Round-Efficient Perfectly Secure Message Transmission Scheme Against General Adversary

In the model of Perfectly Secure Message Transmission Schemes (PSMTs), there are $n$ channels between a sender and a receiver, and they share no key. An infinitely powerful adversary $A$ can corrupt (observe and forge) the messages sent through some subset of $n$ channels. For non-threshold adversaries called $Q^2$, Kumar et al. showed a many round PSMT \cite{KGSR}. In this paper, we show round efficient PSMTs against $Q^2$-adevrsaries. We first give a $3$-round PSMT which runs in polynomial time in the size of the underlying linear secret sharing scheme. We next present a $2$-round PSMT which is inefficient in general. (However, it is efficient for some special case.