A notion of open bisimulation is formulated for the spi calculus, an extension of the π-calculus with cryptographic primitives. This notion of open bisimulation is based on the so-called hedged bisimulation, due to Borgström and Nestmann. Open bisimulation is shown to be sound with respect to hedged bisimulation, and futher, open bisimilarity is shown to be a congruence relation on finite spi p...