Abstract
In the problem of USMT [1, 2] 1, a sender S and a receiver R. are connected by n= 2t+ 1 bi-directional synchronous channels (also called as wires) such that any t out of the n channels are corrupted in Byzantine fashion by an adversary jA. t, having unbounded computing power. S intends to communicate a message m to R (where m£ F and I> 1 with F being a finite field) by executing a protocol such that after interacting in terms of phases, 2 R outputs m with probability at least (1—2~") and At gets no information about m. In [2], it shown that in any single phase USMT protocol with n= 2t+ 1,Xi>'J'+ 1, where 5 denotes the message space of S, X, denotes the set of possible data sent through the ith wire and 0< 6<^ is the error probability. 4 In [2], a single phase inefficient USMT protocol with communication complexity approximately matching the above bound has been proposed. We present a single phase polynomial time USMT protocol whose communication complexity is