Multiplex Coding of Bit Commitment Based on a Discrete Memoryless Channel

The bit commitment can be realized by using a noisy channel. Winter-Nascimento-Imai showed that the bit commitment capacity of a noisy channel is given by C_b = max_pNH(XY) where X and Y are the input and output of the channel. In this paper, the idea of a multiplex coding, which was first introduced into the coding problem of a wiretap channel by Kobayashi-Yamamoto-Ogawa, is applied to the bit commitment coding. The coding theorem is proved for the multiplex coding of bit commitment based on a noisy channel, and it is shown that several mutually independent secrets can be committed at the same time via a nosiy channel attaining the perfect secrecy of each secret with the total coding rate log X, where X is the cardinality of channel input alphabet.