Analysis functions

The following analysis functions are not required for the actual functionalities of the application. For the interested person they offer the possibility to get a feeling for the quality of the generated keys.

The analysis function for this can be accessed via the main menu item Accessories and the menu item Analyses.

Equal distribution ...

FFT Study ...

Pattern comparison & diversity ...

Equal distribution

Equal distribution considers whether all possible values between 1 and 255 occur with equal frequency in the byte sequence of a key bundle. The frequencies are determined and normalized to the maximum frequency so that the values are always between 0.0 and 1.0. Then the mean value (blue horizontal line) of all frequencies is formed, which then represents the equal distribution.

The closer this value is to 1.0, the better the balance in this key bundle. To assess whether there are some outliers despite a good equal distribution value, i.e. whether there are some byte values that are underrepresented, the difference between the maximum and minimum relative frequency is also formed. This scattering should then be close to 0.0 if possible.

FFT Study

A byte sequence with random values corresponds to what is known from acoustics as white noise. If one performs a Fast Fourier Analysis (FFT) with such a signal (course in the upper part of the figure below), the resulting spectrum (course in the lower part) is just as "zapped" as the signal itself.

1024 values of a key bundle and the resulting spectrum are displayed. With the slider (below) the beginning of the 1024 bytes can be shifted over the entire key bundle.

Besides the key bundle files, WAV type files can also be loaded. There are some WAV files with pure sine tones in the folder "FFT-Testwaves", which illustrate how the spectra of periodic progressions look like in contrast to signals with random white noise.

Pattern comparison & diversity

Another important criterion for assessing the quality of a key bundle is the frequency with which patterns of the same length occur within a key bundle or between two key bundles of the same length. For this purpose, starting with length three, the three consecutive bytes are always compared with all other three-byte patterns in the file and the frequency with which these patterns occur is counted.

After that, four-byte patterns of the same length are searched for, and so on until the pattern length at which there are no more identical patterns. It has been shown that three-byte patterns occur almost exclusively only once each in the same or in the other key bundle. So in the example (below) there are 414 three byte long patterns in the key bundle "Pseudo-80K-12098", which each occur once in the key bundle "Pseudo-80K-12099", exactly one such four byte long pattern and longer, equal patterns were not found.

Diversity (or variety) compares the bytes at the same positions between two key bundles of the same length and counts how often the values match (equals) in relation to the total number of values. The diversity then results from "100% - Equals". In addition, the mean distances of the neighboring values are determined.

	The following analysis functions are not required for the actual functionalities of the application. For the interested person they offer the possibility to get a feeling for the quality of the generated keys. The analysis function for this can be accessed via the main menu item *Accessories* and the menu item *Analyses*.

	Equal distribution ... FFT Study ... Pattern comparison & diversity ...
	Equal distribution Equal distribution considers whether all possible values between 1 and 255 occur with equal frequency in the byte sequence of a key bundle. The frequencies are determined and normalized to the maximum frequency so that the values are always between 0.0 and 1.0. Then the mean value (blue horizontal line) of all frequencies is formed, which then represents the equal distribution. The closer this value is to 1.0, the better the balance in this key bundle. To assess whether there are some outliers despite a good equal distribution value, i.e. whether there are some byte values that are underrepresented, the difference between the maximum and minimum relative frequency is also formed. This scattering should then be close to 0.0 if possible.

	FFT Study A byte sequence with random values corresponds to what is known from acoustics as white noise. If one performs a Fast Fourier Analysis (FFT) with such a signal (course in the upper part of the figure below), the resulting spectrum (course in the lower part) is just as "zapped" as the signal itself. 1024 values of a key bundle and the resulting spectrum are displayed. With the slider (below) the beginning of the 1024 bytes can be shifted over the entire key bundle. Besides the key bundle files, WAV type files can also be loaded. There are some WAV files with pure sine tones in the folder "FFT-Testwaves", which illustrate how the spectra of periodic progressions look like in contrast to signals with random white noise.

	Pattern comparison & diversity Another important criterion for assessing the quality of a key bundle is the frequency with which patterns of the same length occur within a key bundle or between two key bundles of the same length. For this purpose, starting with length three, the three consecutive bytes are always compared with all other three-byte patterns in the file and the frequency with which these patterns occur is counted. After that, four-byte patterns of the same length are searched for, and so on until the pattern length at which there are no more identical patterns. It has been shown that three-byte patterns occur almost exclusively only once each in the same or in the other key bundle. So in the example (below) there are 414 three byte long patterns in the key bundle "Pseudo-80K-12098", which each occur once in the key bundle "Pseudo-80K-12099", exactly one such four byte long pattern and longer, equal patterns were not found.

	Diversity (or variety) compares the bytes at the same positions between two key bundles of the same length and counts how often the values match (equals) in relation to the total number of values. The diversity then results from "100% - Equals". In addition, the mean distances of the neighboring values are determined.