On Reverse Elastic Channels and the Asymmetry of Commitment Capacity under Channel Elasticity

TL;DR

This paper characterizes the capacity for cryptographic commitment over reverse elastic channels, revealing an asymmetry where dishonest parties can more severely impact commitment throughput, and proves a related conjecture.

Contribution

It provides a tight capacity characterization for RECs, confirming a recent conjecture, and analyzes the asymmetry in commitment capacity caused by one-sided elasticity.

Findings

RECs always have positive commitment throughput for non-trivial parameters.

A dishonest party with elastic control can significantly reduce commitment capacity.

Channels with one-sided elasticity exhibit a fundamental asymmetry affecting security.

Abstract

Commitment is an important cryptographic primitive. It is well known that noisy channels are a promising resource to realize commitment in an information-theoretically secure manner. However, oftentimes, channel behaviour may be poorly characterized thereby limiting the commitment throughput and/or degrading the security guarantees; particularly problematic is when a dishonest party, unbeknown to the honest one, can maliciously alter the channel characteristics. Reverse elastic channels (RECs) are an interesting class of such unreliable channels, where only a dishonest committer, say, Alice can maliciously alter the channel. RECs have attracted recent interest in the study of several cryptographic primitives. Our principal contribution is the REC commitment capacity characterization; this proves a recent related conjecture. A key result is our tight converse which analyses a specific cheating strategy by Alice. RECs are closely related to the classic unfair noisy channels (UNCs); elastic channels (ECs), where only a dishonest receiver Bob can alter the channel, are similarly related. In stark contrast to UNCs, both RECs and ECs always exhibit positive commitment throughput for all non-trivial parameters. Interestingly, our results show that channels with exclusive one-sided elasticity for dishonest parties, exhibit a fundamental asymmetry where a committer with one-sided elasticity has a more debilitating effect on the commitment throughput than a receiver.