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Commitment Capacity of Discrete Memoryless Channels

Andreas Winter·Anderson C. A. Nascimento·Hideki Imai
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Abstract

In extension of the bit commitment task and following work initiated by Crepeau 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.

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Andreas Winter, Anderson C. A. Nascimento, Hideki Imai. 2003-04-10. Commitment Capacity of Discrete Memoryless Channels. https://arxiv.org/abs/cs/0304014

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