We define a higher-order process calculus with algebraic operations
such as encryption and decryption, and develop a bisimulation proof
method for behavioral equivalence in this calculus.  Such development
has been notoriously difficult because of the subtle interactions
among generative names, processes as data, and the algebraic
operations.  We handle them by carefully defining the calculus and
adopting Sumii et al.'s environmental bisimulation, and thereby give
(to our knowledge) the first ``useful'' proof method in this setting.
We demonstrate the utility of our method through examples involving
both higher-order processes and asymmetric cryptography.