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I would like to ask about the NIST test suite for randomness evaluation. The test suite consists of 15 subtests which evaluate the particular property of the sequence. In fact, each test has an individual of the minimum number of the bitstream (e.g., $10^6$ bits for Random Excursions test or $100$ for Frequency test). What if I want to test the randomness of short sequences like 128 bitstreams. Is there any reference or suggestion about how to modify the NIST test for this task?

Or what if I just neglect those test which requires a huge number of the bitstream. In that case, is the result still reliable?

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  • $\begingroup$ What are "short sequences like 128 bitstreams?" Are you simply wanting to random test a few sequences of 128 bit length? $\endgroup$ – Paul Uszak Sep 8 '18 at 0:03
  • $\begingroup$ What is the total number of bits you have? This is quite important as randomness in many ways is a function of sample length. $\endgroup$ – Paul Uszak Sep 8 '18 at 0:03
  • $\begingroup$ eprint.iacr.org/2010/564.pdf $\endgroup$ – kelalaka Oct 7 '18 at 6:31
  • $\begingroup$ This question was bumped to the homepage by the Community bot. But except for the missing upvotes it seems that a perfectly fine answer has been provided. Korakot, can you indicate if there is anything missing from the given answer? $\endgroup$ – Maarten Bodewes Oct 8 '18 at 14:05
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You will simply not be testing those properties and thus structured nonrandom sequences may pass with respect to tested properties.

For a simplistic example random excursion test fails if the maximum magnitude of the cumulative sums defined by the -1,+1 version of the sequence is too large (much larger than say $2 \sqrt{n}$ where $n$ is the sequence length.

So you can have long runs and fail random excursions but still pass other tests, e.g., the frequency test.

The paper https://arxiv.org/pdf/1208.5740.pdf has some intuitive discussion of what some of the tests are aimed at.

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    $\begingroup$ You've got to love a contemporary scientific publication that draws it's probability curves by hand... $\endgroup$ – Paul Uszak Sep 8 '18 at 11:02
  • $\begingroup$ @PaulUszak, absolutely! $\endgroup$ – kodlu Sep 8 '18 at 13:34

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