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  • in reply to: TrueRNG fails the Chi-square Test #2265

    The generator that I have (v3) does not show this strange behavior (using ent function from ubuntu 18.04) – typical result looks like
    racaf@shen:/lacie/bigrandomdata/truerng$ ent random2.bin
    Entropy = 8.000000 bits per byte.

    Optimum compression would reduce the size
    of this 4437100000 byte file by 0 percent.

    Chi square distribution for 4437100000 samples is 265.26, and randomly
    would exceed this value 31.64 percent of the times.

    Arithmetic mean value of data bytes is 127.5004 (127.5 = random).
    Monte Carlo value for Pi is 3.141643794 (error 0.00 percent).
    Serial correlation coefficient is -0.000010 (totally uncorrelated = 0.0).

    —-
    For 100mb chunks:

    Chi square distribution for 104857600 samples is 295.96, and randomly
    would exceed this value 3.97 percent of the times.

    Chi square distribution for 104857600 samples is 232.56, and randomly
    would exceed this value 84.00 percent of the times.

    Chi square distribution for 104857600 samples is 276.14, and randomly
    would exceed this value 17.35 percent of the times.

    Chi square distribution for 104857600 samples is 236.02, and randomly
    would exceed this value 79.74 percent of the times.

    Chi square distribution for 104857600 samples is 271.25, and randomly
    would exceed this value 23.14 percent of the times.

    Chi square distribution for 104857600 samples is 231.29, and randomly
    would exceed this value 85.42 percent of the times.

    Chi square distribution for 104857600 samples is 303.83, and randomly
    would exceed this value 1.94 percent of the times.

    Chi square distribution for 104857600 samples is 264.75, and randomly
    would exceed this value 32.43 percent of the times.

    Chi square distribution for 104857600 samples is 268.44, and randomly
    would exceed this value 26.95 percent of the times.

    Chi square distribution for 104857600 samples is 285.71, and randomly
    would exceed this value 9.05 percent of the times.

    Chi square distribution for 104857600 samples is 263.80, and randomly
    would exceed this value 33.91 percent of the times.

    Chi square distribution for 104857600 samples is 260.11, and randomly
    would exceed this value 39.97 percent of the times.

    Chi square distribution for 104857600 samples is 285.44, and randomly
    would exceed this value 9.22 percent of the times.

    Chi square distribution for 104857600 samples is 237.08, and randomly
    would exceed this value 78.32 percent of the times.

    Chi square distribution for 104857600 samples is 306.80, and randomly
    would exceed this value 1.45 percent of the times.

    Chi square distribution for 104857600 samples is 228.14, and randomly
    would exceed this value 88.57 percent of the times.

    Chi square distribution for 104857600 samples is 248.90, and randomly
    would exceed this value 59.59 percent of the times.

    Chi square distribution for 104857600 samples is 265.29, and randomly
    would exceed this value 31.59 percent of the times.

    Chi square distribution for 104857600 samples is 263.25, and randomly
    would exceed this value 34.79 percent of the times.

    —-
    But still the question: is there any more detailed information about whitening algorithms, except from the documentation quotes: “entropy mixing algorithm takes in $20$ bits of entropy and outputs $8$ bit to ensure that maximum entropy is maintained. The algorithm uses multiplication in a Galois field similar to a cyclic redundancy check to mix the ADC inputs thoroughly while spreading the entropy evenly across all bits” and “We split the data into multiple streams and use the XOR method to reduce bias (whiten) the output data… A significant amount of time was spent getting the whitening correct without reducing the throughput too much. Currently, the random data is XORed/downselected at about a 20:1 rate to whiten while keeping maximum entropy”

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