Improvements in the computing efficiency of the probabilities of the LIL test for the PRNG evaluation

The evaluation of randomness in pseudorandom numbers generators is of great importance in cryptography. For such an endeavor, there are numerous randomness testing tests. Many have been designed based on important laws of randomness, such as the central limit theorem and the law of large numbers. Recently, a novel test with three variants was proposed by Yongee Wang, based on the law of the iterated logarithm for the evaluation of pseudorandom numbers generators. Wang found severe vulnerabilities in known PRNG utilizing this test's application, which can be of great importance in evaluating cryptographic algorithms and random numbers generators. In this work, a simplification of the expressions given by Wang is presented to calculate the theoretical probabilities applied in the test to allow more efficient implementations for its three variants. (C) 2021 Elsevier B.V. All rights reserved.