Bachelor Thesis
Secret Sharing Schemes
Secret Sharing Schemes (SSS) are used to generate and distribute the shares \(\{s_i\}_{i \in [n]}\) of a secret \(s\) among all nodes in a fixed set \(C=\{P_i\}_{i \in [n]}\), where \([n] := \{1,\dots , n\}\). In a threshold SSS with threshold \(t\), the shares are build in such a way that \(t\) shares are enough to reconstruct \(s\), but every set of \(t-1\) shares reveals nothing about the secret. One of the oldest threshold SSS is Shamir Secret Sharing, which was first introduced in 1979 and is based on Lagrange interpolation.
Another important class of secret sharing schemes is made by Linear Secret Sharing Schemes (LSSS). These schemes use linear operations to share and reconstruct the secret. Compared to threshold SSS, LSSS allow for more general structures of the qualified sets, namely the sets capable of reconstructing the secret from their shares.
The goal of this thesis is to explore the world of secret sharing schemes, along with their properties and applications. The student should also implement one or more secret sharing schemes.