We propose a type system for an imperative programming language, which certifies program time bounds. This type system is based on secure flow information analysis. Each program variable has a level and we prevent information from flowing from low level to higher level variables. We also introduce a downgrading mechanism in order to delineate a broader class of programs. Thus, we propose a relation between security-typed language and implicit computational complexity. We establish a characterization of the class of polynomial time functions.