发表机构
Technische Universität München; Technische Universität Braunschweig; BMFTR Research Hub 6G-life; Technische Universität Dresden; Munich Quantum Valley; Munich Center for Quantum Science and Technology; Universität zu Köln; ICREA（慕尼黑工业大学; 布伦瑞克工业大学; 6G-life研究枢纽; 德累斯顿工业大学; 慕尼黑量子谷; 慕尼黑量子科学与工程中心; 科隆大学; 加泰罗尼亚高级研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究建立了承诺（BC）与确定性识别（DI）的联系，证明可从DI码在两类安全场景中得到高斯信道的可靠BC协议，还确定了其对数线性规模BC容量的下界，完善了此前的容量表征。
AI 中文摘要
我们建立了承诺（BC，一种基础密码原语）与确定性识别（DI，一种后香农通信场景）之间此前未被注意到的联系。具体而言，针对加性高斯白噪声信道$\boldsymbol{\textit{G}}$，我们证明在半诚实好奇和完全不诚实的安全场景中，均可从确定性识别码获得可靠的承诺协议。该视角使BC方案可继承DI码的渐近性能。我们进一步证明，承诺可自然在对数线性（linearithmic） regime 中实现，即消息集大小为$N_n=\text{exp}[\boldsymbol{\textit{Θ}}(n\boldsymbol{\text{log}}n)]$；并确定半诚实好奇场景下对数线性规模BC容量的下界为$\boldsymbol{\textit{C}}_{\text{hBC}}(\boldsymbol{\textit{G}})\boldsymbol{\text{≥}}\frac{1}{2}$，完全不诚实场景下为$\boldsymbol{\textit{C}}_{\text{BC}}(\boldsymbol{\textit{G}})\boldsymbol{\text{≥}}\frac{1}{4}$。这完善了此前仅确定加性高斯白噪声信道$\boldsymbol{\textit{G}}$上承诺容量为无限线性规模的最佳表征。
英文摘要
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.
Comments13 pages, 2 figures
