Research Article

New Statistical Randomness Tests Based on Length of Runs

Table 7

Test results for the binary expansion of , , and .

Statistical test

Frequency test 0.818668 0.393382 0.820816
Block frequency test 0.069195 0.191721 0.578760
Run test 0.489904 0.409869 0.894467
Longest run of ones in a block 0.328344 0.048248 0.537307
Universal statistical test 0.930374 0.915310 0.462562
Linear complexity test 0.927809 0.208269 0.396546
Serial test1 0.924970 0.232328 0.247445
Serial test2 0.719054 0.221747 0.037551
Approximate entropy test 0.707174 0.085060 0.837672
Cumulative sums test—backward 0.373319 0.333600 0.629320
Cumulative sums test—forward 0.242488 0.313745 0.838133
Random excursion test 0.892831 0.844143 0.270246
Random excursions variant test 0.388323 0.760966 0.461287
Runs of length one test 0.241279 0.097072 0.138194
Runs of length two test 0.092391 0.129520 0.158537
Runs of length three test 0.215721 0.114384 0.076582

Two different versions of serial test in NIST test suite.