Preserving the topology from being inferred by external adversaries has become a paramount security issue for network systems (NSs), and adding random noises to the nodal states provides a promising way. Nevertheless, recent works have revealed that the topology cannot be preserved under i.i.d. noises in the asymptotic sense. How to effectively characterize the non-asymptotic preservation performance still remains an open issue. Inspired by the deviation quantification of concentration inequalities, this paper proposes a novel metric named trace-based variance-expectation ratio. This metric effectively captures the decaying rate of the topology inference error, where a slower rate indicates better non-asymptotic preservation performance. We prove that the inference error will always decay to zero asymptotically, as long as the added noises are non-increasing and independent (milder than the i.i.d. condition). Then, the optimal noise design that produces the slowest decaying rate for the error is obtained. More importantly, we amend the noise design by introducing one-lag time dependence, achieving the zero state deviation and the non-zero topology inference error in the asymptotic sense simultaneously. Extensions to a general class of noises with multi-lag time dependence are provided. Comprehensive simulations verify the theoretical findings.

翻译：防止拓扑结构被外部对手推断已成为网络系统（NS）的关键安全问题，而在节点状态中添加随机噪声提供了一种有前景的解决方案。然而，近期研究表明，在渐近意义下，拓扑结构无法通过独立同分布噪声得到保护。如何有效刻画非渐近保护性能仍是一个开放问题。受集中不等式偏差量化的启发，本文提出了一种名为基于迹的方差-期望比的新度量。该度量有效捕捉了拓扑推断误差的衰减速率，其中较慢的速率对应更好的非渐近保护性能。我们证明，只要添加的噪声是非递增且独立的（条件弱于独立同分布），推断误差将始终渐近衰减至零。随后，我们得到了使误差衰减速率最慢的最优噪声设计。更重要的是，我们通过引入单步时滞依赖性修正噪声设计，在渐近意义下同时实现了零状态偏差与非零拓扑推断误差。本文还将结果扩展至具有多步时滞依赖性的广义噪声类别。综合仿真验证了理论发现。