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This paper discusses some aspects of selecting and testing random and pseudorandom number generators. The outputs of such generators may he used in many cryptographic applications, such as the generation of key material. Generators suitable for use in cryptographic applications may need to meet stronger requirements than for other applications. In particular, their outputs must he unpredictable in the absence of knowledge of the inputs. Some criteria for characterizing and selecting appropriate generators are discussed in this document. The subject of statistical testing and its relation to cryptanalysis is also discussed, and some recommended statistical tests are provided. These tests may he useful as a first step in determining whether or not a generator is suitable for a particular cryptographic application. The design and cryptanalysis of generators is outside the scope of this paper.