Commitment over Unreliable Noisy Channels: When Awareness Meets Control

We study commitments over unreliable compound noisy channels, where parties may know the compound channel state but lack control over that state. Commitment is one of the common building blocks for many cryptographic protocols which realize multi-party computational functionalities in a secure manner. A noisy channel, among others, is widely acknowledged as a promising resource for realizing information-theoretically secure cryptographic primitives, including commitment. However, unreliable noisy channels with poorly or imprecisely characterized statistical behaviour can severely degrade commitment guarantees. Our focus is unreliability on account of a compound channel state, albeit under public awareness of that state.Building on prior work, we seek to characterize the optimal commitment throughput or commitment capacity of compound binary symmetric channels when parties may be state-aware. State-awareness implies a passive and publicly known capability of precise channel knowledge (whether said party is honest or dishonest); however, state-awareness precludes any active and private channel state control as in, for instance, the classic unfair noisy channels (UNCs). We present new results on the commitment capacity under all possible configurations where individual parties may (or may not) be state-aware. An important takeaway of our work is the following: even a fairly weak capability of state-awareness (albeit when asymmetric and only at the committer-side) can degrade the commitment throughput to the same extent as under strongly capable parties that can privately control the compound state.