Statistical testing of cryptographic randomness

Security of a cryptographic application is highly related to the quality of randomness of the mechanism used to encrypt a message. A ciphering process used to encrypt a message is mainly based on the cryptographic random numbers. There are numerous methods proposed to generate random numbers for cryptographic applications in the literature. To decide whether a cryptographic random number generator is suitable for cryptographic applications or not, various statistical randomness tests are introduced. In practice, test batteries that contain more than one randomness test are constructed and all the tests in a battery are applied to evaluate the quality of random number generator. In this article, we present a review of test batteries and recent statistical randomness tests used to evaluate output of a cryptographic random number generator. We criticize test batteries in the sense of multiple testing problem, highlight some misuses of statistical notions in hypothesis testing of cryptographic randomness, and discuss potential solutions to multiple testing problem seen in the test batteries