Health-misinformation analysis presents a dual challenge: misleading claims can affect public well-being, while systems designed to detect them may expose sensitive user-submitted text. This motivates privacy-preserving inference for public-health applications in which user queries may contain confidential medical information and trained models and reference databases are maintained on organizational servers. We design a privacy-preserving text inference framework based on CKKS homomorphic encryption for health-misinformation classification and semantic retrieval. The classification pipeline fuses BioBERT embeddings, PCA-reduced MPNet embeddings, and SVD-reduced TF-IDF features, while the retrieval pipeline combines MPNet embeddings with ISCC-SCT semantic fingerprints through late fusion. We evaluate predictive performance and benchmark plaintext versus ciphertext-based execution. The hybrid classifier achieved an accuracy of 0.971 and a macro-F1 score of 0.950, with identical reported metrics under plaintext and ciphertext-based inference. The hybrid late-fusion similarity model achieved a Pearson correlation of 0.8691 with human sentence-pair similarity scores on STS-B. For ciphertext-based retrieval, we evaluated naive and optimized implementations. The optimized implementation uses CKKS single instruction, multiple data (SIMD) packing to compute and return multiple similarity scores together, reducing single-query latency over 7,128 indexed items from 222.028 to 5.168 seconds and communication overhead from 6.11 GB to 2.13 MB. These findings demonstrate the technical feasibility of privacy-preserving text inference for health-misinformation applications and characterize its predictive utility and efficiency trade-offs.

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