English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

NIST SP800-22 is one of the most widely used statistical testing tools forpseudorandom number generators (PRNGs). This tool consists of 15 tests(one-level tests) and two additional tests (two-level tests). Each one-leveltest provides one or more $p$-values. The two-level tests measure theuniformity of the obtained $p$-values for a fixed one-level test. One of thetwo-level tests categorizes the $p$-values into ten intervals of equal length,and apply a chi-squared goodness-of-fit test. This two-level test is often morepowerful than one-level tests, but sometimes it rejects even good PRNGs whenthe sample size at the second level is too large, since it detectsapproximation errors in the computation of $p$-values. In this paper, wepropose a practical upper limit of the sample size in this two-level test, foreach of six tests appeared in SP800-22. These upper limits are derived by thechi-squared discrepancy between the distribution of the approximated $p$-valuesand the uniform distribution $U(0, 1)$. We also computed a "risky" sample sizeat the second level for each one-level test. Our experiments show that thetwo-level test with the proposed upper limit gives appropriate results, whileusing the risky size often rejects even good PRNGs. We also propose anotherimprovement: to use the exact probability for the ten categories in thecomputation of goodness-of-fit at the two-level test. This allows us toincrease the sample size at the second level, and would make the test moresensitive than the NIST's recommending usage.

Study on upper limit of sample sizes for a two-level test in NIST SP800-22