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ugly tests

1. ("true"-random) 10 iterations; 32 random bytes | Result Avg Entropy: 4.82

  $ echo $(echo -n "("; for i in $(seq 1 10); do echo -n $(./generate_constant_stream |head -c 32 |ent |head -1 |awk '{print $3}')"+"; done; echo -n "0)/10") |bc -l
  4.81945500000000000000
2. ("true"-random) 100 iterations; 32 random bytes | Result Avg Entropy: 4.37

  $ echo $(echo -n "("; for i in $(seq 1 100); do echo -n $(./generate_constant_stream |head -c 32 |ent |head -1 |awk '{print $3}')"+"; done; echo -n "0)/100") |bc -l
  4.37395291000000000000
3. ("true"-random) 200 iterations; 32 random bytes | Result Avg Entropy: 4.35

  $ echo $(echo -n "("; for i in $(seq 1 200); do echo -n $(./generate_constant_stream |head -c 32 |ent |head -1 |awk '{print $3}')"+"; done; echo -n "0)/200") |bc -l
  4.34563333000000000000
1. (openssl) 10 iterations; 32 random bytes | Result Avg Entropy: 4.88

  $ echo $(echo -n "("; for i in $(seq 1 10); do echo -n $(openssl rand 32 |ent |head -1 |awk '{print $3}')"+"; done; echo -n "0)/10") |bc -l
  4.88125000000000000000
2. (openssl) 100 iterations; 32 random bytes | Result Avg Entropy: 4.87

  $ echo $(echo -n "("; for i in $(seq 1 100); do echo -n $(openssl rand 32 |ent |head -1 |awk '{print $3}')"+"; done; echo -n "0)/100") |bc -l
  4.87404420000000000000
3. (openssl) 200 iterations; 32 random bytes | Result Avg Entropy: 4.88

  $ echo $(echo -n "("; for i in $(seq 1 200); do echo -n $(openssl rand 32 |ent |head -1 |awk '{print $3}')"+"; done; echo -n "0)/200") |bc -l
  4.87885575000000000000
1. (/dev/urandom) 10 iterations; 32 random bytes | Result Avg Entropy: 4.82

  $ echo $(echo -n "("; for i in $(seq 1 10); do echo -n $(head -c32 < /dev/urandom |ent |head -1 |awk '{print $3}')"+"; done; echo -n "0)/10") |bc -l
  4.82264100000000000000
2. (/dev/urandom) 100 iterations; 32 random bytes | Result Avg Entropy: 4.89

  $ echo $(echo -n "("; for i in $(seq 1 100); do echo -n $(head -c32 < /dev/urandom |ent |head -1 |awk '{print $3}')"+"; done; echo -n "0)/100") |bc -l
  4.88655640000000000000
3. (/dev/urandom) 200 iterations; 32 random bytes | Result Avg Entropy: 4.88

  $ echo $(echo -n "("; for i in $(seq 1 200); do echo -n $(head -c32 < /dev/urandom |ent |head -1 |awk '{print $3}')"+"; done; echo -n "0)/200") |bc -l
  4.88061280000000000000


Can you explain what do these results mean?


The values presented are "N bits per character". 8 is the maximum, 0 is the minimum. The less value is the worse. The ugly test results show that "true"-random tool does not perform better than openssl / /dev/urandom. What makes it even worse is that the entropy decreases with the amount of iterations. These are simple bash tests, you can try on your own, playing with the values. Though, I suggest to understand some theory in the first place:

- randomness https://en.wikipedia.org/wiki/Randomness

- entropy https://en.wikipedia.org/wiki/Entropy_(computing)

- ent http://www.fourmilab.ch/random/


I think it is even worse than I thought...

I've asked the "true"-random tool to give me 3000 of the really "true" numbers (as it claims) and out of 3000 it has thrown to me ~9% of char(0) and ~9% of char(255) values (see the fractions below), whilst the others <0.01% per char between char(1-254).

  ./generate_constant_stream |head -c3000 |ent -c
  Value Char Occurrences Fraction
  0              309   0.103000
  1               33   0.011000
  ...
  ...
  253   �           28   0.009333
  254   �           29   0.009667
  255   �          312   0.104000
  Total:          3000   1.000000

  Entropy = 6.861709 bits per byte.
Update

Running it without the char(0)/char(255) neither did outperform /dev/urandom, but only running terribly slow (~5mins on i7) and using 100% of a CPU core:

  $ ./generate_constant_stream | cat - | sed -u 's/\x00//g;s/\xff//g' |head -c3000 |ent -c
  Entropy = 7.737683 bits per byte.

  $ cat /dev/urandom | sed -u 's/\x00//g;s/\xff//g' |head -c3000 |ent -c
  Entropy = 7.924493 bits per byte.




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