HTTPS website fingerprinting (WF) aims to identify visited websites from metadata observable in encrypted traffic. However, real-world deployments introduce a significant out-of-distribution (OOD) problem caused by temporal and geographic changes, while previously unseen websites are common in open-world scenarios. Existing methods primarily learn from raw TCP packet sequences and struggle to capture stable and generalizable website representations, resulting in performance degradation under practical conditions. We propose CipherSight, a TLS-record-based hierarchical framework for robust HTTPS WF. Unlike existing approaches that rely on TCP packet sequences and are sensitive to transport-layer artifacts, CipherSight learns website representations from TLS records by jointly encoding multiple record-level attributes. It introduces a hierarchical architecture that captures both intra-flow dependencies among TLS records and inter-flow interactions across concurrent flows, enabling the model to exploit structural patterns in HTTPS traffic. Besides, to learn robust representations, CipherSight employs a masked record modeling (MRM) task to capture contextual traffic semantics and leverages fine-grained record-resource annotations as privileged supervision through structure-aware objectives and semantic distillation. Experiments show that CipherSight achieves 95.41% accuracy across more than 2,000 website classes in the closed-world setting and maintains over 90% accuracy under both temporal and geographic drift, consistently outperforming all evaluated baselines.

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