Multiparty Computation Based on Connectivity of Graphs
In this paper, we contribute the construction of practical perfect multiparty computation protocols based on the connectivity of graphs.
Statistical Multiparty Computation Based on Random Walks on Graphs
With respect to a special class of access structures based on connectivity of graphs, we start from a linear secret sharing scheme and turn it into a secret sharing scheme with perfect security and exponentially small error probability by randomizing the reconstruction algorithm through random walks on graphs. It reduces the polynomial work space to logarithmic. Then we build the corresponding statistical multiparty computation protocol by using the secret sharing scheme. The results of this paper also imply the inherent connections and influences among secret sharing, randomized algorithms, and secure multi-party computation.