Analyze and evaluate outputs

The directory analysis contains all analyze and evaluation tools.

For more details on their parameters, call the scripts with -h.

Allan variance

You can compute the Allan Variance for a ring-oscillator time series, whether it’s obtained from measurement or from emulation. The Python script allanvariance.py can plot the normalized Allan Variance versus the samples accumulation. For instance, you can use the following command to plot the Allan Variance of an emulated ring-oscillator:

$ python allanvariance.py -t "Plot title" ro.txt allanvar.png

Allan variance example for a 500Mz ring oscillator

Please note that the Allan variance can also be plotted for the COSO output values in order to estimate respective thermal and flicker noise contributions.

COSO counter distribution

You can visualize the counter values generated by the COSO, whether emulated or obtained from the FPGA board, by creating a histogram using the following Python script:

$ python distribution.py --log -t "Plot title" coso.txt distribution.png

COSO values with RO pair at 500MHz and 505MHz

The provided example illustrates the generation of a COSO log-distribution plot using data from produced through emulator of two ring-oscillators at 500MHz and 505MHz.

Entropy estimation

Entropy estimators take binary files as input. The script tobinary.py can be used to convert ERO, MURO and COSO text output files to binary. This script takes one integer per line (value should be 0, 1 or n), then extracts the less significant bit (LSB) for each line and pack successive bits to bytes.

You can estimate entropy of the generated binary streams with the script entropy.py that offers different estimators:

Shannon entropy (Wikipedia)
Most Common Value (from NIST SP800-90B)
Markov (from NIST SP800-90B)
T8 from BSI AIS 20/31 test procedure B

Estimators can be computed for different samples width, from 1 bit numbers to 32 bits numbers.

$ python entropy.py -e mcv -b 8 ero.bin

The example above computes the Most Common Value (MCV) estimator on 8 bits samples read from the ero.bin binary file.

Auto-correlation

The Python script autocorrelation.py plots the autocorrelations for a random binary file, reading the file by words of b bits. The d parameter limits the maximum correlation lag (depth) of the signal with itself.

$ python autocorrelation.py -b 8 -d 100 -t "Plot title" coso.bin autocorr.png

This example plots the autocorrelation of the signal in a maximum lag of 100 samples of 8 bits each.