Commitment over Gaussian channels with deterministic identification codes
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 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 Nn=exp [Θ(nlog n)], and we establish a lower bound on the linearithmic-scale BC capacity of ĊhBC(𝒢)≥1/2 in the honest but curious case and ĊBC(𝒢)≥1/4 in the fully dishonest picture. This refines the best previously known characterisation of the commitment capacity over 𝒢, which established only an infinite linear-scale capacity.
Related
- Deterministic Identification over Additive Gaussian Channels
- Secure Deterministic Identification with Feedback and Sensing over State-Dependent Wiretap Channels
- Gaussian Identification in MIMO Channels
- Identification for Inverse Gaussian Channels
- Classical Commitment over Quantum Channels with Limited Entanglement Assistance
BibTeX
@misc{colomer2026commitment,
title = {{Commitment over Gaussian channels with deterministic identification codes}},
author = {Pau Colomer and Christian Deppe and Holge Boche and Andreas Winter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12413},
eprint = {2610.12413},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12413},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Commitment over Gaussian channels with deterministic identification codes
AU - Pau Colomer
AU - Christian Deppe
AU - Holge Boche
AU - Andreas Winter
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12413
UR - https://arxiv.org/abs/2610.12413
AB - 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 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(nlog n)], and we establish a lower bound on the linearithmic-scale BC capacity of Ċ_hBC(𝒢)≥1/2 in the honest but curious case and Ċ_BC(𝒢)≥1/4 in the fully dishonest picture. This refines the best previously known characterisation of the commitment capacity over 𝒢, which established only an infinite linear-scale capacity.
ER -