The HAVEGE unpredictable random number generator

On line testing

7 March 2002


The online testing we provide is derived  (adapted) from the NIST  statistical  suite for random number generator. For  practical and theoretical description  of the tests , the reader should consult the NIST report.

The minimum size of the sequence we analyze is 1 Mbyte and up to 256 Mbytes.   Those tests were not originally  written for analyzing such huge sequences of random numbers. Therefore, some performance gaps  were encountered. Many tests  were too CPU hungry and memory hungry to be run  in a reasonable time ( a few minutes for 1 Mbyte).  We adapted those tests to run faster and with using less memory when possible. When despites our efforts, the response time was still too large, we run the test on a  few "randomly" chosen subsequences.

We describe our usage of  each of the tests.

o Test 1 (Frequency test ), Test 2 (Block Frequency test ), Test 3 (Runs test), Test 14 ( Cumulative Sums)

Each of these tests  are  run on  randomly selected subsequences  for each of the size   128 bits, 256 bits, .. up to the complete sequence.

o Test 4 (Longest runs tests)

We chose to 8 runs on randomly chosen 750000 bits sequences.

o Test 5: Binary matrix rank test

This test is very CPU hungry.  We chose to run it   on only  8 randomly selected 38,192 bits sequences.
and Test 4 (Longest runs tests)

o Test 6:  Discrete Fourier transfom

This test is very CPU hungry.  We chose to run it   on only  8 randomly selected  1Mbits sequences.

o Test 7:  Non Overlapping  Template Matching

On a single randomly selected  1Mbits sequence, we run the 148 template matchings for templates of length 9.

o Test 8  (Overlapping  Template Matching), Test 10 ( Lempel-Ziv compression ), Test 12  (serial test , m=14) , Test 15 (Random Excursion) , Test 16 (Random Excursion Variant)

We chose to run these tests on only  8 randomly selected  1000000 bits sequences.

o Test 9 :  Maurer's Universal Tests

This test is run for all possible values higher than 6 on the beginning of the sequence.

o Test 11:  Linear Complexity 

This test is the most  CPU hungry of the collection. We chose to run it   on  a single randomly selected  4731*341 bits sequences.

o Test 13 :  Approximate Entropy

We  run this test for values from 3 to 16 on the whole sequence.

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