The final quarter of the 20th century has seen the establishment of a global computational infrastructure. This and the advent of programming languages such as Java, supporting mobile distributed computing, has posed a significant challenge to computer sciences. The infrastructure can support commerce, medicine and government, but only if communications and computing can be secured against catastrophic failure and malicious interference. This text discusses all aspects of secure computation and communication, focusing especially on the mathematical foundations on which programming languages and communication systems are built. It considers the role of semantics in system performance and responsiveness, and covers constructive type theory, work on linear logic, game semantics and feasible mathematics.