Equal neighbouring outputs probabilities




Frequencies of occurrence of the following situations were measured in the consecutive 256byte substrings of the
2^43.1byte keystream generated by the VMPC Stream Cipher. S(X) denotes Xth output byte of the Cipher:
Situation 1.1. S(X)=S(X 1) occurred zero times in a given 256byte substream
(each generated byte was different from its proceeding byte). Probability = 0.36715975
Situation 1.2. S(X1)=S(X1 1) occurred 1 time in a given 256byte substream
(one byte was equal to its proceeding byte and 255 bytes were different
from their proceeding bytes). Probability = 0.36859959
Situation 1.3. S(Xn)=S(Xn 1) occurred 2 times in a given 256byte substream
(e.g. S(18)=S(17), S(245)=S(244) and S(X)S(X 1) for X in {0..255} / {18,245})
Probability = 0.18429980
Situation 1.4. S(Xn)=S(Xn 1) occurred 3 times in a given 256byte substream.
Probability = 0.061192351
Situation 1.5. S(Xn)=S(Xn 1) occurred 4 times in a given 256byte substream.
Probability = 0.015178103
Situation 1.6. S(Xn)=S(Xn 1) occurred 5 times in a given 256byte substream.
Probability = 0.002999907
Situation 1.7. S(Xn)=S(Xn 1) occurred over 5 times in a given 256byte substream.
Probability = 0.000570499
Situation 2.1. S(X)=S(X 2) occurred zero times in a given 256byte substream.
Probability = 0.36715975
Situation 2.2. S(X1)=S(X1 2) occurred 1 time in a given 256byte substream.
Probability = 0.36859959
Situation 2.3. S(Xn)=S(Xn 2) occurred 2 times in a given 256byte substream
(e.g. S(18)=S(16), S(245)=S(243) and S(X)S(X 2) for X in {0..255} / {18,245})
Probability = 0.18429980
Situation 2.4. S(Xn)=S(Xn 2) occurred 3 times in a given 256byte substream.
Probability = 0.061192351
Situation 2.5. S(Xn)=S(Xn 2) occurred 4 times in a given 256byte substream.
Probability = 0.015178103
Situation 2.6. S(Xn)=S(Xn 2) occurred 5 times in a given 256byte substream.
Probability = 0.002999907
Situation 2.7. S(Xn)=S(Xn 2) occurred over 5 times in a given 256byte substream.
Probability = 0.000570499
Frequencies of occurrence of situations 1.1  2.7. were measured. None
of the observed frequencies showed a statistically significant deviation from its
expected value.
The average total numbers of situations, where S(Xn)=S(Xn 1) and S(Xn)=S(Xn 2), were measured
in the generated keystream and the observed numbers showed no statistically significant
deviations from their expected values of 1.
by Bartosz Zoltak

