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Many sensitive applications require that data remain confidential and undisclosed, even for intrusion detection objectives. For this purpose, the detection of anomalies in encrypted data has become increasingly vital. Deep learning models are becoming good tools to detect anomalies in encrypted data without the need to pass through data decryption. This paper presents a systematic review focusing on the advancements made in deep learning models for intrusion detection over encrypted data with privacy preservation. This study aims to guide researchers on how to select the right tools to set up an intrusion detection system over encrypted data with privacy preservation. The study presented the context and challenges of intrusion detection on encrypted data and how machine learning-based solutions can circumvent these challenges. The paper looks at recently proposed solutions, examines metrics for assessing model performance, and evaluates frequently used reference datasets. Deep learning models are also evaluated with statistics on the most frequent models, datasets, and encryption tools. The performance metrics of the studied solutions are investigated as a function of the encryption tools, the deployed deep learning models, the privacy preservation tools, the deployed datasets, and the eventual additional tools and algorithms. Our recommendations help researchers evaluate their proposals for preserving privacy and detecting intrusions on encrypted data using deep learning techniques. [ABSTRACT FROM AUTHOR]