Retractable Commitment over Noisy Channels

Consider a commitment protocol between two parties, Alice and Bob, in which Alice may (i) commit to a message using a non-redundant discrete memoryless channel whose outputs are observed by Bob; and (ii) later reveal her committed message to Bob who must decide whether Alice is revealing the message she actually committed to. A commitment protocol should meet three standard requirements: concealment, bindingness, and soundness, to ensure that no party may act dishonestly. Our objective is to study whether one can enforce a fourth requirement that would allow Alice to retract a commitment before the reveal phase starts without Bob detecting that she ever participated in the commit phase of the protocol. We positively answer this question and characterize the commitment capacity for such a setting by relying on tools developed for covert communication.A full version of the paper is available at https://bloch.ece.gatech.edu/ITWretractablecommitment.pdf.