Almost Secure (1-Round, n-Channel) Message Transmission Scheme

It is known that perfectly secure (1-round, n-channel) message transmission (MT) schemes exist if and only if n ≥ 3t + 1, where t is the number of channels that the adversary can corrupt. Then does there exist an almost secure MT scheme for n = 2t + 1 ? In this paper, we first sum up a number flaws of the previous almost secure MT scheme presented at Crypto 2004 . We next show an equivalence between almost secure MT schemes and secret sharing schemes with cheaters. By using our equivalence, we derive a lower bound on the communication complexity of almost secure MT schemes. Finally, we present a near optimum scheme which meets our bound approximately. This is the first construction of provably secure almost secure (1-round, n-channel) MT schemes for n = 2t + 1.