Cloud data provenance, or "what has happened to my data in the cloud", is a critical data security component which addresses pressing data accountability and data governance issues in cloud computing systems. In this paper, we present Progger (Provenance Logger), a kernel-space logger which potentially empowers all cloud stakeholders to trace their data. Logging from the kernel space empowers security analysts to collect provenance from the lowest possible atomic data actions, and enables several higher-level tools to be built for effective end-to-end tracking of data provenance. Within the last few years, there has been an increasing number of proposed kernel space provenance tools but they faced several critical data security and integrity problems. Some of these prior tools' limitations include (1) the inability to provide log tamper-evidence and prevention of fake/manual entries, (2) accurate and granular timestamp synchronisation across several machines, (3) log space requirements and growth, and (4) the efficient logging of root usage of the system. Progger has resolved all these critical issues, and as such, provides high assurance of data security and data activity audit. With this in mind, the paper will discuss these elements of high-assurance cloud data provenance, describe the design of Progger and its efficiency, and present compelling results which paves the way for Progger being a foundation tool used for data activity tracking across all cloud systems.