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Equal neighbouring outputs probabilities

 

 
Frequencies of occurrence of the following situations were measured in the consecutive 256-byte sub-strings of the 2^43.1-byte keystream generated by the VMPC Stream Cipher. S(X) denotes X-th output byte of the Cipher:



Situation 1.1. S(X)=S(X -1) occurred zero times in a given 256-byte 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 256-byte 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 256-byte 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 256-byte substream. Probability = 0.061192351

Situation 1.5. S(Xn)=S(Xn -1) occurred 4 times in a given 256-byte substream. Probability = 0.015178103

Situation 1.6. S(Xn)=S(Xn -1) occurred 5 times in a given 256-byte substream. Probability = 0.002999907

Situation 1.7. S(Xn)=S(Xn -1) occurred over 5 times in a given 256-byte substream. Probability = 0.000570499



Situation 2.1. S(X)=S(X -2) occurred zero times in a given 256-byte substream. Probability = 0.36715975

Situation 2.2. S(X1)=S(X1 -2) occurred 1 time in a given 256-byte substream. Probability = 0.36859959

Situation 2.3. S(Xn)=S(Xn -2) occurred 2 times in a given 256-byte 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 256-byte substream. Probability = 0.061192351

Situation 2.5. S(Xn)=S(Xn -2) occurred 4 times in a given 256-byte substream. Probability = 0.015178103

Situation 2.6. S(Xn)=S(Xn -2) occurred 5 times in a given 256-byte substream. Probability = 0.002999907

Situation 2.7. S(Xn)=S(Xn -2) occurred over 5 times in a given 256-byte 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




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