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Numbers of equal bytes of the keystream, 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 and then 256 bytes of output were generated by the VMPC Stream Cipher.
Test 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 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 X-th byte of the stream generated by the Cipher from one key and S2(X) denotes X-th 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 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 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




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