New Statistical Randomness Tests Based on Length of Runs

Table 6

Test results for the 128-bit outputs of AES finalists.

Statistical tests	Rijndael	Serpent	Mars	RC6	Twofish
Frequency test	0.877073	0.385771	0.100285	0.813306	0.667550
Block frequency test	0.722551	0.159257	0.801489	0.475342	0.199609
Run test	0.703085	0.000651	0.003002	0.006542	0.006737
Longest run of ones in a block	0.031990	0.661453	0.229015	0.338937	0.308989
Universal statistical test	0.006504	0.048462	0.007328	0.108877	0.023687
Linear complexity test	0.308490	0.231002	0.159494	0.662083	0.452449
Serial test^1	0.016532	0.249989	0.748831	0.307892	0.629330
Serial test^2	0.444775	0.504040	0.226215	0.602572	0.923866
Approximate entropy test	0.001276	0.070437	0.322856	0.053931	0.220444
Cumulative sums test—backward	0.271617	0.627426	0.152360	0.822441	0.838133
Cumulative sums test—forward	0.362406	0.501622	0.057094	0.971814	0.877082
Random excursion test	0.949243	0.143578	0.455967	0.307333	0.409744
Random excursions variant test	0.816055	0.042998	0.515433	0.160018	0.041629
Runs of length one test	0.535513	0.076538	0.021622	0.055930	0.008255
Runs of length two test	0.095602	0.339466	0.051861	0.057043	0.309454
Runs of length three test	0.359483	0.213636	0.388663	0.318248	0.081348

Two different versions of serial test in NIST test suite.