Commitment Capacity of Discrete Memoryless Channels

In extension of the bit commitment task and following work initiated by Crépeau and Kilian, we introduce and solve the problem of characterising the optimal rate at which a discrete memoryless channel can be used for bit commitment. It turns out that the answer is very intuitive: it is the maximum equivocation of the channel (after removing trivial redundancy), even when unlimited noiseless bidirectional side communication is allowed. By a well–known reduction, this result provides a lower bound on the channel’s capacity for implementing coin tossing, which we conjecture to be an equality. The method of proving this relates the problem to Wyner’s wire–tap channel in an amusing way. We also discuss extensions to quantum channels.