Simple and communication complexity efficient almost secure and perfectly secure message transmission schemes

Recently Kurosawa and Suzuki considered almost secure (1-phase n-channel) message transmission when n=(2t+1). The authors gave a lower bound on the communication complexity and presented an exponential time algorithm achieving this bound. In this paper we present a polynomial time protocol achieving the same security properties for the same network conditions. Additionally, we introduce and formalize new security parameters to message transmission protocols which we feel are missing and necessary in the literature. We also focus on 2-phase protocols. We present a protocol achieving perfectly secure message transmission of a single message with O(n2) communication complexity in polynomial time. This is an improvement on previous protocols which achieve perfectly secure message transmission of a single message with a communication complexity of O(n3).