Commitment is a key primitive which resides at the heart of several cryptographic protocols. Noisy channels can help realize information-theoretically secure commitment schemes, however, their imprecise statistical characterization can severely impair such schemes, especially their security guarantees. Keeping our focus on channel unreliability in this work, we study commitment over unreliable continuous alphabet channels called the Gaussian unfair noisy channels or Gaussian UNCs. We present the first results on the optimal throughput or commitment capacity of Gaussian UNCs. It is known that classical Gaussian channels have infinite commitment capacity, even under finite transmit power constraints. For unreliable Gaussian UNCs, we prove the surprising result that their commitment capacity may be finite, and in some cases, zero. When commitment is possible, we present achievable rate lower bounds by constructing positive - throughput protocols under given input power constraint, and (two-sided) channel elasticity at committer Alice and receiver Bob. Our achievability results establish an interesting fact - Gaussian UNCs with zero elasticity have infinite commitment capacity - which brings a completely new perspective to why classic Gaussian channels, i.e., Gaussian UNCs with zero elasticity, have infinite capacity. Finally, we precisely characterize the positive commitment capacity threshold for a Gaussian UNC in terms of the channel elasticity, when the transmit power tends to infinity.

翻译：承诺是多种密码协议中的核心基础原语。噪声信道有助于实现信息论安全的承诺方案，然而其统计特性的不精确刻画会严重削弱此类方案，尤其是其安全保证。本文聚焦于信道的不可靠性，研究在称为高斯不公平噪声信道（Gaussian UNC）的不可靠连续字母表信道上的承诺问题。我们首次给出了高斯UNC信道的最优吞吐量（即承诺容量）的研究结果。已知经典高斯信道在有限发射功率约束下仍具有无限承诺容量。而对于不可靠的高斯UNC信道，我们证明了其承诺容量可能是有限的，甚至在某些情况下为零这一令人惊讶的结果。当承诺可行时，我们通过在给定输入功率约束及承诺方Alice与接收方Bob（双边）信道弹性条件下构造正吞吐量协议，给出了可达速率下界。我们的可达性结果揭示了一个有趣的事实——零弹性的高斯UNC信道具有无限承诺容量——这为经典高斯信道（即零弹性高斯UNC信道）为何具有无限容量提供了全新视角。最后，当发射功率趋于无穷时，我们精确刻画了高斯UNC信道正承诺容量阈值与信道弹性的关系。