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Numbers of equal elements in the permutations, resulting from change of key

 

 
Test 1. 2^33.2 pairs of 128-bit, 2^33.2 pairs of 256-bit and 2^33.2 pairs of 512-bit keys, differing by each possible value in each possible (one at a time) position of the key, were used to generate 256-element permutations with the VMPC Key Scheduling Algorithm.

Test 2. 2^33.2 pairs of 128-bit, 2^33.2 pairs of 256-bit and 2^33.2 pairs of 512-bit 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 256-element 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 X-th element of the permutation generated from one key and P2(X) denotes X-th 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 1-6 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




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