A Randomness Test Based on the Distribution of Position for Pre-Specified Pattern

Random numbers and sequences are widely used in various areas, especially the cryptography for information security. Statistical randomness test is used to evaluate the deviation from randomness. There are lots of statistical randomness tests. However, most of the randomness tests focused on the number of occurrences of pre-specified pattern, and lost the information of the distribution of occurrence position. Hence, in this paper, I proposed a new test focusing on the distribution of occurrence position of pre-specified pattern, and proved it by mathematical method. The experimental results show that there has a consistency between the new test and NIST test suite, and in the sense of the distribution of occurrence position of the pre-specified pattern, the new test has advantage over the NIST test suite.