Key quality

Some statistical studies were conducted to assess the key qualities. This includes in particular the uniform distribution of the key values (i.e. that all 255 bytes without the zero occur as equally often as possible in the key) and the uniqueness of the patterns in one and between the keys.

The uniform distribution was investigated with different key bundle sizes. The occurrence of all 255 byte values was counted and then a normalization to the maximum value was performed. The mean value of all these normalized values should then be as close as possible to 1.0. In addition, however, the scatter of the values must also be considered, then all values should be as close to 1.0 as possible. Therefore, the difference between the maximum and minimum value is also considered and this should be as close to 0.0 as possible.

The figures on the left show the normalized, averaged frequency values as a function of key bundle size, as well as the scatter between the values. As can be clearly seen, the quality becomes very good from about 1MB key bundle size onwards, both in terms of uniformity and scatter.

The illustrations on the right show how many three-byte patterns (absolute and relativ) appear one more time within a key bundle. That they appear more than once is extremely rare. Four byte patterns are rarely duplicated (between 2 and 10 times) and five byte patterns have not been found at all.