We introduce the spi calculus, an extension of the pi calculus designed for describing and analyzing cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols; the spi calculus enables us to consider cryptographic issues in more detail. We represent protocols as processes in the spi calculus and state their security properties in terms of coarse-grained notions of protocol equivalence.