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Understanding the flow of information is an important aspect in computer security. There has been a recent move towards tracking information in hardware and understanding the flow of individual bits through Boolean functions. Such gate level information flow tracking (GLIFT) provides a precise understanding of all flows of information. This paper presents a theoretical analysis of GLIFT. It formalizes the problem, provides fundamental definitions and properties, introduces precise symbolic representations of the GLIFT logic for basic Boolean functions, and gives analytic and quantitative analysis of the GLIFT logic.