On Secret Sharing Schemes

The concept of secret sharing has been introduced independently by Shamir and Blakley, as a tool to protect a secret from getting exposed or from being lost. It allows a so-called dealer to share a secret among the members of a set P , which are usually called players or participants, in such a way that only certain specified subsets of players are able to reconstruct the secret while smaller subsets have no information about this secret at all. Since then the research on this topic has been extensive. In this paper we are going to present an overview of some approaches for building secrets sharing schemes based on well studied objects like matroids and error-correcting codes on one hand. We will start with introducing the Shamir’s polynomial scheme. Then we will talk about the relations between ideal Secret Sharing, matroids and error-correcting codes. On the other hand we will introduce linear SSS for general access structures and we will explain the approach by Cramer, Damgard and Maurer based on Monotone Span Programs. We will complete by considering error-set codes as a generalization of the notion of codes.