
1. VMPC OneWay Function
1) Description of the algorithm of inverting a klevel VMPC function for nelement
permutations, with example average running times; by Bartosz Zoltak, more here
2) Observation that for a random permutation P of n>1 elements and 1level VMPC
function (Q[x]=P[P[P[x]]+1]), the event Q[x]=P[x+1] occurs with probability 2/n (rather than 1/n);
reported by Francois Grieu, more here

2. VMPC Stream Cipher
1) Average computational effort required to break the VMPC Stream Cipher  by recovering the
cipher's internal state from the generated output  is approximated at over 2^900 computational
operations; by Bartosz Zoltak, more here
2) Singleoutputs probabilities. Frequencies of occurrence of each of
the 256 possible outputvalues showed no statistically significant deviation from the expected
value of 1 / 2^8; by Greg Rose, more here
3) Singleoutputs on given positions probabilities. Frequencies of occurrence
of each possible outputvalue on each of the possible 256 positions (for each possible
value of n) showed no statistically significant deviation from the expected
value of 1 / 2^16; by Greg Rose, more here
4) Digraph probabilities. Frequencies of occurrence of each possible pair
of neighboring outputs showed no statistically significant deviation from the expected
value of 1 / 2^16; by Bartosz Zoltak, more here
5) Digraphs on given positions probabilities. Frequencies of occurrence of each possible pair
of neighboring outputs on each of the possible 256 positions (for each possible value of n)
showed no statistically significant deviation from the expected
value of 1 / 2^24; by Bartosz Zoltak and Greg Rose, more here
6) Trigraph probabilities. Frequencies of occurrence of each possible set
of three consecutive outputs showed no statistically significant deviation from the expected
value of 1 / 2^24; by Bartosz Zoltak and Greg Rose, more here
7) First outputs probabilities. Frequencies of occurrence of each possible value of each of the
first 256 bytes generated directly after running the VMPC Key Scheduling Algorithm
showed no statistically significant deviation from the expected frequency of 1 / 2^8,
by Bartosz Zoltak, more here
8) Equal neighboring outputs probabilities. Frequencies of occurrence of situations where there
occurs a given number (0,1,2,3,4,5 and over 5) of direct (generated consecutively) and indirect
(separated by one more output) equal neighboring outputs in the consecutive 256byte
substreams of the cipher's output and the average total number of direct and indirect equal neighbors 
showed no statistically significant deviation from their expected values,
by Bartosz Zoltak, more here
9) Short cycles. Analysis of scaleddown variants of the cipher show that probability of
entering a short cycle for the full cipher is negligibly low.
9.1) Probability of entering a cycle shorter than 2^1000 is estimated to be about
1 / 2^700, by Bartosz Zoltak, more here
9.2) No short cycles analogous to the Finney states defined for the alleged
RC4 algorithm can occur in the VMPC Stream Cipher; by Bartosz Zoltak, more here
10) Binary derivatives of bit output sequences probabilities.
Distributions of first, second and third binary derivatives of all 7 bits output sequences (for 7bit words)
were tested. None of the measured frequencies showed a statistically significant deviation from its expected value of 1 / 2,
by Bartosz Zoltak, more here
11) The DIEHARD battery of statistical tests by George Marsaglia reported no bias in the ouput generated by the Cipher, more here
12) The NIST statistical tests suite reported no bias in the output generated by the Cipher, more here
13) Battery of statistical tests by David Sexton reported no bias in the ouput generated by the Cipher, more here

3. VMPC Key Scheduling Algorithm
Diffusion of changes of the cryptographic key. A change of one bit of the cryptographic key of size 128, 256 and
512 bits shows to cause a randomlike change in the generated permutation. Points 1,2,3. Tests were run without the
Initialization Vector.
1) Frequencies of occurrence of situations where in two permutations, generated from keys
differing in one byte, there occurs a given number (0,1,2,3,4,5) of equal elements in
the corresponding positions and the average number of equal elements in the
corresponding positions  showed no statistically significant deviation from their expected
values; by Bartosz Zoltak, more here
2) Frequencies of occurrence of situations where in two 256byte streams generated by
the VMPC Stream Cipher directly after running the VMPC KSA for keys
differing in one byte, there occurs a given number (0,1,2,3,4,5) of equal elements in
the corresponding positions and the average number of equal elements in the
corresponding positions  showed no statistically significant deviation from their expected
values; by Bartosz Zoltak, more here
3) Frequencies of occurrence of situations where the elements in each of the corresponding
positions of the permutations, generated from keys differing in one byte, are equal 
showed no statistically significant deviation from their expected values,
by Bartosz Zoltak, more here

4. VMPCMAC scheme
1) Description of the best known forgery attack against the VMPCMAC scheme;
by Bartosz Zoltak, more here

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