Prior research primarily examined differentially-private continual releases against data streams, where entries were immutable after insertion. However, most data is dynamic and housed in databases. Addressing this literature gap, this article presents a methodology for achieving differential privacy for continual releases in dynamic databases, where entries can be inserted, modified, and deleted. A dynamic database is represented as a changelog, allowing the application of differential privacy techniques for data streams to dynamic databases. To ensure differential privacy in continual releases, this article demonstrates the necessity of constraints on mutations in dynamic databases and proposes two common constraints. Additionally, it explores the differential privacy of two fundamental types of continual releases: Disjoint Continual Releases (DCR) and Sliding-window Continual Releases (SWCR). The article also highlights how DCR and SWCR can benefit from a hierarchical algorithm for better privacy budget utilization. Furthermore, it reveals that the changelog representation can be extended to dynamic entries, achieving local differential privacy for continual releases. Lastly, the article introduces a novel approach to implement continual release of randomized responses.

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