC); Secret Sharing Schemes; Visual Secret Sharing Schemes

Definition

Access structure: [2]

Definition 1

Let $\mathcal{P}$ be a set of parties. An access structure ${\Gamma }_{\mathcal{P}}$ is a subset of the powerset ${2}^{\mathcal{P}}$. (Each element ${\Gamma }_{\mathcal{P}}$ is considered trusted, e.g., has  access to a shared secret.) ${\Gamma }_{\mathcal{P}}$ is monotone if for each element of ${\Gamma }_{\mathcal{P}}$ each superset belongs to ${\Gamma }_{\mathcal{P}}$, formally: when $\mathcal{A}\subseteq \mathcal{B}\subseteq \mathcal{P}$ and $\mathcal{A}\in {\Gamma }_{\mathcal{P}}$ then $\mathcal{B}\in {\Gamma }_{\mathcal{P}}$.

Adversary structure: [1]

Definition 2

An adversary structure is the complement of an access structure, formally, if ${\Gamma }_{\mathcal{P}}$ is an access structure, then ${2}^{\mathcal{P}}\setminus {\Gamma }_{\mathcal{P}}$is an adversary...