New Statistical Randomness Tests Based on Length of Runs

Random sequences and random numbers constitute a necessary part of cryptography. Many cryptographic protocols depend on random values. Randomness is measured by statistical tests and hence security evaluation of a cryptographic algorithm deeply depends on statistical randomness tests. In this work we focus on statistical distributions of runs of lengths one, two, and three. Using these distributions we state three new statistical randomness tests. New tests use χ2 distribution and, therefore, exact values of probabilities are needed. Probabilities associated runs of lengths one, two, and three are stated. Corresponding probabilities are divided into five subintervals of equal probabilities. Accordingly, three new statistical tests are defined and pseudocodes for these new statistical tests are given. New statistical tests are designed to detect the deviations in the number of runs of various lengths from a random sequence. Together with some other statistical tests, we analyse our tests’ results on outputs of well-known encryption algorithms and on binary expansions of e, π, and 2. Experimental results show the performance and sensitivity of our tests.