Commitment over Gaussian channels with deterministic identification codes

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 $N_n=\exp [\mathrm{\Theta }(n\log n)]$, and we establish a lower bound on the linearithmic-scale BC capacity of ${\dot{C}}_{\text{hBC}}(\mathcal{G})\ge \frac{1}{2}$ in the honest but curious case and ${\dot{C}}_{\text{BC}}(\mathcal{G})\ge \frac{1}{4}$ 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.