Communication codes enable secure commitment over noisy channels
Commitment over Gaussian channels with deterministic identification codes
Information Theory
Summary
The paper finds a new link between two ways of sending and securing messages over noisy communication channels. By using special codes called deterministic identification codes, the authors show it’s possible to create secure commitment schemes—tools that let one party lock in a secret and reveal it later. These schemes work even when the other party tries to cheat or just listens carefully. This approach improves on previous methods and establishes clearer limits on how large message sets can be while still being secure.
What this means in practice
- •For wireless communication engineers: Design communication protocols that securely commit messages over noisy Gaussian channels using deterministic identification codes.
- •For secure hardware developers: Develop hardware modules that implement reliable commitment protocols resistant to dishonest parties in noisy environments.
A theory result. No direct application yet.
Authors
Pau Colomer, Christian Deppe, Holge Boche, Andreas Winter
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.