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Weightedness and Structural Characterization of Hierarchical Simple Games

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Secret sharing schemes—first introduced by Shamir (1979) and now widely used in many cryptographic protocols—is a tool designed for securely storing information that is highly sensitive and highly important. The set of all authorised coalitions of a secret sharing scheme is known as the access structure. It can also be modeled by a simple game. In the theory of simple games seniority of players is usually modeled by assigning to players different weights. Shamir (1979) also suggested (independently from any literature on simple games) to model seniority of users in access structure by assigning weights to them. However this approach was not actively pursued. Instead, Simmons (1990) introduced the concept of a hierarchical access structures. In this talk we will compare these two different approaches to model seniority of players. Also we will characterize hierarchical access structures from game theoretical point of view.

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