Home Forums TrueRNG Hardware random number generator Unreachable random numbers?

This topic contains 10 replies, has 3 voices, and was last updated by  Quadko 1 year, 2 months ago.

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  • #1747

    Quadko
    Member

    I’ve got a more general (t)RNG question that’s been bugging me a while – if there’s a better place to ask, please feel free to point me there, and I may just be displaying my ignorance.

    Using random numbers for software testing rather than crypto related (fuzz testing, wide range of input values testing, etc.), it seems like there are “ungeneratable” numbers using all the RNG methods I’ve seen. Maybe I’m wrong? In particular, there seems to be huge bias against runs of identical bits, even to the point where such runs are whitened out. With a coin I “can” get 32 heads, it’s just unlikely. With the (t|ps)RNG methods I’ve read they appear impossible. (For example, the “proof” of randomness of a method being an image of static with no solid lines in it…)

    And I don’t just mean “unlikely”, but downright impossible to generate more than N 0s or 1s, because either the psudorandom method or the digitization method and processing window apparently disallows it.

    This is great for an XOR pad – zero bytes are even suppressed sometimes when they are possible. But for test data, if I can never generate a 32 or 64 bit number (int or real) with more than a run of 3 (or 5 or 10 or whatever) 0 or 1 bits, it seems like whole classes of interesting numbers are excluded from such tests, including all 0 and all 1 values, but also all numbers with 16 same-bit runs in them.

    Or does the bias exist but there are tricks around this like always XORing two randomly generated bitstrings or other more complicated but mathematically proven algorithms?

    Anyway, any thoughts, or anything I should go read, or am I totally off-base?

    #1748

    ubld.it
    Keymaster

    Quadko,

    For the TrueRNG, each bit has probability of 0.5. The probability of getting 2 1′s in a row is 0.5 x 0.5 =0.25. Or 0.5^2. The probability of getting 32 1′s in a row is 0.5^32 = 2.3283064e-10 or about 1 in 4294967296 which would occur about every 24 minutes with the TrueRNGpro at 3 Mbps.

    With most pseudo random generators, you will never see 32 zeros but will see every other state unless it is running through a FIPS-140-2 filter which eliminates certain patterns.

    #1749

    ubld.it
    Keymaster

    It’s also worth mentioning that with the TrueRNGPro, you can turn off the whitening algorithm. This gives you access to the raw random numbers before any xoring or merging of samples is done.

    Typically the reason you see a even distribution is due to the whitening. The raw values (if they are of interest to you) produce more of a bell curve. Which when plotted — look like a bell. The center of the bell being the most common values, and the outlayers 0 and 255 being the least common number. Some of our customers are more interested in this or implement their own whitening algorithm using this data. This is more in line with your flipping a coin analogy and getting heads more times in a row than you do from a random number generator.

    As for the ‘un-generatable’ numbers, I’m still a little confused because if you check the distribution of a sample set, you will see that all bytes have a pretty even distribution, if you count the frequency of each byte (which you can do with “ent -c” in linux) . If you were to plot the count of each byte, they will be within the same order of magnitude of each other, which means all numbers are generated at about the same frequency.

    I hope this helps further answer your question.

    • This reply was modified 1 year, 3 months ago by  ubld.it.
    #1754

    Quadko
    Member

    Thanks for the details! Again, I may just be putting my ignorance on display and I appreciate the info and discussion. I think your comment about whitening vs. raw and the bell curve is likely what I have in mind. If you don’t mind clarification discussion:

    I certainly understand for physical processes generating unbiased bits we are absolutely good. And I haven’t gotten to play with TrueRNG yet, so this is purely a theoretical understanding question from looking at PRNG and random.org articles and data in the past, and wondering if it applies to something like TrueRNGPro.

    When articles talk about using sound sources or random.org’s atmospheric samples, they talk about adjusting the A->D 0/1 bit conversion levels range based on a running window analyzing bit deviation from 50%, so input data doesn’t drift toward all zeros or ones because of input amplitude changes. But isn’t an artifact of that reducing the chance to generate “honest” runs of such bits? Similar considerations appear with the selection of PRNG algorithm details. Maybe this doesn’t apply to all physical methods of generating bits?

    (Trivial example of my fear/understanding: a heuristic A->D window or PRNG algorithm forced to produce exactly 50% 0::1 ratio across 4 bits would be bad! That forces the random values to be: 1100, 1010, 1001, 0101, 0110, 0011. Only 6 values out of 16 allowed by algorithm, and neither the “interesting for testing purposes” extremes of 0000 or 1111 included!)

    So I was under the impression that an artifact of heuristic tuning is the longer runs of bits are made even less likely than the purely statistical likelihood of a 50% per coin-flip run. In another example poor quality algorithm, perhaps generating 8 zero bits in a row is a perfect 1 in 2^8 likelihood. But generating 16 zero bits in a row is only half as likely as a perfect 1 in 2^16, and the algorithm will never allow the generation 32 zero bits in a row.

    I also thought this was acceptable and on purpose because of the use in cryptography – all zero bytes are often unwanted, much less 4 or 8 of them in a row.

    Even assuming I’m not just ignorant of the real details, possible I am down some weird thought path and need my thinking corrected? Perhaps the statistical degradation involved don’t kick in until 2^billion or something, and the analysis window makes sure we have appropriate approximately 50% bit distribution over a megabyte, not something short and bad like a window of 64 bits?

    Again, this question in my brain was around randomly testing inputs in a 2^32 or 2^64 input space and wondering if the numbers really were equally possible or if binary numbers with “long” runs of same bits in the larger space were less likely. (ex: is 0×0000001 w/ run of 27 0s really as likely as numbers like 0xa5a5a5a5 with runs of only 2)? Easily solved for testing purposes by randomly/exhaustively testing ranges around interesting numbers like zero, but piqued my curiosity about generating randomness.

    • This reply was modified 1 year, 3 months ago by  Quadko.
    #1757

    Quadko
    Member

    * Last paragraph: “27 0s” – what was I thinking? 31 zero bytes is what I meant, of course. :)

    #1771

    euler357
    Member

    Yes, the outputs that you get from a TrueRNG/TrueRNGpro running in normal mode are equally probable.

    We use the avalanche effect in a semiconductor junction in two generators which are captured by 10 bit ADCs. The ADC bias is dealt with using an algorithm that maximizes the entropy and “spreads” the bias across the entire sample.

    Each 10 bit ADC sample from each generator has about 6.5 – 7 bits of Shannon entropy. These are combined using an entropy mixing algorithm (multiplication in a galois field — similar to a CRC) to concentrate the entropy. This takes in eight 10-bit samples and outputs four 8 bit bytes. So we are taking in 52 to 56 bits of entropy and mixing them to saturate the entropy across all 32 output bits (i.e. maximizing entropy). This is then XOR’d with a whitening sequence.

    So, yes, the probability of getting each byte is equal. The reality of a capture will show some variation among the bytes actually captured. Similarly, each 32 bit word will be equally likely. In a pseudo random generator, the algorithm usually guarantees that each symbol will appear an equal number of times in a finite sequence. The issue is that if a generator has a period of 256 bytes (small number for the sake of this argument) and you have 255 bytes output, then you know exactly what the next byte will be. It may be harder to guess if you have a longer period but the problem is the same.

    Here is the frequency count output of the ent tool ran on a 1MB capture from a TrueRNGpro (running under Linux on a Raspberry PI 3). The actual counts of each byte vary between runs with no discernible pattern. You can see below that the occurance of each byte is about 4000 counts (1024000 / 256).

    root@raspberrypi:/home/pi/workspace/TrueRNG_Windows_Python# ent -c test.bin
    Value Char Occurrences Fraction
      0             4113   0.004017
      1             3918   0.003826
      2             3993   0.003899
      3             4072   0.003977
      4             4071   0.003976
      5             3983   0.003890
      6             3870   0.003779
      7             4044   0.003949
      8             4129   0.004032
      9             4022   0.003928
     10             4021   0.003927
     11             3928   0.003836
     12             4006   0.003912
     13             3912   0.003820
     14             3954   0.003861
     15             4035   0.003940
     16             4073   0.003978
     17             3925   0.003833
     18             3972   0.003879
     19             4058   0.003963
     20             3942   0.003850
     21             3945   0.003853
     22             4015   0.003921
     23             4038   0.003943
     24             3887   0.003796
     25             3893   0.003802
     26             4090   0.003994
     27             4048   0.003953
     28             3978   0.003885
     29             3931   0.003839
     30             4011   0.003917
     31             3965   0.003872
     32             4002   0.003908
     33   !         4045   0.003950
     34   "         4002   0.003908
     35   #         4084   0.003988
     36   $         3904   0.003812
     37   %         4023   0.003929
     38   &         4034   0.003939
     39   '         3877   0.003786
     40   (         3913   0.003821
     41   )         3909   0.003817
     42   *         4041   0.003946
     43   +         3967   0.003874
     44   ,         4036   0.003941
     45   -         3967   0.003874
     46   .         4022   0.003928
     47   /         4031   0.003937
     48   0         3994   0.003900
     49   1         4042   0.003947
     50   2         3980   0.003887
     51   3         3960   0.003867
     52   4         4092   0.003996
     53   5         3861   0.003771
     54   6         3939   0.003847
     55   7         3949   0.003856
     56   8         4021   0.003927
     57   9         4035   0.003940
     58   :         4040   0.003945
     59   ;         4123   0.004026
     60   <         3997   0.003903
     61   =         3977   0.003884
     62   >         4053   0.003958
     63   ?         3957   0.003864
     64   @         4103   0.004007
     65   A         3928   0.003836
     66   B         4016   0.003922
     67   C         4051   0.003956
     68   D         3935   0.003843
     69   E         3950   0.003857
     70   F         4024   0.003930
     71   G         3997   0.003903
     72   H         4058   0.003963
     73   I         3948   0.003855
     74   J         3928   0.003836
     75   K         4133   0.004036
     76   L         4053   0.003958
     77   M         3976   0.003883
     78   N         4070   0.003975
     79   O         4068   0.003973
     80   P         4037   0.003942
     81   Q         3994   0.003900
     82   R         4010   0.003916
     83   S         3981   0.003888
     84   T         4114   0.004018
     85   U         3960   0.003867
     86   V         3940   0.003848
     87   W         4020   0.003926
     88   X         4056   0.003961
     89   Y         3937   0.003845
     90   Z         3946   0.003854
     91   [         4105   0.004009
     92   \         4050   0.003955
     93   ]         4044   0.003949
     94   ^         4076   0.003980
     95   _         3870   0.003779
     96   X         3955   0.003862
     97   a         3982   0.003889
     98   b         3935   0.003843
     99   c         3912   0.003820
    100   d         3962   0.003869
    101   e         4069   0.003974
    102   f         3989   0.003896
    103   g         3963   0.003870
    104   h         3904   0.003812
    105   i         4014   0.003920
    106   j         3970   0.003877
    107   k         4054   0.003959
    108   l         4016   0.003922
    109   m         3977   0.003884
    110   n         3986   0.003893
    111   o         4012   0.003918
    112   p         3926   0.003834
    113   q         4030   0.003936
    114   r         4019   0.003925
    115   s         4011   0.003917
    116   t         3890   0.003799
    117   u         4036   0.003941
    118   v         3897   0.003806
    119   w         3955   0.003862
    120   x         4006   0.003912
    121   y         3988   0.003895
    122   z         3907   0.003815
    123   {         4042   0.003947
    124   |         4032   0.003938
    125   }         4044   0.003949
    126   ~         3921   0.003829
    127             4000   0.003906
    128             4032   0.003938
    129             4059   0.003964
    130             4109   0.004013
    131             3932   0.003840
    132             3992   0.003898
    133             3981   0.003888
    134             4022   0.003928
    135             4028   0.003934
    136             4066   0.003971
    137             3983   0.003890
    138             3941   0.003849
    139             3957   0.003864
    140             3886   0.003795
    141             4041   0.003946
    142             3957   0.003864
    143             3986   0.003893
    144             3898   0.003807
    145             4110   0.004014
    146             3935   0.003843
    147             4010   0.003916
    148             4094   0.003998
    149             3938   0.003846
    150             3952   0.003859
    151             3970   0.003877
    152             3974   0.003881
    153             4013   0.003919
    154             3971   0.003878
    155             4021   0.003927
    156             4064   0.003969
    157             4061   0.003966
    158             4138   0.004041
    159             4004   0.003910
    160             4145   0.004048
    161   ▒         4006   0.003912
    162   ▒         4087   0.003991
    163   ▒         3890   0.003799
    164   ▒         3992   0.003898
    165   ▒         3941   0.003849
    166   ▒         4137   0.004040
    167   ▒         4017   0.003923
    168   ▒         4011   0.003917
    169   ▒         3993   0.003899
    170   ▒         3881   0.003790
    171   ▒         4037   0.003942
    172   ▒         3988   0.003895
    173   ▒         4020   0.003926
    174   ▒         4130   0.004033
    175   ▒         4059   0.003964
    176   ▒         3991   0.003897
    177   ▒         3947   0.003854
    178   ▒         3965   0.003872
    179   ▒         4053   0.003958
    180   ▒         3962   0.003869
    181   ▒         4027   0.003933
    182   ▒         3902   0.003811
    183   ▒         3871   0.003780
    184   ▒         4088   0.003992
    185   ▒         4071   0.003976
    186   ▒         4070   0.003975
    187   ▒         4021   0.003927
    188   ▒         3923   0.003831
    189   ▒         3967   0.003874
    190   ▒         3991   0.003897
    191   ▒         3905   0.003813
    192   ▒         4125   0.004028
    193   ▒         3934   0.003842
    194   ▒         4063   0.003968
    195   ▒         3880   0.003789
    196   ▒         4064   0.003969
    197   ▒         4037   0.003942
    198   ▒         4028   0.003934
    199   ▒         4057   0.003962
    200   ▒         4024   0.003930
    201   ▒         3988   0.003895
    202   ▒         3943   0.003851
    203   ▒         3950   0.003857
    204   ▒         3924   0.003832
    205   ▒         4079   0.003983
    206   ▒         4062   0.003967
    207   ▒         3945   0.003853
    208   ▒         4047   0.003952
    209   ▒         3923   0.003831
    210   ▒         4008   0.003914
    211   ▒         3938   0.003846
    212   ▒         4095   0.003999
    213   ▒         3943   0.003851
    214   ▒         4089   0.003993
    215   ▒         3965   0.003872
    216   ▒         3876   0.003785
    217   ▒         4022   0.003928
    218   ▒         4100   0.004004
    219   ▒         4097   0.004001
    220   ▒         4036   0.003941
    221   ▒         3963   0.003870
    222   ▒         4082   0.003986
    223   ▒         4106   0.004010
    224   ▒         4019   0.003925
    225   ▒         4049   0.003954
    226   ▒         3945   0.003853
    227   ▒         4023   0.003929
    228   ▒         4002   0.003908
    229   ▒         4029   0.003935
    230   ▒         4042   0.003947
    231   ▒         4048   0.003953
    232   ▒         4004   0.003910
    233   ▒         3884   0.003793
    234   ▒         3947   0.003854
    235   ▒         3953   0.003860
    236   ▒         4111   0.004015
    237   ▒         4042   0.003947
    238   ▒         4033   0.003938
    239   ▒         4059   0.003964
    240   ▒         3976   0.003883
    241   ▒         3996   0.003902
    242   ▒         4120   0.004023
    243   ▒         4098   0.004002
    244   ▒         3983   0.003890
    245   ▒         3971   0.003878
    246   ▒         4027   0.003933
    247   ▒         3931   0.003839
    248   ▒         4020   0.003926
    249   ▒         4024   0.003930
    250   ▒         3939   0.003847
    251   ▒         3935   0.003843
    252   ▒         3965   0.003872
    253   ▒         3937   0.003845
    254   ▒         3938   0.003846
    255   ▒         3843   0.003753
    
    Total:       1024000   1.000000
    
    Entropy = 7.999812 bits per byte.
    
    Optimum compression would reduce the size
    of this 1024000 byte file by 0 percent.
    
    Chi square distribution for 1024000 samples is 266.78, and randomly
    would exceed this value 50.00 percent of the times.
    
    Arithmetic mean value of data bytes is 127.5356 (127.5 = random).
    Monte Carlo value for Pi is 3.141973211 (error 0.01 percent).
    Serial correlation coefficient is 0.000399 (totally uncorrelated = 0.0).
    • This reply was modified 1 year, 3 months ago by  euler357.
    • This reply was modified 1 year, 3 months ago by  euler357.
    #1772

    euler357
    Member

    Here is another run:

    root@raspberrypi:/home/pi/workspace/TrueRNG_Windows_Python# ent -c test.bin
    Value Char Occurrences Fraction
      0             3853   0.003763
      1             4002   0.003908
      2             4085   0.003989
      3             4008   0.003914
      4             4010   0.003916
      5             3903   0.003812
      6             4044   0.003949
      7             3982   0.003889
      8             4003   0.003909
      9             3987   0.003894
     10             3970   0.003877
     11             3954   0.003861
     12             3988   0.003895
     13             3982   0.003889
     14             4114   0.004018
     15             3962   0.003869
     16             4079   0.003983
     17             4028   0.003934
     18             3982   0.003889
     19             4047   0.003952
     20             3946   0.003854
     21             4023   0.003929
     22             4010   0.003916
     23             3990   0.003896
     24             3996   0.003902
     25             4033   0.003938
     26             4016   0.003922
     27             3920   0.003828
     28             3956   0.003863
     29             3915   0.003823
     30             4011   0.003917
     31             3926   0.003834
     32             3976   0.003883
     33   !         4061   0.003966
     34   "         4044   0.003949
     35   #         4060   0.003965
     36   $         4075   0.003979
     37   %         4059   0.003964
     38   &         3949   0.003856
     39   '         3960   0.003867
     40   (         3958   0.003865
     41   )         3900   0.003809
     42   *         3947   0.003854
     43   +         3993   0.003899
     44   ,         3975   0.003882
     45   -         4037   0.003942
     46   .         3936   0.003844
     47   /         3980   0.003887
     48   0         3855   0.003765
     49   1         4032   0.003938
     50   2         3999   0.003905
     51   3         3919   0.003827
     52   4         4094   0.003998
     53   5         3900   0.003809
     54   6         3943   0.003851
     55   7         4033   0.003938
     56   8         3990   0.003896
     57   9         3960   0.003867
     58   :         4021   0.003927
     59   ;         3992   0.003898
     60   <         3954   0.003861
     61   =         3875   0.003784
     62   >         4014   0.003920
     63   ?         4075   0.003979
     64   @         4008   0.003914
     65   A         4091   0.003995
     66   B         4049   0.003954
     67   C         3990   0.003896
     68   D         4014   0.003920
     69   E         3976   0.003883
     70   F         3865   0.003774
     71   G         4077   0.003981
     72   H         3958   0.003865
     73   I         4034   0.003939
     74   J         3980   0.003887
     75   K         3991   0.003897
     76   L         3933   0.003841
     77   M         3927   0.003835
     78   N         3929   0.003837
     79   O         3967   0.003874
     80   P         4101   0.004005
     81   Q         3943   0.003851
     82   R         4058   0.003963
     83   S         4005   0.003911
     84   T         3951   0.003858
     85   U         4060   0.003965
     86   V         3944   0.003852
     87   W         3975   0.003882
     88   X         3912   0.003820
     89   Y         3999   0.003905
     90   Z         3910   0.003818
     91   [         4008   0.003914
     92   \         4008   0.003914
     93   ]         3952   0.003859
     94   ^         3972   0.003879
     95   _         3933   0.003841
     96   X         4026   0.003932
     97   a         4015   0.003921
     98   b         3846   0.003756
     99   c         3953   0.003860
    100   d         3971   0.003878
    101   e         3992   0.003898
    102   f         4095   0.003999
    103   g         4013   0.003919
    104   h         3906   0.003814
    105   i         3889   0.003798
    106   j         3885   0.003794
    107   k         4029   0.003935
    108   l         4021   0.003927
    109   m         3961   0.003868
    110   n         3982   0.003889
    111   o         3938   0.003846
    112   p         4048   0.003953
    113   q         3966   0.003873
    114   r         4012   0.003918
    115   s         4042   0.003947
    116   t         4092   0.003996
    117   u         3873   0.003782
    118   v         4071   0.003976
    119   w         4099   0.004003
    120   x         3936   0.003844
    121   y         4119   0.004022
    122   z         4082   0.003986
    123   {         4025   0.003931
    124   |         3993   0.003899
    125   }         4148   0.004051
    126   ~         4063   0.003968
    127             3908   0.003816
    128             3969   0.003876
    129             4080   0.003984
    130             4058   0.003963
    131             4066   0.003971
    132             3954   0.003861
    133             3958   0.003865
    134             4051   0.003956
    135             4033   0.003938
    136             3983   0.003890
    137             4082   0.003986
    138             4029   0.003935
    139             3928   0.003836
    140             3904   0.003812
    141             4073   0.003978
    142             3919   0.003827
    143             3959   0.003866
    144             4014   0.003920
    145             3980   0.003887
    146             3958   0.003865
    147             4026   0.003932
    148             4006   0.003912
    149             4031   0.003937
    150             3979   0.003886
    151             4031   0.003937
    152             4032   0.003938
    153             3985   0.003892
    154             3990   0.003896
    155             4096   0.004000
    156             4021   0.003927
    157             3929   0.003837
    158             3984   0.003891
    159             4058   0.003963
    160             4084   0.003988
    161   ▒         4012   0.003918
    162   ▒         3910   0.003818
    163   ▒         3977   0.003884
    164   ▒         4022   0.003928
    165   ▒         4114   0.004018
    166   ▒         4019   0.003925
    167   ▒         4112   0.004016
    168   ▒         3993   0.003899
    169   ▒         3939   0.003847
    170   ▒         4009   0.003915
    171   ▒         3952   0.003859
    172   ▒         4102   0.004006
    173   ▒         3963   0.003870
    174   ▒         3982   0.003889
    175   ▒         3949   0.003856
    176   ▒         4031   0.003937
    177   ▒         4015   0.003921
    178   ▒         3999   0.003905
    179   ▒         4110   0.004014
    180   ▒         3941   0.003849
    181   ▒         4040   0.003945
    182   ▒         4153   0.004056
    183   ▒         4072   0.003977
    184   ▒         4015   0.003921
    185   ▒         4048   0.003953
    186   ▒         4093   0.003997
    187   ▒         3981   0.003888
    188   ▒         3963   0.003870
    189   ▒         4060   0.003965
    190   ▒         4006   0.003912
    191   ▒         3966   0.003873
    192   ▒         4016   0.003922
    193   ▒         3987   0.003894
    194   ▒         4059   0.003964
    195   ▒         4018   0.003924
    196   ▒         4133   0.004036
    197   ▒         4004   0.003910
    198   ▒         4043   0.003948
    199   ▒         4002   0.003908
    200   ▒         4041   0.003946
    201   ▒         3996   0.003902
    202   ▒         3942   0.003850
    203   ▒         3993   0.003899
    204   ▒         4096   0.004000
    205   ▒         3944   0.003852
    206   ▒         4131   0.004034
    207   ▒         3975   0.003882
    208   ▒         4044   0.003949
    209   ▒         3981   0.003888
    210   ▒         3951   0.003858
    211   ▒         3958   0.003865
    212   ▒         3964   0.003871
    213   ▒         4019   0.003925
    214   ▒         4091   0.003995
    215   ▒         3897   0.003806
    216   ▒         4054   0.003959
    217   ▒         4111   0.004015
    218   ▒         4090   0.003994
    219   ▒         4042   0.003947
    220   ▒         3886   0.003795
    221   ▒         4027   0.003933
    222   ▒         4081   0.003985
    223   ▒         3912   0.003820
    224   ▒         4128   0.004031
    225   ▒         3880   0.003789
    226   ▒         3981   0.003888
    227   ▒         3989   0.003896
    228   ▒         3956   0.003863
    229   ▒         4025   0.003931
    230   ▒         4002   0.003908
    231   ▒         3902   0.003811
    232   ▒         3990   0.003896
    233   ▒         4091   0.003995
    234   ▒         3970   0.003877
    235   ▒         4021   0.003927
    236   ▒         3903   0.003812
    237   ▒         3916   0.003824
    238   ▒         3972   0.003879
    239   ▒         4131   0.004034
    240   ▒         4135   0.004038
    241   ▒         3972   0.003879
    242   ▒         4051   0.003956
    243   ▒         3952   0.003859
    244   ▒         3979   0.003886
    245   ▒         4000   0.003906
    246   ▒         4039   0.003944
    247   ▒         3984   0.003891
    248   ▒         3908   0.003816
    249   ▒         4054   0.003959
    250   ▒         3945   0.003853
    251   ▒         3913   0.003821
    252   ▒         4067   0.003972
    253   ▒         3992   0.003898
    254   ▒         4011   0.003917
    255   ▒         4045   0.003950
    
    Total:       1024000   1.000000
    
    Entropy = 7.999824 bits per byte.
    
    Optimum compression would reduce the size
    of this 1024000 byte file by 0 percent.
    
    Chi square distribution for 1024000 samples is 249.37, and randomly
    would exceed this value 50.00 percent of the times.
    
    Arithmetic mean value of data bytes is 127.6448 (127.5 = random).
    Monte Carlo value for Pi is 3.134355994 (error 0.23 percent).
    Serial correlation coefficient is -0.000823 (totally uncorrelated = 0.0).
    • This reply was modified 1 year, 3 months ago by  euler357.
    #1783

    Quadko
    Member

    Thanks, and I appreciate the data. Tracking says my device comes tomorrow; I’m looking forward to getting it plugged in.

    #1816

    Quadko
    Member

    I got it all plugged in and pulling data from my C# test code in windows. Very cool!

    I’m thankful for the other forums and online, my naive initial use of the COM Port had both the DTR and “only pulling one byte” problems. Fixing those got me running at speed.

    For fun, the first thing I did with it was fun a counter of “runs of bits”, comparing the standard .NET CSPRNG and TrueRNGPro. Both look great, and in a few hours generate runs of 31+ 1 or 0 bits in a row (I don’t check alignment, so that’s not same as generating a specific number, but the RNG doesn’t care!) It’s easy to see the .5 falloff of each byte length.

    Just for fun, here’s the top of the data I’m getting (ran for different bitcounts/time, and TRNG is still running, I plan to run it a few more hours):

    Key:

    [#same bits in a row] [bit 1 or 0]: # times occurred
    So the CSPRNG line 1 says "Algorithm generated 41 1 bits in a row 1 time in 1.4T bits in 3ish hours."

    And if I did my math correctly, it would take lots of years to generate an all 0 or all 1 64 bit number at current bit rattes, but that’s just the math. So for testing purposes, definitely test random data around interesting classes & values, not across full range – exactly what we already know.

    TrueRNGPro

    
    6,687,032,320 bits in 1956.70s
    
    31 1: 2
    31 0: 1
    30 1: 1
    30 0: 2
    29 1: 4
    28 1: 3
    28 0: 7
    27 1: 12
    27 0: 8
    26 1: 28
    26 0: 11
    25 1: 52
    25 0: 48
    24 1: 91
    24 0: 109
    23 1: 201
    23 0: 185
    

    .NET CSPRNG RNGCryptoServiceProvider

    CSPRNG 
    1,444,732,073,984 bits in 10732.15s
    
    41 1: 1
    39 1: 1
    38 1: 1
    38 0: 7
    37 1: 1
    37 0: 1
    36 1: 5
    36 0: 7
    35 1: 11
    35 0: 12
    34 1: 29
    34 0: 22
    33 1: 53
    33 0: 42
    32 1: 85
    32 0: 86
    31 1: 165
    31 0: 158
    30 1: 313
    30 0: 349
    29 1: 684
    29 0: 670
    
    • This reply was modified 1 year, 2 months ago by  Quadko.
    • This reply was modified 1 year, 2 months ago by  Quadko.
    #1822

    euler357
    Member

    Glad it’s working for you.

    Chris

    #1827

    Quadko
    Member

    Left it running overnight, posting top results to record them, and now moving on to other usage projects. :)
    TrueRNGPro

    218,209,027,072 bits in 63937.71s
    
    38 1: 1
    36 1: 1
    35 1: 1
    35 0: 1
    34 1: 4
    34 0: 4
    33 1: 9
    33 0: 3
    32 1: 16
    32 0: 13
    31 1: 25
    31 0: 24
    30 1: 55
    30 0: 45
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