The HAVEGE unpredictable random number generator

Examples of online analysis

06 march 2002

Outputs of HAVEGE on an UltraSparc II 300 Mhz



100 Mbytes of random numbers are generated and analyzed online.

Command : HAVEGEUII 300 100 1 150  output

The ouput file is displayed below.



Frequency test

128 bits sequence, p_value= 0.859684
256 bits sequence, p_value= 1.000000
512 bits sequence, p_value= 0.376759
1024 bits sequence, p_value= 0.661749
2048 bits sequence, p_value= 0.330915
4096 bits sequence, p_value= 0.491768
8192 bits sequence, p_value= 0.439287
16384 bits sequence, p_value= 0.937729
32768 bits sequence, p_value= 0.816523
65536 bits sequence, p_value= 0.832936
131072 bits sequence, p_value= 0.658531
262144 bits sequence, p_value= 0.802587
524288 bits sequence, p_value= 0.182167
1048576 bits sequence, p_value= 0.905164
2097152 bits sequence, p_value= 0.552606
4194304 bits sequence, p_value= 0.374179
8388608 bits sequence, p_value= 0.591582
16777216 bits sequence, p_value= 0.419311
33554432 bits sequence, p_value= 0.557003
67108864 bits sequence, p_value= 0.645019
134217728 bits sequence, p_value= 0.709617
268435456 bits sequence, p_value= 0.774776
536870912 bits sequence, p_value= 0.799939
838860800 bits sequence, p_value= 0.858762
 

 Block Frequency test

 128 bits sequence, p_value= 0.483376
 256 bits sequence, p_value= 0.680433
 512 bits sequence, p_value= 0.276756
 1024 bits sequence, p_value= 0.548780
 2048 bits sequence, p_value= 0.276756
 4096 bits sequence, p_value= 0.379230
 8192 bits sequence, p_value= 0.432627
 16384 bits sequence, p_value= 0.353969
 32768 bits sequence, p_value= 0.936701
 65536 bits sequence, p_value= 0.625353
 131072 bits sequence, p_value= 0.273888
 262144 bits sequence, p_value= 0.407183
 524288 bits sequence, p_value= 0.197956
 1048576 bits sequence, p_value= 0.145931
 2097152 bits sequence, p_value= 0.562344
 4194304 bits sequence, p_value= 0.373247
 8388608 bits sequence, p_value= 0.168498
 16777216 bits sequence, p_value= 0.617735
 33554432 bits sequence, p_value= 0.671134
 67108864 bits sequence, p_value= 0.560338
 134217728 bits sequence, p_value= 0.469776
 268435456 bits sequence, p_value= 0.648090
 536870912 bits sequence, p_value= 0.925306
 838860800 bits sequence, p_value= 0.735832
 

 Runs test

p_value=0.759846
p_value=0.051207
p_value=0.454054
p_value=0.731047
p_value=0.890744
p_value=0.382762
p_value=0.087370
p_value=0.486471
p_value=0.301210
p_value=0.793620
p_value=0.094539
p_value=0.837608
p_value=0.449758
p_value=0.337060
p_value=0.651226
p_value=0.605505
p_value=0.277494
p_value=0.823108
p_value=0.604689
p_value=0.496332
p_value=0.195909
p_value=0.551010
p_value=0.972627
p_value=0.640123
 

 LongestRunOfOnes

p_value= 0.452923
p_value= 0.696923
p_value= 0.509776
p_value= 0.111741
p_value= 0.945824
p_value= 0.711365
p_value= 0.661593
p_value= 0.167634
 

 Binary Matrix Rank test on 8 random 38,912 bit slices
 

 
p_value= 0.680524
p_value= 0.078820
p_value= 0.722524
p_value= 0.389055
p_value= 0.840029
p_value= 0.775061
p_value= 0.968938
p_value= 0.851100
 

 Discrete Fourier test by slice of 1 Mbits

 

 8 random slices are picked

p_value= 0.119935
p_value= 0.654603
p_value= 0.366867
p_value= 0.947455
p_value= 0.285921
p_value= 0.683209
p_value= 0.052187
p_value= 0.160628
 

          NON OVERLAPPING TEMPLATE MATCHING TEST
          1 random 1Mbit  slices

p_value= 0.741156
p_value= 0.748837
p_value= 0.373995
p_value= 0.528670
p_value= 0.410872
p_value= 0.752896
p_value= 0.862964
p_value= 0.475462
p_value= 0.322668
p_value= 0.714829
p_value= 0.605851
p_value= 0.167922
p_value= 0.788741
p_value= 0.433580
p_value= 0.336998
p_value= 0.578483
p_value= 0.012833
p_value= 0.070643
p_value= 0.632228
p_value= 0.995253
p_value= 0.157002
p_value= 0.245307
p_value= 0.057591
p_value= 0.071814
p_value= 0.765761
p_value= 0.458390
p_value= 0.557501
p_value= 0.532822
p_value= 0.909380
p_value= 0.967903
p_value= 0.500774
p_value= 0.316068
p_value= 0.033295
p_value= 0.759018
p_value= 0.580923
p_value= 0.596944
p_value= 0.716706
p_value= 0.504836
p_value= 0.058903
p_value= 0.919207
p_value= 0.562667
p_value= 0.255507
p_value= 0.368880
p_value= 0.251753
p_value= 0.988772
p_value= 0.926278
p_value= 0.334758
p_value= 0.363489
p_value= 0.320536
p_value= 0.436893
p_value= 0.510342
p_value= 0.645025
p_value= 0.714008
p_value= 0.684963
p_value= 0.392638
p_value= 0.692709
p_value= 0.418097
p_value= 0.547061
p_value= 0.921768
p_value= 0.148659
p_value= 0.647231
p_value= 0.981731
p_value= 0.464767
p_value= 0.936727
p_value= 0.343981
p_value= 0.933019
p_value= 0.248911
p_value= 0.533638
p_value= 0.547568
p_value= 0.303615
p_value= 0.262685
p_value= 0.380271
p_value= 0.406828
p_value= 0.867105
p_value= 0.741156
p_value= 0.452703
p_value= 0.646722
p_value= 0.013228
p_value= 0.095036
p_value= 0.644841
p_value= 0.402998
p_value= 0.199285
p_value= 0.509260
p_value= 0.629006
p_value= 0.875725
p_value= 0.720178
p_value= 0.534399
p_value= 0.334779
p_value= 0.082728
p_value= 0.309445
p_value= 0.562944
p_value= 0.150478
p_value= 0.496118
p_value= 0.242753
p_value= 0.659930
p_value= 0.512616
p_value= 0.449502
p_value= 0.649452
p_value= 0.729131
p_value= 0.716039
p_value= 0.427608
p_value= 0.669270
p_value= 0.234398
p_value= 0.218611
p_value= 0.531600
p_value= 0.700618
p_value= 0.516155
p_value= 0.043620
p_value= 0.415492
p_value= 0.503613
p_value= 0.871849
p_value= 0.892030
p_value= 0.329177
p_value= 0.683386
p_value= 0.535801
p_value= 0.490233
p_value= 0.208148
p_value= 0.466971
p_value= 0.495062
p_value= 0.197246
p_value= 0.395356
p_value= 0.577132
p_value= 0.426312
p_value= 0.214130
p_value= 0.595738
p_value= 0.210847
p_value= 0.825829
p_value= 0.906252
p_value= 0.373690
p_value= 0.568125
p_value= 0.330247
p_value= 0.727501
p_value= 0.326004
p_value= 0.818805
p_value= 0.600159
p_value= 0.153962
p_value= 0.329634
p_value= 0.717665
p_value= 0.388288
p_value= 0.860919
p_value= 0.018228
p_value= 0.722355
p_value= 0.054301
p_value= 0.154984
p_value= 0.907564
p_value= 0.056430
p_value= 0.626138
p_value= 0.867105
 

          OVERLAPPING TEMPLATE MATCHING TEST
          8 random 1000000 bits slices

m= 9, p_value= 0.945348
m= 9, p_value= 0.656550
m= 9, p_value= 0.545016
m= 9, p_value= 0.226722
m= 9, p_value= 0.353541
m= 9, p_value= 0.153744
m= 9, p_value= 0.175219
m= 9, p_value= 0.050390
 

 Maurer's Universal test

 For each of the L parameters, we test  the beginning of the sequence

L= 6    p_value 0.973904        exp_value= 5.217705     phi = 5.217623
L= 7    p_value 0.881806        exp_value= 6.196251     phi = 6.196536
L= 8    p_value 0.231790        exp_value= 7.183666     phi = 7.185372
L= 9    p_value 0.061617        exp_value= 8.176425     phi = 8.174466
L= 10   p_value 0.366241        exp_value= 9.172324     phi = 9.171636
L= 11   p_value 0.972803        exp_value= 10.170032    phi = 10.170013
L= 12   p_value 0.258765        exp_value= 11.168765    phi = 11.169212
L= 13   p_value 0.336290        exp_value= 12.168070    phi = 12.168343
L= 14   p_value 0.288814        exp_value= 13.167693    phi = 13.167908
L= 15   p_value 0.561631        exp_value= 14.167488    phi = 14.167393
 

          LEMPEL-ZIV COMPRESSION TEST: 8 random slices of  1000000 bits

p_value= 0.016713
p_value= 0.932605
p_value= 0.200019
p_value= 0.628152
p_value= 0.537151
p_value= 0.037837
p_value= 0.671411
p_value= 0.946555
 

          LINEAR COMPLEXITY TEST: 1 SLICE OF 4731 * 371 bits

p_value= 0.183616
 

          SERIAL TEST  BY SLICE OF 1000000 bits

p_value1= 0.183158
p_value2= 0.376814
p_value1= 0.875064
p_value2= 0.851663
p_value1= 0.067615
p_value2= 0.106389
p_value1= 0.308652
p_value2= 0.659158
p_value1= 0.297667
p_value2= 0.211565
p_value1= 0.914168
p_value2= 0.514937
p_value1= 0.261324
p_value2= 0.200530
p_value1= 0.863348
p_value2= 0.954832
 

          APPROXIMATE ENTROPY TEST

m= 3,    p_value= 0.304343, Entropy per 3 bits 3.000000
m= 4,    p_value= 0.198516, Entropy per 4 bits 4.000000
m= 5,    p_value= 0.270585, Entropy per 5 bits 5.000000
m= 6,    p_value= 0.679001, Entropy per 6 bits 6.000000
m= 7,    p_value= 0.813160, Entropy per 7 bits 7.000000
m= 8,    p_value= 0.302308, Entropy per 8 bits 8.000000
m= 9,    p_value= 0.603694, Entropy per 9 bits 9.000000
m= 10,   p_value= 0.445297, Entropy per 10 bits 9.999999
m= 11,   p_value= 0.400090, Entropy per 11 bits 10.999998
m= 12,   p_value= 0.164173, Entropy per 12 bits 11.999996
m= 13,   p_value= 0.142385, Entropy per 13 bits 12.999993
m= 14,   p_value= 0.254275, Entropy per 14 bits 13.999986
m= 15,   p_value= 0.243901, Entropy per 15 bits 14.999972
m= 16,   p_value= 0.039251, Entropy per 16 bits 15.999943
 

          CUSUM  TEST

128 bits sequence, forward p_value= 0.949266
128 bits sequence, reverse p_value= 0.818770
256 bits sequence, forward p_value= 0.629223
256 bits sequence, reverse p_value= 0.422245
512 bits sequence, forward p_value= 0.614230
512 bits sequence, reverse p_value= 0.139984
1024 bits sequence, forward p_value= 0.857965
1024 bits sequence, reverse p_value= 0.573148
2048 bits sequence, forward p_value= 0.654761
2048 bits sequence, reverse p_value= 0.186156
4096 bits sequence, forward p_value= 0.789313
4096 bits sequence, reverse p_value= 0.338189
8192 bits sequence, forward p_value= 0.584515
8192 bits sequence, reverse p_value= 0.362407
16384 bits sequence, forward p_value= 0.968242
16384 bits sequence, reverse p_value= 0.870750
32768 bits sequence, forward p_value= 0.856883
32768 bits sequence, reverse p_value= 0.665021
65536 bits sequence, forward p_value= 0.764070
65536 bits sequence, reverse p_value= 0.934663
131072 bits sequence, forward p_value= 0.803919
131072 bits sequence, reverse p_value= 0.859177
262144 bits sequence, forward p_value= 0.383817
262144 bits sequence, reverse p_value= 0.573148
524288 bits sequence, forward p_value= 0.149186
524288 bits sequence, reverse p_value= 0.299447
1048576 bits sequence, forward p_value= 0.646275
1048576 bits sequence, reverse p_value= 0.748584
2097152 bits sequence, forward p_value= 0.832744
2097152 bits sequence, reverse p_value= 0.475104
4194304 bits sequence, forward p_value= 0.309802
4194304 bits sequence, reverse p_value= 0.426159
8388608 bits sequence, forward p_value= 0.824575
8388608 bits sequence, reverse p_value= 0.858605
16777216 bits sequence, forward p_value= 0.371042
16777216 bits sequence, reverse p_value= 0.678039
33554432 bits sequence, forward p_value= 0.868093
33554432 bits sequence, reverse p_value= 0.735251
67108864 bits sequence, forward p_value= 0.749611
67108864 bits sequence, reverse p_value= 0.841357
134217728 bits sequence, forward p_value= 0.652841
134217728 bits sequence, reverse p_value= 0.837686
268435456 bits sequence, forward p_value= 0.605395
268435456 bits sequence, reverse p_value= 0.866301
536870912 bits sequence, forward p_value= 0.857960
536870912 bits sequence, reverse p_value= 0.786349
838860800 bits sequence, forward p_value= 0.960978
838860800 bits sequence, reverse p_value= 0.861488
 

          RANDOM EXCURSION TEST: 8 SLICE OF 1000000 bits

p_value= 0.415327
p_value= 0.284268
p_value= 0.071051
p_value= 0.071260
p_value= 0.034064
p_value= 0.911566
p_value= 0.932834
p_value= 0.996834

                ---------------------------------------------
                WARNING:  TEST NOT APPLICABLE.  THERE ARE AN
          INSUFFICIENT NUMBER OF CYCLES.
                ---------------------------------------------

                ---------------------------------------------
                WARNING:  TEST NOT APPLICABLE.  THERE ARE AN
          INSUFFICIENT NUMBER OF CYCLES.
                ---------------------------------------------

p_value= 0.311816
p_value= 0.747248
p_value= 0.416256
p_value= 0.813414
p_value= 0.081590
p_value= 0.502168
p_value= 0.947755
p_value= 0.776549

                ---------------------------------------------
                WARNING:  TEST NOT APPLICABLE.  THERE ARE AN
          INSUFFICIENT NUMBER OF CYCLES.
                ---------------------------------------------

                ---------------------------------------------
                WARNING:  TEST NOT APPLICABLE.  THERE ARE AN
          INSUFFICIENT NUMBER OF CYCLES.
                ---------------------------------------------

                ---------------------------------------------
                WARNING:  TEST NOT APPLICABLE.  THERE ARE AN
          INSUFFICIENT NUMBER OF CYCLES.
                ---------------------------------------------

                ---------------------------------------------
                WARNING:  TEST NOT APPLICABLE.  THERE ARE AN
          INSUFFICIENT NUMBER OF CYCLES.
                ---------------------------------------------
 
 

          RANDOM EXCURSION TEST VARIANT: 8 SLICES OF 1000000 bits

p_value= 0.413484
p_value= 0.426051
p_value= 0.381549
p_value= 0.323357
p_value= 0.241159
p_value= 0.353148
p_value= 0.271935
p_value= 0.087208
p_value= 0.123223
p_value= 0.289280
p_value= 0.366088
p_value= 0.575425
p_value= 0.642468
p_value= 0.653020
p_value= 0.616333
p_value= 0.794470
p_value= 0.827704
p_value= 0.567021
 

                WARNING:  TEST NOT APPLICABLE.  THERE ARE AN
          INSUFFICIENT NUMBER OF CYCLES.
                ---------------------------------------------
 

                WARNING:  TEST NOT APPLICABLE.  THERE ARE AN
          INSUFFICIENT NUMBER OF CYCLES.
                ---------------------------------------------

p_value= 0.433615
p_value= 0.482533
p_value= 0.482533
p_value= 0.453921
p_value= 0.405503
p_value= 0.340977
p_value= 0.651901
p_value= 0.937229
p_value= 0.541846
p_value= 0.481187
p_value= 0.210476
p_value= 0.157923
p_value= 0.258981
p_value= 0.206007
p_value= 0.128595
p_value= 0.150013
p_value= 0.261292
p_value= 0.433587
p_value= 0.816124
 

                WARNING:  TEST NOT APPLICABLE.  THERE ARE AN
          INSUFFICIENT NUMBER OF CYCLES.
                ---------------------------------------------
 

                WARNING:  TEST NOT APPLICABLE.  THERE ARE AN
          INSUFFICIENT NUMBER OF CYCLES.
                ---------------------------------------------
 

                WARNING:  TEST NOT APPLICABLE.  THERE ARE AN
          INSUFFICIENT NUMBER OF CYCLES.
                ---------------------------------------------
 

                WARNING:  TEST NOT APPLICABLE.  THERE ARE AN
          INSUFFICIENT NUMBER OF CYCLES.
                ---------------------------------------------