[Cryptography] Dieharder & symmetric cryptosystems

[Michel Arboi]

In May 2019, I noticed strange results of the Dieharder statistical test
suite with Linux /dev/urandom
Very often, dieharder reported inconclusive "WEAK" results on some tests,
even when running "dieharder -a -g 501 -k 2 -Y 1", which looks suspicious
(-Y 1 = "resolve ambiguity" mode)
(WEAK is inconclusive, FAIL reports a real weakness.See the thread "
Dieharder & /dev/urandom" on this ML, starting from 2019-05-14)

A totally predictable PRNG which just hashes (SHA1) a counter with a
constant string passes all Dieharder tests with flying colours. I expected
a cryptographic PRNG to exhibit the same behaviour.

Now, I noticed that AES_OFB produces the same suspicious results. Once
again, I cannot explain this. As far as I know, AES_OFB should be totally
unpredictable and immune from any statistical weaknesses. I do not get any
FAIL, but I don't understand why Dieharder reports so many inconclusive
results.

$  dieharder -a -g 205 -k 2 -Y 1
#=============================================================================#
#            dieharder version 3.31.1 Copyright 2003 Robert G.
Brown          #
#=============================================================================#
   rng_name    |rands/second|   Seed   |
        AES_OFB|  2.45e+07  |3424392396|
#=============================================================================#
        test_name   |ntup| tsamples |psamples|  p-value |Assessment
#=============================================================================#
   diehard_birthdays|   0|       100|     100|0.55850015|  PASSED
[snip]
    diehard_2dsphere|   2|      8000|     100|0.31695338|  PASSED
    diehard_3dsphere|   3|      4000|     100|0.72645403|  PASSED
     diehard_squeeze|   0|    100000|     100|0.99526250|   WEAK
     diehard_squeeze|   0|    100000|     200|0.75277078|  PASSED
[snip]
      rgb_lagged_sum|   2|   1000000|     100|0.97574458|  PASSED
      rgb_lagged_sum|   3|   1000000|     100|0.99541232|   WEAK
      rgb_lagged_sum|   3|   1000000|     200|0.87608184|  PASSED
[snip]
      rgb_lagged_sum|   2|   1000000|     100|0.97574458|  PASSED
      rgb_lagged_sum|   3|   1000000|     100|0.99541232|   WEAK
      rgb_lagged_sum|   3|   1000000|     200|0.87608184|  PASSED
[snip]
        dab_monobit2|  12|  65000000|       1|0.58649430|  PASSED
$

I am looking for any kind of explanation.Is there a bug in Dieharder? Did I
over-estimated the importance of WEAK results? Is OFB_AES known to be
slightly biased?

-- 
Michel Arboi
PGP key ID : 0x85A1C6A1 - 0x05054F8485A1C6A1
Fingerprint: 1DC3 8857 B930 0B6B 9420  5D56 0505 4F84 85A1 C6A1
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