Security log collection and storage are essential for organizations worldwide. Log analysis can help recognize probable security breaches and is often required by law. However, many organizations commission log management to Cloud Service Providers (CSPs), where the logs are collected, processed, and stored. Existing methods for log anomaly detection rely on unencrypted (plaintext) data, which can be a security risk. Logs often contain sensitive information about an organization or its customers. A more secure approach is always to keep logs encrypted (ciphertext). This paper presents “SigML++”, an extension of “SigML” for supervised log anomaly detection on encrypted data. SigML++ uses Fully Homomorphic Encryption (FHE) according to the Cheon–Kim–Kim–Song (CKKS) scheme to encrypt the logs and then uses an Artificial Neural Network (ANN) to approximate the sigmoid (σ(x)) activation function probabilistically for the intervals [−10,10] and [−50,50]. This allows SigML++ to perform log anomaly detection without decrypting the logs. Experiments show that SigML++ can achieve better low-order polynomial approximations for Logistic Regression (LR) and Support Vector Machine (SVM) than existing methods. This makes SigML++ a promising new approach for secure log anomaly detection.