Numbers of equal elements in the permutations, 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.
Test 2. 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.
In Test 1 and in Test 2  frequencies of occurrence of the following situations were measured.
P1(X) denotes Xth element of the permutation generated from one key and P2(X) denotes Xth
element of the permutation generated from the changed key:
Situation 1. P1(X)=P2(X) occurred zero times
(the generated permutations had all their corresponding element different). Probability = 0.3678794412
Situation 2. P1(X1)=P2(X1) occurred 1 time
(the generated permutations had one corresponding element equal and all other elements different). Probability = 0.3678794412 (equal to that from situation 1).
Situation 3. P1(Xn)=P2(Xn) occurred 2 times. Probability = 0.1839397206
Situation 4. P1(Xn)=P2(Xn) occurred 3 times. Probability = 0.0613132402
Situation 5. P1(Xn)=P2(Xn) occurred 4 times. Probability = 0.0153283100
Situation 6. P1(Xn)=P2(Xn) occurred 5 times. Probability = 0.0030656620
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 elements of the permutations, measured
in Test 1 and in Test 2, showed no statistically significant deviations from
their expected values of 1.
by Bartosz Zoltak

