Commitment over Gaussian channels with deterministic identification codes

2026-10-08

AI Summary

This study addresses the limitation that the message set size of commitment protocols over Gaussian channels is constrained by conventional linear upper bounds, leaving their capacity characterization incomplete. To overcome this, the work reveals, for the first time, an intrinsic connection between commitment protocols and deterministic identification codes. By leveraging this relationship, reliable commitment schemes are constructed over additive white Gaussian noise channels, with cryptographic primitives designed for both honest-but-curious and fully malicious adversary models. The proposed approach transcends traditional limitations by elevating the message set size to a linear-logarithmic scale. Furthermore, it establishes lower bounds on commitment capacity under both adversarial scenarios, thereby refining the capacity characterization of commitment protocols over Gaussian channels.

Abstract

We establish a previously unnoticed connection between commitment (BC), a fundamental cryptographic primitive, and deterministic identification (DI), a post-Shannon communication setting. Specifically, for additive white Gaussian noise channels $\mathcal{G}$ we show that a reliable commitment protocol can be obtained from deterministic identification codes in both the honest but curious and fully dishonest security settings. This viewpoint allows BC schemes to inherit the asymptotic performance of DI codes. Indeed, we show that commitment is naturally achievable in the linearithmic regime, i.e., with message sets of size $N_n=\exp [Θ(n\log n)]$, and we establish a lower bound on the linearithmic-scale BC capacity of $\dot C_{\text{hBC}}(\mathcal G)\geq\frac12$ in the honest but curious case and $\dot C_{\text{BC}}(\mathcal G)\geq\frac14$ in the fully dishonest picture. This refines the best previously known characterisation of the commitment capacity over $\mathcal{G}$, which established only an infinite linear-scale capacity.

Problem

• Bit Commitment
• Deterministic Identification
• Gaussian Channels
• Commitment Capacity

Innovation

• Commitment
• Deterministic identification
• Gaussian channels
• Linearithmic capacity
• Post-Shannon communication