TITLE:
A New Approach for the DFT NIST Test Applicable for Non-Stationary Input Sequences
AUTHORS:
Yehonatan Avraham, Monika Pinchas
KEYWORDS:
Wigner Distribution, Shape Parameter, Generalized Gaussian Distribution, Random Number Generator, True Random Number Generator, Pseudo Random Number Generator
JOURNAL NAME:
Journal of Signal and Information Processing,
Vol.12 No.1,
February
26,
2021
ABSTRACT: The National Institute of Standards and Technology
(NIST) document is a list of fifteen tests for estimating the probability of
signal randomness degree. Test number six in
the NIST document is the Discrete Fourier Transform (DFT) test suitable
for stationary incoming sequences. But, for cases where the input sequence is
not stationary, the DFT test provides inaccurate results. For these cases, test
number seven and eight (the Non-overlapping Template Matching Test and the
Overlapping Template Matching Test) of the NIST document were designed to
classify those non-stationary sequences. But, even with test number seven and
eight of the NIST document, the results are not always accurate. Thus, the NIST
test does not give a proper answer for the non-stationary input sequence case.
In this paper, we offer a new algorithm or
test, which may replace the NIST tests number six, seven and eight. The proposed test is applicable also for
non-stationary sequences and supplies more accurate results than the existing tests (NIST tests number six, seven
and eight), for non-stationary sequences. The new proposed test is based
on the Wigner function and on the Generalized Gaussian Distribution (GGD). In
addition, this new proposed algorithm alarms
and indicates on suspicious places of cyclic sections in the tested sequence. Thus, it gives us the option to repair
or to remove the suspicious places of cyclic sections (this part is beyond the scope of this paper), so that after that, the repaired
or the shortened sequence (original
sequence with removed sections) will result as a sequence with high probability of random degree.