Increasingly, administrative data is being used for statistical purposes, such as for registry-based census taking. Due to privacy concerns, this often requires linking separate files containing information on the same unit without revealing the identity of the unit. If the linkage has to be done without a unique identification number, it is necessary to compare keys derived from personal identifiers. When dealing with large files such as census data, comparing each possible pair of keys for two files is impossible. Therefore, special algorithms (blocking methods) must be used to reduce the number of comparisons needed. If the identifiers have to be encrypted due to privacy concerns, the number of available algorithms for record linkage and blocking is very limited. This paper describes the combination of a recently introduced encryption method for identifiers with a novel algorithm for blocking. Simulations show that the performance of these techniques allows their use for Big Data applications, censuses and population registries.