Numbers of equal bytes of the keystream, resulting from change of key




Test 1. 2^33.2 pairs of 128bit, 2^33.2 pairs of 256bit and 2^33.2 pairs of 512bit keys,
differing by each possible value in each possible (one at a time) position of the key, were
used to generate 256element permutations with the VMPC Key Scheduling Algorithm and then
256 bytes of output were generated by the VMPC Stream Cipher.
Test 2.^33.2 pairs of 128bit, 2^33.2 pairs of 256bit and 2^33.2 pairs of 512bit keys,
differing by each possible value in the last position of the key (the position of the key which
is last to be used for the first time by the KSA), were
used to generate 256element permutations with the VMPC Key Scheduling Algorithm and then
256 bytes of output were generated by the VMPC Stream Cipher.
In Test 1 and Test 2  frequencies of occurrence of the following situations were measured.
S1(X) denotes Xth byte of the stream generated by the Cipher from one key and S2(X) denotes Xth
byte of the stream generated by the Cipher from the changed key:
Situation 1. S1(X)=S2(X) occurred zero times
(the generated streams had all their corresponding bytes different). Probability = 0.36715975
Situation 2. S1(X1)=S2(X1) occurred 1 time
(the generated streams had one corresponding byte equal and all other bytes different). Probability = 0.36859959.
Situation 3. S1(Xn)=S2(Xn) occurred 2 times. Probability = 0.18429980
Situation 4. S1(Xn)=S2(Xn) occurred 3 times. Probability = 0.061192351
Situation 5. S1(Xn)=S2(Xn) occurred 4 times. Probability = 0.015178103
Situation 6. S1(Xn)=S2(Xn) occurred 5 times. Probability = 0.002999907
The measured frequencies of occurrence of situations 16 in Test 1 and in Test 2
showed no statistically significant deviations from their expected values.
The average total numbers of equal corresponding bytes of streams generated in Test 1 and in Test 2
showed no statistically significant deviations from their expected values of 1.
by Bartosz Zoltak

