Always-on hardware Trojans pose a serious challenge to integrated circuit trust, as they remain active during normal operation and are difficult to detect in post-deployment settings without trusted golden references. This paper presents a reference-free detection framework based on cross-scale persistence analysis of electromagnetic (EM) side-channels, targeting always-on parasitic hardware behavior. The proposed method analyzes EM emissions across multiple time-frequency resolutions and constructs stability maps that capture the consistency of spectral features over repeated executions. Gaussian Mixture Models (GMMs) with Bayesian Information Criterion (BIC) based model selection are used to characterize statistical structure at each scale. We introduce cross-scale saturation, variability, and median mixture complexity metrics that quantify whether statistical structure evolves naturally or remains persistently anchored across resolutions. Experimental results on AES implementations show that Trojan-free designs exhibit scale-dependent variability consistent with transient switching behavior, while always-on Trojans produce persistent statistical signatures that suppress cross-scale evolution. Furthermore, different Trojan classes, such as workload-correlated leakage-information Trojans and independent ring-oscillator Trojans, exhibit distinct persistence patterns. These findings demonstrate that cross-scale persistence provides a physically interpretable and robust assurance signal for unsupervised, reference-free detection of always-on hardware Trojans.

翻译：始终在线硬件木马对集成电路信任构成严峻挑战，因其在正常操作期间保持激活状态，并且在缺乏可信黄金参考的后部署环境中难以检测。本文提出一种基于电磁侧信道跨尺度持续性分析的无参考检测框架，针对始终在线的寄生硬件行为。该方法分析多个时频分辨率下的电磁辐射，并构建稳定性图谱以捕获重复执行过程中频谱特征的一致性。采用基于贝叶斯信息准则模型选择的高斯混合模型来表征每个尺度下的统计结构。我们引入了跨尺度饱和性、变异性和中位数混合复杂度度量，用以量化统计结构是自然演变还是在不同分辨率间持续锚定。在AES实现上的实验结果表明，无木马设计展现出与瞬态开关行为一致的尺度依赖性变异性，而始终在线木马则产生抑制跨尺度演变的持续性统计特征。此外，不同类型的木马，例如与工作负载相关的泄漏信息木马和独立的环形振荡器木马，展现出不同的持续性模式。这些发现表明，跨尺度持续性为无监督、无参考的始终在线硬件木马检测提供了物理可解释且鲁棒的保证信号。