We compare two views of symmetric cryptographic primitives in the context of the systems that use them. We express those systems in a simple programming language; each of the views yields a semantics for the language. One of the semantics treats cryptographic operations formally (that is, symbolically). The other semantics is more detailed and computational; it treats cryptographic operations as functions on bitstrings. Each semantics leads to a definition of equivalence of systems with respect to eavesdroppers. We establish the soundness of the formal definition with respect to the computational one. This result provides a precise computational justification for formal reasoning about security against eavesdroppers.