Long-tailed encrypted traffic classification requires accurate recognition of infrequent classes under limited computational budgets. We propose Curv-Tail, a lightweight, end-to-end packet--byte framework trained without a separate pretraining stage. Mixed-resolution tokenization preserves exact packet-length identities within a bounded range and coarsens larger values to limit the vocabulary. An auxiliary objective predicts observed length tokens from contextual packet features before pooling, encouraging length-token retention beyond flow-level supervision. Compact temporal encoders process packet sequences and directional byte patches, and Lorentz prototypes with a shared learnable curvature magnitude classify their fused representation. On NUDT-Mobile and DataCon-Website under natural class frequencies, Curv-Tail achieves three-seed mean Tail-F1 scores of 85.70% and 46.30%, exceeding the strongest evaluated baselines by 2.91 and 1.89 percentage points, respectively. In 300-class profiling on an RTX 4090 with FP32 and batch size 256, Curv-Tail uses 98.48% fewer parameters and achieves 10.2 times the batch inference throughput of MM4Flow.

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