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In attempting to solve the problems of data security, researchers, and practititioners are placing increasing emphasis on encryption. An important class of encryption schemes is that of substitution-permutation (SP) encryption networks. A variant of the SP network has been chosen by the National Bureau of Standards as the data encryption standard. In this paper, we introduce the concept of completeness, which captures the intuitive notion of complexity of SP networks. The completeness property is examined and a technique for designigning complete SP networks is demonstrated.