This paper investigates mechanisms that guarantee secure information flow in a computer system. These mechanisms are examined within a mathematical framework suitable for formulating the requirements of secure information flow among security classes. The central component of the model is a lattice structure derived from the security classes and justified by the semantics of information flow. The lattice properties permit concise formulations of the security requirements of different existing systems and facilitate the construction of mechanisms that enforce security. The model provides a unifying view of all systems that restrict information flow, enables a classification of them according to security objectives, and suggests some new approaches. It also leads to the construction of automatic program certification mechanisms for verifying the secure flow of information through a program.