Cloud-based healthcare analytics platforms process sensitive patient data — electronic health records, genomic sequences, diagnostic imaging metadata — under contractual and regulatory obligations requiring data confidentiality that conflict with the computational access needed for analytics operations. Homomorphic encryption (HE), which allows arbitrary computations on encrypted data without decryption, resolves this conflict by enabling the cloud server to execute analytics functions while the patient data remains encrypted throughout. This paper investigates the deployment of three HE schemes — CKKS, BFV, and BGV — over polynomial quotient rings Rq = Zq [x]/(xn + 1) for five representative healthcare analytics tasks: logistic regression, linear regression, neural network inference, decision tree evaluation, and SVM classification. The CKKS scheme’s approximate arithmetic over complex numbers enables direct floating-point healthcare parameter computation with controlled approximation error, while BFV provides exact integer arithmetic for classification tasks. A noise budget management algorithm dynamically allocates multiplicative depth budget across computation layers to maximize accuracy while preventing noise overflow. Experimental evaluation on the MIMIC-III clinical dataset (8,069 ICU admissions, 17 features) demonstrates that HE-assisted logistic regression achieves 93.8% accuracy versus 94.2% in plaintext, a degradation of only 0.4 percentage points attributable to CKKS approximation error, with cloud-to-client communication of 312 KB and 127 ms end-to-end inference latency. HIPAA and GDPR compliance is formally verified through the encrypted processing guarantee: the cloud server has zero access to plaintext patient data at any computation stage.