DieHard_Tests_Analyses.md

Dieharder Test Report for the file esp32_diehard_1180000.txt

Summary: Most tests passed with p-values in acceptable ranges, but several tests showed "WEAK" results.

Tests with "WEAK" results:

1. diehard_bitstream

• p-value: 0.9988
  Although this p-value is high, the test evaluates the distribution of bits in the random number stream. A "WEAK" result may indicate an underlying structure in the bits, which could suggest that the randomness is not sufficient, even though it might seem acceptable at first glance.

2. diehard_oqso

• p-value: 0.9965
  The "oqso" test checks for autocorrelations between bits in a random number stream. A high p-value close to 1 may suggest dependencies in the data, making the generator less random than expected.

3. sts_serial (5)

• p-value: 0.9956
  The "serial" test analyzes bit sequences in successive windows. A high p-value (close to 1) may indicate some repetitive structure in the bit sequences, which is not ideal for a random number generator.

4. rgb_lagged_sum (3)

• p-value: 0.9995
  The "lagged sum" test checks the sums of pixel values from an image generated by the random numbers. A p-value this high suggests that the sum of values does not vary sufficiently.

5. rgb_lagged_sum (4)

• p-value: 0.00067
  This test gives a very low p-value, which may indicate a significant anomaly. It suggests that the sums for these "lagged sums" are not evenly distributed, pointing to a weakness in the random number distribution.

6. rgb_lagged_sum (20)

• p-value: 0.6563
  While this p-value is in an acceptable range, it is relatively low compared to the other tests, which might indicate a lack of sufficient randomization in this particular "lagged sum" test.

Conclusion

The "WEAK" results from several tests (notably "bitstream", "oqso", and "lagged sum") suggest structural or dependency issues in the generated random numbers, although the p-values remain generally within an acceptable range.