Continuous authentication (CA) strengthens session security by repeatedly verifying the user during device interaction, yet it inherently relies on highly sensitive behavioral traces (e.g., fine-grained touch dynamics) that are often outsourced to cloud/edge services for scalable inference. This raises a fundamental privacy-in-use challenge: protecting behavioral features during computation, not only in transit or at rest. Fully homomorphic encryption (FHE) offers a principled solution, but deploying modern CA models under FHE remains difficult due to non-linearities and attention-style operations that incur high ciphertext cost. We propose FBAN, a TFHE-compatible Bottleneck Attention Network and an end-to-end encrypted CA framework. FBAN is designed for integer-only execution via a two-stage pipeline (floating-point pretraining followed by quantization-aware training) and is compiled into TFHE circuits for homomorphic inference. We further specify a client-server protocol with session-bound blinding and decrypt-and-return verification, enabling the server to authenticate users without observing raw behavioral features. We provide a cryptographic security analysis against an honest-but-curious server under TFHE IND-CPA security, and formalize resistance to replay and impersonation without the TFHE secret key. Experiments on two public touchscreen datasets demonstrate that FBAN achieves strong authentication utility under encrypted inference while maintaining a lightweight model footprint, with TFHE parameters instantiated at $\geq 128$-bit security.

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